/****************************************************************************** ** Filename: cluster.c ** Purpose: Routines for clustering points in N-D space ** Author: Dan Johnson ** History: 5/29/89, DSJ, Created. ** ** (c) Copyright Hewlett-Packard Company, 1988. ** Licensed under the Apache License, Version 2.0 (the "License"); ** you may not use this file except in compliance with the License. ** You may obtain a copy of the License at ** http://www.apache.org/licenses/LICENSE-2.0 ** Unless required by applicable law or agreed to in writing, software ** distributed under the License is distributed on an "AS IS" BASIS, ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. ** See the License for the specific language governing permissions and ** limitations under the License. ******************************************************************************/ #include "oldheap.h" #include "const.h" #include "cluster.h" #include "emalloc.h" #include "helpers.h" #include "matrix.h" #include "tprintf.h" #include "danerror.h" #include "freelist.h" #include #define HOTELLING 1 // If true use Hotelling's test to decide where to split. #define FTABLE_X 10 // Size of FTable. #define FTABLE_Y 100 // Size of FTable. // Table of values approximating the cumulative F-distribution for a confidence of 1%. const double FTable[FTABLE_Y][FTABLE_X] = { {4052.19, 4999.52, 5403.34, 5624.62, 5763.65, 5858.97, 5928.33, 5981.10, 6022.50, 6055.85,}, {98.502, 99.000, 99.166, 99.249, 99.300, 99.333, 99.356, 99.374, 99.388, 99.399,}, {34.116, 30.816, 29.457, 28.710, 28.237, 27.911, 27.672, 27.489, 27.345, 27.229,}, {21.198, 18.000, 16.694, 15.977, 15.522, 15.207, 14.976, 14.799, 14.659, 14.546,}, {16.258, 13.274, 12.060, 11.392, 10.967, 10.672, 10.456, 10.289, 10.158, 10.051,}, {13.745, 10.925, 9.780, 9.148, 8.746, 8.466, 8.260, 8.102, 7.976, 7.874,}, {12.246, 9.547, 8.451, 7.847, 7.460, 7.191, 6.993, 6.840, 6.719, 6.620,}, {11.259, 8.649, 7.591, 7.006, 6.632, 6.371, 6.178, 6.029, 5.911, 5.814,}, {10.561, 8.022, 6.992, 6.422, 6.057, 5.802, 5.613, 5.467, 5.351, 5.257,}, {10.044, 7.559, 6.552, 5.994, 5.636, 5.386, 5.200, 5.057, 4.942, 4.849,}, { 9.646, 7.206, 6.217, 5.668, 5.316, 5.069, 4.886, 4.744, 4.632, 4.539,}, { 9.330, 6.927, 5.953, 5.412, 5.064, 4.821, 4.640, 4.499, 4.388, 4.296,}, { 9.074, 6.701, 5.739, 5.205, 4.862, 4.620, 4.441, 4.302, 4.191, 4.100,}, { 8.862, 6.515, 5.564, 5.035, 4.695, 4.456, 4.278, 4.140, 4.030, 3.939,}, { 8.683, 6.359, 5.417, 4.893, 4.556, 4.318, 4.142, 4.004, 3.895, 3.805,}, { 8.531, 6.226, 5.292, 4.773, 4.437, 4.202, 4.026, 3.890, 3.780, 3.691,}, { 8.400, 6.112, 5.185, 4.669, 4.336, 4.102, 3.927, 3.791, 3.682, 3.593,}, { 8.285, 6.013, 5.092, 4.579, 4.248, 4.015, 3.841, 3.705, 3.597, 3.508,}, { 8.185, 5.926, 5.010, 4.500, 4.171, 3.939, 3.765, 3.631, 3.523, 3.434,}, { 8.096, 5.849, 4.938, 4.431, 4.103, 3.871, 3.699, 3.564, 3.457, 3.368,}, { 8.017, 5.780, 4.874, 4.369, 4.042, 3.812, 3.640, 3.506, 3.398, 3.310,}, { 7.945, 5.719, 4.817, 4.313, 3.988, 3.758, 3.587, 3.453, 3.346, 3.258,}, { 7.881, 5.664, 4.765, 4.264, 3.939, 3.710, 3.539, 3.406, 3.299, 3.211,}, { 7.823, 5.614, 4.718, 4.218, 3.895, 3.667, 3.496, 3.363, 3.256, 3.168,}, { 7.770, 5.568, 4.675, 4.177, 3.855, 3.627, 3.457, 3.324, 3.217, 3.129,}, { 7.721, 5.526, 4.637, 4.140, 3.818, 3.591, 3.421, 3.288, 3.182, 3.094,}, { 7.677, 5.488, 4.601, 4.106, 3.785, 3.558, 3.388, 3.256, 3.149, 3.062,}, { 7.636, 5.453, 4.568, 4.074, 3.754, 3.528, 3.358, 3.226, 3.120, 3.032,}, { 7.598, 5.420, 4.538, 4.045, 3.725, 3.499, 3.330, 3.198, 3.092, 3.005,}, { 7.562, 5.390, 4.510, 4.018, 3.699, 3.473, 3.305, 3.173, 3.067, 2.979,}, { 7.530, 5.362, 4.484, 3.993, 3.675, 3.449, 3.281, 3.149, 3.043, 2.955,}, { 7.499, 5.336, 4.459, 3.969, 3.652, 3.427, 3.258, 3.127, 3.021, 2.934,}, { 7.471, 5.312, 4.437, 3.948, 3.630, 3.406, 3.238, 3.106, 3.000, 2.913,}, { 7.444, 5.289, 4.416, 3.927, 3.611, 3.386, 3.218, 3.087, 2.981, 2.894,}, { 7.419, 5.268, 4.396, 3.908, 3.592, 3.368, 3.200, 3.069, 2.963, 2.876,}, { 7.396, 5.248, 4.377, 3.890, 3.574, 3.351, 3.183, 3.052, 2.946, 2.859,}, { 7.373, 5.229, 4.360, 3.873, 3.558, 3.334, 3.167, 3.036, 2.930, 2.843,}, { 7.353, 5.211, 4.343, 3.858, 3.542, 3.319, 3.152, 3.021, 2.915, 2.828,}, { 7.333, 5.194, 4.327, 3.843, 3.528, 3.305, 3.137, 3.006, 2.901, 2.814,}, { 7.314, 5.179, 4.313, 3.828, 3.514, 3.291, 3.124, 2.993, 2.888, 2.801,}, { 7.296, 5.163, 4.299, 3.815, 3.501, 3.278, 3.111, 2.980, 2.875, 2.788,}, { 7.280, 5.149, 4.285, 3.802, 3.488, 3.266, 3.099, 2.968, 2.863, 2.776,}, { 7.264, 5.136, 4.273, 3.790, 3.476, 3.254, 3.087, 2.957, 2.851, 2.764,}, { 7.248, 5.123, 4.261, 3.778, 3.465, 3.243, 3.076, 2.946, 2.840, 2.754,}, { 7.234, 5.110, 4.249, 3.767, 3.454, 3.232, 3.066, 2.935, 2.830, 2.743,}, { 7.220, 5.099, 4.238, 3.757, 3.444, 3.222, 3.056, 2.925, 2.820, 2.733,}, { 7.207, 5.087, 4.228, 3.747, 3.434, 3.213, 3.046, 2.916, 2.811, 2.724,}, { 7.194, 5.077, 4.218, 3.737, 3.425, 3.204, 3.037, 2.907, 2.802, 2.715,}, { 7.182, 5.066, 4.208, 3.728, 3.416, 3.195, 3.028, 2.898, 2.793, 2.706,}, { 7.171, 5.057, 4.199, 3.720, 3.408, 3.186, 3.020, 2.890, 2.785, 2.698,}, { 7.159, 5.047, 4.191, 3.711, 3.400, 3.178, 3.012, 2.882, 2.777, 2.690,}, { 7.149, 5.038, 4.182, 3.703, 3.392, 3.171, 3.005, 2.874, 2.769, 2.683,}, { 7.139, 5.030, 4.174, 3.695, 3.384, 3.163, 2.997, 2.867, 2.762, 2.675,}, { 7.129, 5.021, 4.167, 3.688, 3.377, 3.156, 2.990, 2.860, 2.755, 2.668,}, { 7.119, 5.013, 4.159, 3.681, 3.370, 3.149, 2.983, 2.853, 2.748, 2.662,}, { 7.110, 5.006, 4.152, 3.674, 3.363, 3.143, 2.977, 2.847, 2.742, 2.655,}, { 7.102, 4.998, 4.145, 3.667, 3.357, 3.136, 2.971, 2.841, 2.736, 2.649,}, { 7.093, 4.991, 4.138, 3.661, 3.351, 3.130, 2.965, 2.835, 2.730, 2.643,}, { 7.085, 4.984, 4.132, 3.655, 3.345, 3.124, 2.959, 2.829, 2.724, 2.637,}, { 7.077, 4.977, 4.126, 3.649, 3.339, 3.119, 2.953, 2.823, 2.718, 2.632,}, { 7.070, 4.971, 4.120, 3.643, 3.333, 3.113, 2.948, 2.818, 2.713, 2.626,}, { 7.062, 4.965, 4.114, 3.638, 3.328, 3.108, 2.942, 2.813, 2.708, 2.621,}, { 7.055, 4.959, 4.109, 3.632, 3.323, 3.103, 2.937, 2.808, 2.703, 2.616,}, { 7.048, 4.953, 4.103, 3.627, 3.318, 3.098, 2.932, 2.803, 2.698, 2.611,}, { 7.042, 4.947, 4.098, 3.622, 3.313, 3.093, 2.928, 2.798, 2.693, 2.607,}, { 7.035, 4.942, 4.093, 3.618, 3.308, 3.088, 2.923, 2.793, 2.689, 2.602,}, { 7.029, 4.937, 4.088, 3.613, 3.304, 3.084, 2.919, 2.789, 2.684, 2.598,}, { 7.023, 4.932, 4.083, 3.608, 3.299, 3.080, 2.914, 2.785, 2.680, 2.593,}, { 7.017, 4.927, 4.079, 3.604, 3.295, 3.075, 2.910, 2.781, 2.676, 2.589,}, { 7.011, 4.922, 4.074, 3.600, 3.291, 3.071, 2.906, 2.777, 2.672, 2.585,}, { 7.006, 4.917, 4.070, 3.596, 3.287, 3.067, 2.902, 2.773, 2.668, 2.581,}, { 7.001, 4.913, 4.066, 3.591, 3.283, 3.063, 2.898, 2.769, 2.664, 2.578,}, { 6.995, 4.908, 4.062, 3.588, 3.279, 3.060, 2.895, 2.765, 2.660, 2.574,}, { 6.990, 4.904, 4.058, 3.584, 3.275, 3.056, 2.891, 2.762, 2.657, 2.570,}, { 6.985, 4.900, 4.054, 3.580, 3.272, 3.052, 2.887, 2.758, 2.653, 2.567,}, { 6.981, 4.896, 4.050, 3.577, 3.268, 3.049, 2.884, 2.755, 2.650, 2.563,}, { 6.976, 4.892, 4.047, 3.573, 3.265, 3.046, 2.881, 2.751, 2.647, 2.560,}, { 6.971, 4.888, 4.043, 3.570, 3.261, 3.042, 2.877, 2.748, 2.644, 2.557,}, { 6.967, 4.884, 4.040, 3.566, 3.258, 3.039, 2.874, 2.745, 2.640, 2.554,}, { 6.963, 4.881, 4.036, 3.563, 3.255, 3.036, 2.871, 2.742, 2.637, 2.551,}, { 6.958, 4.877, 4.033, 3.560, 3.252, 3.033, 2.868, 2.739, 2.634, 2.548,}, { 6.954, 4.874, 4.030, 3.557, 3.249, 3.030, 2.865, 2.736, 2.632, 2.545,}, { 6.950, 4.870, 4.027, 3.554, 3.246, 3.027, 2.863, 2.733, 2.629, 2.542,}, { 6.947, 4.867, 4.024, 3.551, 3.243, 3.025, 2.860, 2.731, 2.626, 2.539,}, { 6.943, 4.864, 4.021, 3.548, 3.240, 3.022, 2.857, 2.728, 2.623, 2.537,}, { 6.939, 4.861, 4.018, 3.545, 3.238, 3.019, 2.854, 2.725, 2.621, 2.534,}, { 6.935, 4.858, 4.015, 3.543, 3.235, 3.017, 2.852, 2.723, 2.618, 2.532,}, { 6.932, 4.855, 4.012, 3.540, 3.233, 3.014, 2.849, 2.720, 2.616, 2.529,}, { 6.928, 4.852, 4.010, 3.538, 3.230, 3.012, 2.847, 2.718, 2.613, 2.527,}, { 6.925, 4.849, 4.007, 3.535, 3.228, 3.009, 2.845, 2.715, 2.611, 2.524,}, { 6.922, 4.846, 4.004, 3.533, 3.225, 3.007, 2.842, 2.713, 2.609, 2.522,}, { 6.919, 4.844, 4.002, 3.530, 3.223, 3.004, 2.840, 2.711, 2.606, 2.520,}, { 6.915, 4.841, 3.999, 3.528, 3.221, 3.002, 2.838, 2.709, 2.604, 2.518,}, { 6.912, 4.838, 3.997, 3.525, 3.218, 3.000, 2.835, 2.706, 2.602, 2.515,}, { 6.909, 4.836, 3.995, 3.523, 3.216, 2.998, 2.833, 2.704, 2.600, 2.513,}, { 6.906, 4.833, 3.992, 3.521, 3.214, 2.996, 2.831, 2.702, 2.598, 2.511,}, { 6.904, 4.831, 3.990, 3.519, 3.212, 2.994, 2.829, 2.700, 2.596, 2.509,}, { 6.901, 4.829, 3.988, 3.517, 3.210, 2.992, 2.827, 2.698, 2.594, 2.507,}, { 6.898, 4.826, 3.986, 3.515, 3.208, 2.990, 2.825, 2.696, 2.592, 2.505,}, { 6.895, 4.824, 3.984, 3.513, 3.206, 2.988, 2.823, 2.694, 2.590, 2.503} }; /* define the variance which will be used as a minimum variance for any dimension of any feature. Since most features are calculated from numbers with a precision no better than 1 in 128, the variance should never be less than the square of this number for parameters whose range is 1. */ #define MINVARIANCE 0.0004 /* define the absolute minimum number of samples which must be present in order to accurately test hypotheses about underlying probability distributions. Define separately the minimum samples that are needed before a statistical analysis is attempted; this number should be equal to MINSAMPLES but can be set to a lower number for early testing when very few samples are available. */ #define MINSAMPLESPERBUCKET 5 #define MINSAMPLES (MINBUCKETS * MINSAMPLESPERBUCKET) #define MINSAMPLESNEEDED 1 /* define the size of the table which maps normalized samples to histogram buckets. Also define the number of standard deviations in a normal distribution which are considered to be significant. The mapping table will be defined in such a way that it covers the specified number of standard deviations on either side of the mean. BUCKETTABLESIZE should always be even. */ #define BUCKETTABLESIZE 1024 #define NORMALEXTENT 3.0 struct TEMPCLUSTER { CLUSTER *Cluster; CLUSTER *Neighbor; }; struct STATISTICS { FLOAT32 AvgVariance; FLOAT32 *CoVariance; FLOAT32 *Min; // largest negative distance from the mean FLOAT32 *Max; // largest positive distance from the mean }; struct BUCKETS { DISTRIBUTION Distribution; // distribution being tested for uinT32 SampleCount; // # of samples in histogram FLOAT64 Confidence; // confidence level of test FLOAT64 ChiSquared; // test threshold uinT16 NumberOfBuckets; // number of cells in histogram uinT16 Bucket[BUCKETTABLESIZE];// mapping to histogram buckets uinT32 *Count; // frequency of occurence histogram FLOAT32 *ExpectedCount; // expected histogram }; struct CHISTRUCT{ uinT16 DegreesOfFreedom; FLOAT64 Alpha; FLOAT64 ChiSquared; }; // For use with KDWalk / MakePotentialClusters struct ClusteringContext { HEAP *heap; // heap used to hold temp clusters, "best" on top TEMPCLUSTER *candidates; // array of potential clusters KDTREE *tree; // kd-tree to be searched for neighbors inT32 next; // next candidate to be used }; typedef FLOAT64 (*DENSITYFUNC) (inT32); typedef FLOAT64 (*SOLVEFUNC) (CHISTRUCT *, double); #define Odd(N) ((N)%2) #define Mirror(N,R) ((R) - (N) - 1) #define Abs(N) ( ( (N) < 0 ) ? ( -(N) ) : (N) ) //--------------Global Data Definitions and Declarations---------------------- /* the following variables describe a discrete normal distribution which is used by NormalDensity() and NormalBucket(). The constant NORMALEXTENT determines how many standard deviations of the distribution are mapped onto the fixed discrete range of x. x=0 is mapped to -NORMALEXTENT standard deviations and x=BUCKETTABLESIZE is mapped to +NORMALEXTENT standard deviations. */ #define SqrtOf2Pi 2.506628275 static const FLOAT64 kNormalStdDev = BUCKETTABLESIZE / (2.0 * NORMALEXTENT); static const FLOAT64 kNormalVariance = (BUCKETTABLESIZE * BUCKETTABLESIZE) / (4.0 * NORMALEXTENT * NORMALEXTENT); static const FLOAT64 kNormalMagnitude = (2.0 * NORMALEXTENT) / (SqrtOf2Pi * BUCKETTABLESIZE); static const FLOAT64 kNormalMean = BUCKETTABLESIZE / 2; /* define lookup tables used to compute the number of histogram buckets that should be used for a given number of samples. */ #define LOOKUPTABLESIZE 8 #define MAXDEGREESOFFREEDOM MAXBUCKETS static const uinT32 kCountTable[LOOKUPTABLESIZE] = { MINSAMPLES, 200, 400, 600, 800, 1000, 1500, 2000 }; // number of samples static const uinT16 kBucketsTable[LOOKUPTABLESIZE] = { MINBUCKETS, 16, 20, 24, 27, 30, 35, MAXBUCKETS }; // number of buckets /*------------------------------------------------------------------------- Private Function Prototypes --------------------------------------------------------------------------*/ void CreateClusterTree(CLUSTERER *Clusterer); void MakePotentialClusters(ClusteringContext *context, CLUSTER *Cluster, inT32 Level); CLUSTER *FindNearestNeighbor(KDTREE *Tree, CLUSTER *Cluster, FLOAT32 *Distance); CLUSTER *MakeNewCluster(CLUSTERER *Clusterer, TEMPCLUSTER *TempCluster); inT32 MergeClusters (inT16 N, register PARAM_DESC ParamDesc[], register inT32 n1, register inT32 n2, register FLOAT32 m[], register FLOAT32 m1[], register FLOAT32 m2[]); void ComputePrototypes(CLUSTERER *Clusterer, CLUSTERCONFIG *Config); PROTOTYPE *MakePrototype(CLUSTERER *Clusterer, CLUSTERCONFIG *Config, CLUSTER *Cluster); PROTOTYPE *MakeDegenerateProto(uinT16 N, CLUSTER *Cluster, STATISTICS *Statistics, PROTOSTYLE Style, inT32 MinSamples); PROTOTYPE *TestEllipticalProto(CLUSTERER *Clusterer, CLUSTERCONFIG *Config, CLUSTER *Cluster, STATISTICS *Statistics); PROTOTYPE *MakeSphericalProto(CLUSTERER *Clusterer, CLUSTER *Cluster, STATISTICS *Statistics, BUCKETS *Buckets); PROTOTYPE *MakeEllipticalProto(CLUSTERER *Clusterer, CLUSTER *Cluster, STATISTICS *Statistics, BUCKETS *Buckets); PROTOTYPE *MakeMixedProto(CLUSTERER *Clusterer, CLUSTER *Cluster, STATISTICS *Statistics, BUCKETS *NormalBuckets, FLOAT64 Confidence); void MakeDimRandom(uinT16 i, PROTOTYPE *Proto, PARAM_DESC *ParamDesc); void MakeDimUniform(uinT16 i, PROTOTYPE *Proto, STATISTICS *Statistics); STATISTICS *ComputeStatistics (inT16 N, PARAM_DESC ParamDesc[], CLUSTER * Cluster); PROTOTYPE *NewSphericalProto(uinT16 N, CLUSTER *Cluster, STATISTICS *Statistics); PROTOTYPE *NewEllipticalProto(inT16 N, CLUSTER *Cluster, STATISTICS *Statistics); PROTOTYPE *NewMixedProto(inT16 N, CLUSTER *Cluster, STATISTICS *Statistics); PROTOTYPE *NewSimpleProto(inT16 N, CLUSTER *Cluster); BOOL8 Independent (PARAM_DESC ParamDesc[], inT16 N, FLOAT32 * CoVariance, FLOAT32 Independence); BUCKETS *GetBuckets(CLUSTERER* clusterer, DISTRIBUTION Distribution, uinT32 SampleCount, FLOAT64 Confidence); BUCKETS *MakeBuckets(DISTRIBUTION Distribution, uinT32 SampleCount, FLOAT64 Confidence); uinT16 OptimumNumberOfBuckets(uinT32 SampleCount); FLOAT64 ComputeChiSquared(uinT16 DegreesOfFreedom, FLOAT64 Alpha); FLOAT64 NormalDensity(inT32 x); FLOAT64 UniformDensity(inT32 x); FLOAT64 Integral(FLOAT64 f1, FLOAT64 f2, FLOAT64 Dx); void FillBuckets(BUCKETS *Buckets, CLUSTER *Cluster, uinT16 Dim, PARAM_DESC *ParamDesc, FLOAT32 Mean, FLOAT32 StdDev); uinT16 NormalBucket(PARAM_DESC *ParamDesc, FLOAT32 x, FLOAT32 Mean, FLOAT32 StdDev); uinT16 UniformBucket(PARAM_DESC *ParamDesc, FLOAT32 x, FLOAT32 Mean, FLOAT32 StdDev); BOOL8 DistributionOK(BUCKETS *Buckets); void FreeStatistics(STATISTICS *Statistics); void FreeBuckets(BUCKETS *Buckets); void FreeCluster(CLUSTER *Cluster); uinT16 DegreesOfFreedom(DISTRIBUTION Distribution, uinT16 HistogramBuckets); int NumBucketsMatch(void *arg1, // BUCKETS *Histogram, void *arg2); // uinT16 *DesiredNumberOfBuckets); int ListEntryMatch(void *arg1, void *arg2); void AdjustBuckets(BUCKETS *Buckets, uinT32 NewSampleCount); void InitBuckets(BUCKETS *Buckets); int AlphaMatch(void *arg1, // CHISTRUCT *ChiStruct, void *arg2); // CHISTRUCT *SearchKey); CHISTRUCT *NewChiStruct(uinT16 DegreesOfFreedom, FLOAT64 Alpha); FLOAT64 Solve(SOLVEFUNC Function, void *FunctionParams, FLOAT64 InitialGuess, FLOAT64 Accuracy); FLOAT64 ChiArea(CHISTRUCT *ChiParams, FLOAT64 x); BOOL8 MultipleCharSamples(CLUSTERER *Clusterer, CLUSTER *Cluster, FLOAT32 MaxIllegal); double InvertMatrix(const float* input, int size, float* inv); //--------------------------Public Code-------------------------------------- /** MakeClusterer ********************************************************** Parameters: SampleSize number of dimensions in feature space ParamDesc description of each dimension Operation: This routine creates a new clusterer data structure, initializes it, and returns a pointer to it. Return: pointer to the new clusterer data structure Exceptions: None History: 5/29/89, DSJ, Created. ****************************************************************************/ CLUSTERER * MakeClusterer (inT16 SampleSize, const PARAM_DESC ParamDesc[]) { CLUSTERER *Clusterer; int i; // allocate main clusterer data structure and init simple fields Clusterer = (CLUSTERER *) Emalloc (sizeof (CLUSTERER)); Clusterer->SampleSize = SampleSize; Clusterer->NumberOfSamples = 0; Clusterer->NumChar = 0; // init fields which will not be used initially Clusterer->Root = NULL; Clusterer->ProtoList = NIL_LIST; // maintain a copy of param descriptors in the clusterer data structure Clusterer->ParamDesc = (PARAM_DESC *) Emalloc (SampleSize * sizeof (PARAM_DESC)); for (i = 0; i < SampleSize; i++) { Clusterer->ParamDesc[i].Circular = ParamDesc[i].Circular; Clusterer->ParamDesc[i].NonEssential = ParamDesc[i].NonEssential; Clusterer->ParamDesc[i].Min = ParamDesc[i].Min; Clusterer->ParamDesc[i].Max = ParamDesc[i].Max; Clusterer->ParamDesc[i].Range = ParamDesc[i].Max - ParamDesc[i].Min; Clusterer->ParamDesc[i].HalfRange = Clusterer->ParamDesc[i].Range / 2; Clusterer->ParamDesc[i].MidRange = (ParamDesc[i].Max + ParamDesc[i].Min) / 2; } // allocate a kd tree to hold the samples Clusterer->KDTree = MakeKDTree (SampleSize, ParamDesc); // Initialize cache of histogram buckets to minimize recomputing them. for (int d = 0; d < DISTRIBUTION_COUNT; ++d) { for (int c = 0; c < MAXBUCKETS + 1 - MINBUCKETS; ++c) Clusterer->bucket_cache[d][c] = NULL; } return Clusterer; } // MakeClusterer /** MakeSample *********************************************************** Parameters: Clusterer clusterer data structure to add sample to Feature feature to be added to clusterer CharID unique ident. of char that sample came from Operation: This routine creates a new sample data structure to hold the specified feature. This sample is added to the clusterer data structure (so that it knows which samples are to be clustered later), and a pointer to the sample is returned to the caller. Return: Pointer to the new sample data structure Exceptions: ALREADYCLUSTERED MakeSample can't be called after ClusterSamples has been called History: 5/29/89, DSJ, Created. *****************************************************************************/ SAMPLE* MakeSample(CLUSTERER * Clusterer, const FLOAT32* Feature, inT32 CharID) { SAMPLE *Sample; int i; // see if the samples have already been clustered - if so trap an error if (Clusterer->Root != NULL) DoError (ALREADYCLUSTERED, "Can't add samples after they have been clustered"); // allocate the new sample and initialize it Sample = (SAMPLE *) Emalloc (sizeof (SAMPLE) + (Clusterer->SampleSize - 1) * sizeof (FLOAT32)); Sample->Clustered = FALSE; Sample->Prototype = FALSE; Sample->SampleCount = 1; Sample->Left = NULL; Sample->Right = NULL; Sample->CharID = CharID; for (i = 0; i < Clusterer->SampleSize; i++) Sample->Mean[i] = Feature[i]; // add the sample to the KD tree - keep track of the total # of samples Clusterer->NumberOfSamples++; KDStore (Clusterer->KDTree, Sample->Mean, (char *) Sample); if (CharID >= Clusterer->NumChar) Clusterer->NumChar = CharID + 1; // execute hook for monitoring clustering operation // (*SampleCreationHook)( Sample ); return (Sample); } // MakeSample /** ClusterSamples *********************************************************** Parameters: Clusterer data struct containing samples to be clustered Config parameters which control clustering process Operation: This routine first checks to see if the samples in this clusterer have already been clustered before; if so, it does not bother to recreate the cluster tree. It simply recomputes the prototypes based on the new Config info. If the samples have not been clustered before, the samples in the KD tree are formed into a cluster tree and then the prototypes are computed from the cluster tree. In either case this routine returns a pointer to a list of prototypes that best represent the samples given the constraints specified in Config. Return: Pointer to a list of prototypes Exceptions: None History: 5/29/89, DSJ, Created. *******************************************************************************/ LIST ClusterSamples(CLUSTERER *Clusterer, CLUSTERCONFIG *Config) { //only create cluster tree if samples have never been clustered before if (Clusterer->Root == NULL) CreateClusterTree(Clusterer); //deallocate the old prototype list if one exists FreeProtoList (&Clusterer->ProtoList); Clusterer->ProtoList = NIL_LIST; //compute prototypes starting at the root node in the tree ComputePrototypes(Clusterer, Config); return (Clusterer->ProtoList); } // ClusterSamples /** FreeClusterer ************************************************************* Parameters: Clusterer pointer to data structure to be freed Operation: This routine frees all of the memory allocated to the specified data structure. It will not, however, free the memory used by the prototype list. The pointers to the clusters for each prototype in the list will be set to NULL to indicate that the cluster data structures no longer exist. Any sample lists that have been obtained via calls to GetSamples are no longer valid. Return: None Exceptions: None History: 6/6/89, DSJ, Created. *******************************************************************************/ void FreeClusterer(CLUSTERER *Clusterer) { if (Clusterer != NULL) { memfree (Clusterer->ParamDesc); if (Clusterer->KDTree != NULL) FreeKDTree (Clusterer->KDTree); if (Clusterer->Root != NULL) FreeCluster (Clusterer->Root); // Free up all used buckets structures. for (int d = 0; d < DISTRIBUTION_COUNT; ++d) { for (int c = 0; c < MAXBUCKETS + 1 - MINBUCKETS; ++c) if (Clusterer->bucket_cache[d][c] != NULL) FreeBuckets(Clusterer->bucket_cache[d][c]); } memfree(Clusterer); } } // FreeClusterer /** FreeProtoList ************************************************************ Parameters: ProtoList pointer to list of prototypes to be freed Operation: This routine frees all of the memory allocated to the specified list of prototypes. The clusters which are pointed to by the prototypes are not freed. Return: None Exceptions: None History: 6/6/89, DSJ, Created. *****************************************************************************/ void FreeProtoList(LIST *ProtoList) { destroy_nodes(*ProtoList, FreePrototype); } // FreeProtoList /** FreePrototype ************************************************************ Parameters: Prototype prototype data structure to be deallocated Operation: This routine deallocates the memory consumed by the specified prototype and modifies the corresponding cluster so that it is no longer marked as a prototype. The cluster is NOT deallocated by this routine. Return: None Exceptions: None History: 5/30/89, DSJ, Created. *******************************************************************************/ void FreePrototype(void *arg) { //PROTOTYPE *Prototype) PROTOTYPE *Prototype = (PROTOTYPE *) arg; // unmark the corresponding cluster (if there is one if (Prototype->Cluster != NULL) Prototype->Cluster->Prototype = FALSE; // deallocate the prototype statistics and then the prototype itself if (Prototype->Distrib != NULL) memfree (Prototype->Distrib); if (Prototype->Mean != NULL) memfree (Prototype->Mean); if (Prototype->Style != spherical) { if (Prototype->Variance.Elliptical != NULL) memfree (Prototype->Variance.Elliptical); if (Prototype->Magnitude.Elliptical != NULL) memfree (Prototype->Magnitude.Elliptical); if (Prototype->Weight.Elliptical != NULL) memfree (Prototype->Weight.Elliptical); } memfree(Prototype); } // FreePrototype /** NextSample ************************************************************ Parameters: SearchState ptr to list containing clusters to be searched Operation: This routine is used to find all of the samples which belong to a cluster. It starts by removing the top cluster on the cluster list (SearchState). If this cluster is a leaf it is returned. Otherwise, the right subcluster is pushed on the list and we continue the search in the left subcluster. This continues until a leaf is found. If all samples have been found, NULL is returned. InitSampleSearch() must be called before NextSample() to initialize the search. Return: Pointer to the next leaf cluster (sample) or NULL. Exceptions: None History: 6/16/89, DSJ, Created. ****************************************************************************/ CLUSTER *NextSample(LIST *SearchState) { CLUSTER *Cluster; if (*SearchState == NIL_LIST) return (NULL); Cluster = (CLUSTER *) first_node (*SearchState); *SearchState = pop (*SearchState); while (TRUE) { if (Cluster->Left == NULL) return (Cluster); *SearchState = push (*SearchState, Cluster->Right); Cluster = Cluster->Left; } } // NextSample /** Mean *********************************************************** Parameters: Proto prototype to return mean of Dimension dimension whose mean is to be returned Operation: This routine returns the mean of the specified prototype in the indicated dimension. Return: Mean of Prototype in Dimension Exceptions: none History: 7/6/89, DSJ, Created. *********************************************************************/ FLOAT32 Mean(PROTOTYPE *Proto, uinT16 Dimension) { return (Proto->Mean[Dimension]); } // Mean /** StandardDeviation ************************************************* Parameters: Proto prototype to return standard deviation of Dimension dimension whose stddev is to be returned Operation: This routine returns the standard deviation of the prototype in the indicated dimension. Return: Standard deviation of Prototype in Dimension Exceptions: none History: 7/6/89, DSJ, Created. **********************************************************************/ FLOAT32 StandardDeviation(PROTOTYPE *Proto, uinT16 Dimension) { switch (Proto->Style) { case spherical: return ((FLOAT32) sqrt ((double) Proto->Variance.Spherical)); case elliptical: return ((FLOAT32) sqrt ((double) Proto->Variance.Elliptical[Dimension])); case mixed: switch (Proto->Distrib[Dimension]) { case normal: return ((FLOAT32) sqrt ((double) Proto->Variance.Elliptical[Dimension])); case uniform: case D_random: return (Proto->Variance.Elliptical[Dimension]); case DISTRIBUTION_COUNT: ASSERT_HOST(!"Distribution count not allowed!"); } } return 0.0f; } // StandardDeviation /*--------------------------------------------------------------------------- Private Code ----------------------------------------------------------------------------*/ /** CreateClusterTree ******************************************************* Parameters: Clusterer data structure holdings samples to be clustered Operation: This routine performs a bottoms-up clustering on the samples held in the kd-tree of the Clusterer data structure. The result is a cluster tree. Each node in the tree represents a cluster which conceptually contains a subset of the samples. More precisely, the cluster contains all of the samples which are contained in its two sub-clusters. The leaves of the tree are the individual samples themselves; they have no sub-clusters. The root node of the tree conceptually contains all of the samples. Return: None (the Clusterer data structure is changed) Exceptions: None History: 5/29/89, DSJ, Created. ******************************************************************************/ void CreateClusterTree(CLUSTERER *Clusterer) { ClusteringContext context; HEAPENTRY HeapEntry; TEMPCLUSTER *PotentialCluster; // each sample and its nearest neighbor form a "potential" cluster // save these in a heap with the "best" potential clusters on top context.tree = Clusterer->KDTree; context.candidates = (TEMPCLUSTER *) Emalloc(Clusterer->NumberOfSamples * sizeof(TEMPCLUSTER)); context.next = 0; context.heap = MakeHeap(Clusterer->NumberOfSamples); KDWalk(context.tree, (void_proc)MakePotentialClusters, &context); // form potential clusters into actual clusters - always do "best" first while (GetTopOfHeap(context.heap, &HeapEntry) != EMPTY) { PotentialCluster = (TEMPCLUSTER *)HeapEntry.Data; // if main cluster of potential cluster is already in another cluster // then we don't need to worry about it if (PotentialCluster->Cluster->Clustered) { continue; } // if main cluster is not yet clustered, but its nearest neighbor is // then we must find a new nearest neighbor else if (PotentialCluster->Neighbor->Clustered) { PotentialCluster->Neighbor = FindNearestNeighbor(context.tree, PotentialCluster->Cluster, &HeapEntry.Key); if (PotentialCluster->Neighbor != NULL) { HeapStore(context.heap, &HeapEntry); } } // if neither cluster is already clustered, form permanent cluster else { PotentialCluster->Cluster = MakeNewCluster(Clusterer, PotentialCluster); PotentialCluster->Neighbor = FindNearestNeighbor(context.tree, PotentialCluster->Cluster, &HeapEntry.Key); if (PotentialCluster->Neighbor != NULL) { HeapStore(context.heap, &HeapEntry); } } } // the root node in the cluster tree is now the only node in the kd-tree Clusterer->Root = (CLUSTER *) RootOf(Clusterer->KDTree); // free up the memory used by the K-D tree, heap, and temp clusters FreeKDTree(context.tree); Clusterer->KDTree = NULL; FreeHeap(context.heap); memfree(context.candidates); } // CreateClusterTree /** MakePotentialClusters ************************************************** Parameters: context ClusteringContext (see definition above) Cluster current cluster being visited in kd-tree walk Level level of this cluster in the kd-tree Operation: This routine is designed to be used in concert with the KDWalk routine. It will create a potential cluster for each sample in the kd-tree that is being walked. This potential cluster will then be pushed on the heap. ******************************************************************************/ void MakePotentialClusters(ClusteringContext *context, CLUSTER *Cluster, inT32 Level) { HEAPENTRY HeapEntry; int next = context->next; context->candidates[next].Cluster = Cluster; HeapEntry.Data = (char *) &(context->candidates[next]); context->candidates[next].Neighbor = FindNearestNeighbor(context->tree, context->candidates[next].Cluster, &HeapEntry.Key); if (context->candidates[next].Neighbor != NULL) { HeapStore(context->heap, &HeapEntry); context->next++; } } // MakePotentialClusters /** FindNearestNeighbor ********************************************************* Parameters: Tree kd-tree to search in for nearest neighbor Cluster cluster whose nearest neighbor is to be found Distance ptr to variable to report distance found Operation: This routine searches the specified kd-tree for the nearest neighbor of the specified cluster. It actually uses the kd routines to find the 2 nearest neighbors since one of them will be the original cluster. A pointer to the nearest neighbor is returned, if it can be found, otherwise NULL is returned. The distance between the 2 nodes is placed in the specified variable. Return: Pointer to the nearest neighbor of Cluster, or NULL Exceptions: none History: 5/29/89, DSJ, Created. 7/13/89, DSJ, Removed visibility of kd-tree node data struct ********************************************************************************/ CLUSTER * FindNearestNeighbor(KDTREE * Tree, CLUSTER * Cluster, FLOAT32 * Distance) #define MAXNEIGHBORS 2 #define MAXDISTANCE MAX_FLOAT32 { CLUSTER *Neighbor[MAXNEIGHBORS]; FLOAT32 Dist[MAXNEIGHBORS]; int NumberOfNeighbors; inT32 i; CLUSTER *BestNeighbor; // find the 2 nearest neighbors of the cluster KDNearestNeighborSearch(Tree, Cluster->Mean, MAXNEIGHBORS, MAXDISTANCE, &NumberOfNeighbors, (void **)Neighbor, Dist); // search for the nearest neighbor that is not the cluster itself *Distance = MAXDISTANCE; BestNeighbor = NULL; for (i = 0; i < NumberOfNeighbors; i++) { if ((Dist[i] < *Distance) && (Neighbor[i] != Cluster)) { *Distance = Dist[i]; BestNeighbor = Neighbor[i]; } } return BestNeighbor; } // FindNearestNeighbor /** MakeNewCluster ************************************************************* Parameters: Clusterer current clustering environment TempCluster potential cluster to make permanent Operation: This routine creates a new permanent cluster from the clusters specified in TempCluster. The 2 clusters in TempCluster are marked as "clustered" and deleted from the kd-tree. The new cluster is then added to the kd-tree. Return: Pointer to the new permanent cluster Exceptions: none History: 5/29/89, DSJ, Created. 7/13/89, DSJ, Removed visibility of kd-tree node data struct ********************************************************************************/ CLUSTER *MakeNewCluster(CLUSTERER *Clusterer, TEMPCLUSTER *TempCluster) { CLUSTER *Cluster; // allocate the new cluster and initialize it Cluster = (CLUSTER *) Emalloc( sizeof(CLUSTER) + (Clusterer->SampleSize - 1) * sizeof(FLOAT32)); Cluster->Clustered = FALSE; Cluster->Prototype = FALSE; Cluster->Left = TempCluster->Cluster; Cluster->Right = TempCluster->Neighbor; Cluster->CharID = -1; // mark the old clusters as "clustered" and delete them from the kd-tree Cluster->Left->Clustered = TRUE; Cluster->Right->Clustered = TRUE; KDDelete(Clusterer->KDTree, Cluster->Left->Mean, Cluster->Left); KDDelete(Clusterer->KDTree, Cluster->Right->Mean, Cluster->Right); // compute the mean and sample count for the new cluster Cluster->SampleCount = MergeClusters(Clusterer->SampleSize, Clusterer->ParamDesc, Cluster->Left->SampleCount, Cluster->Right->SampleCount, Cluster->Mean, Cluster->Left->Mean, Cluster->Right->Mean); // add the new cluster to the KD tree KDStore(Clusterer->KDTree, Cluster->Mean, Cluster); return Cluster; } // MakeNewCluster /** MergeClusters ************************************************************ Parameters: N # of dimensions (size of arrays) ParamDesc array of dimension descriptions n1, n2 number of samples in each old cluster m array to hold mean of new cluster m1, m2 arrays containing means of old clusters Operation: This routine merges two clusters into one larger cluster. To do this it computes the number of samples in the new cluster and the mean of the new cluster. The ParamDesc information is used to ensure that circular dimensions are handled correctly. Return: The number of samples in the new cluster. Exceptions: None History: 5/31/89, DSJ, Created. *********************************************************************************/ inT32 MergeClusters(inT16 N, PARAM_DESC ParamDesc[], inT32 n1, inT32 n2, FLOAT32 m[], FLOAT32 m1[], FLOAT32 m2[]) { inT32 i, n; n = n1 + n2; for (i = N; i > 0; i--, ParamDesc++, m++, m1++, m2++) { if (ParamDesc->Circular) { // if distance between means is greater than allowed // reduce upper point by one "rotation" to compute mean // then normalize the mean back into the accepted range if ((*m2 - *m1) > ParamDesc->HalfRange) { *m = (n1 * *m1 + n2 * (*m2 - ParamDesc->Range)) / n; if (*m < ParamDesc->Min) *m += ParamDesc->Range; } else if ((*m1 - *m2) > ParamDesc->HalfRange) { *m = (n1 * (*m1 - ParamDesc->Range) + n2 * *m2) / n; if (*m < ParamDesc->Min) *m += ParamDesc->Range; } else *m = (n1 * *m1 + n2 * *m2) / n; } else *m = (n1 * *m1 + n2 * *m2) / n; } return n; } // MergeClusters /** ComputePrototypes ******************************************************* Parameters: Clusterer data structure holding cluster tree Config parameters used to control prototype generation Operation: This routine decides which clusters in the cluster tree should be represented by prototypes, forms a list of these prototypes, and places the list in the Clusterer data structure. Return: None Exceptions: None History: 5/30/89, DSJ, Created. *******************************************************************************/ void ComputePrototypes(CLUSTERER *Clusterer, CLUSTERCONFIG *Config) { LIST ClusterStack = NIL_LIST; CLUSTER *Cluster; PROTOTYPE *Prototype; // use a stack to keep track of clusters waiting to be processed // initially the only cluster on the stack is the root cluster if (Clusterer->Root != NULL) ClusterStack = push (NIL_LIST, Clusterer->Root); // loop until we have analyzed all clusters which are potential prototypes while (ClusterStack != NIL_LIST) { // remove the next cluster to be analyzed from the stack // try to make a prototype from the cluster // if successful, put it on the proto list, else split the cluster Cluster = (CLUSTER *) first_node (ClusterStack); ClusterStack = pop (ClusterStack); Prototype = MakePrototype(Clusterer, Config, Cluster); if (Prototype != NULL) { Clusterer->ProtoList = push (Clusterer->ProtoList, Prototype); } else { ClusterStack = push (ClusterStack, Cluster->Right); ClusterStack = push (ClusterStack, Cluster->Left); } } } // ComputePrototypes /** MakePrototype *********************************************************** Parameters: Clusterer data structure holding cluster tree Config parameters used to control prototype generation Cluster cluster to be made into a prototype Operation: This routine attempts to create a prototype from the specified cluster that conforms to the distribution specified in Config. If there are too few samples in the cluster to perform a statistical analysis, then a prototype is generated but labelled as insignificant. If the dimensions of the cluster are not independent, no prototype is generated and NULL is returned. If a prototype can be found that matches the desired distribution then a pointer to it is returned, otherwise NULL is returned. Return: Pointer to new prototype or NULL Exceptions: None History: 6/19/89, DSJ, Created. *******************************************************************************/ PROTOTYPE *MakePrototype(CLUSTERER *Clusterer, CLUSTERCONFIG *Config, CLUSTER *Cluster) { STATISTICS *Statistics; PROTOTYPE *Proto; BUCKETS *Buckets; // filter out clusters which contain samples from the same character if (MultipleCharSamples (Clusterer, Cluster, Config->MaxIllegal)) return NULL; // compute the covariance matrix and ranges for the cluster Statistics = ComputeStatistics(Clusterer->SampleSize, Clusterer->ParamDesc, Cluster); // check for degenerate clusters which need not be analyzed further // note that the MinSamples test assumes that all clusters with multiple // character samples have been removed (as above) Proto = MakeDegenerateProto( Clusterer->SampleSize, Cluster, Statistics, Config->ProtoStyle, (inT32) (Config->MinSamples * Clusterer->NumChar)); if (Proto != NULL) { FreeStatistics(Statistics); return Proto; } // check to ensure that all dimensions are independent if (!Independent(Clusterer->ParamDesc, Clusterer->SampleSize, Statistics->CoVariance, Config->Independence)) { FreeStatistics(Statistics); return NULL; } if (HOTELLING && Config->ProtoStyle == elliptical) { Proto = TestEllipticalProto(Clusterer, Config, Cluster, Statistics); if (Proto != NULL) { FreeStatistics(Statistics); return Proto; } } // create a histogram data structure used to evaluate distributions Buckets = GetBuckets(Clusterer, normal, Cluster->SampleCount, Config->Confidence); // create a prototype based on the statistics and test it switch (Config->ProtoStyle) { case spherical: Proto = MakeSphericalProto(Clusterer, Cluster, Statistics, Buckets); break; case elliptical: Proto = MakeEllipticalProto(Clusterer, Cluster, Statistics, Buckets); break; case mixed: Proto = MakeMixedProto(Clusterer, Cluster, Statistics, Buckets, Config->Confidence); break; case automatic: Proto = MakeSphericalProto(Clusterer, Cluster, Statistics, Buckets); if (Proto != NULL) break; Proto = MakeEllipticalProto(Clusterer, Cluster, Statistics, Buckets); if (Proto != NULL) break; Proto = MakeMixedProto(Clusterer, Cluster, Statistics, Buckets, Config->Confidence); break; } FreeStatistics(Statistics); return Proto; } // MakePrototype /** MakeDegenerateProto ****************************************************** Parameters: N number of dimensions Cluster cluster being analyzed Statistics statistical info about cluster Style type of prototype to be generated MinSamples minimum number of samples in a cluster Operation: This routine checks for clusters which are degenerate and therefore cannot be analyzed in a statistically valid way. A cluster is defined as degenerate if it does not have at least MINSAMPLESNEEDED samples in it. If the cluster is found to be degenerate, a prototype of the specified style is generated and marked as insignificant. A cluster is also degenerate if it does not have at least MinSamples samples in it. If the cluster is not degenerate, NULL is returned. Return: Pointer to degenerate prototype or NULL. Exceptions: None History: 6/20/89, DSJ, Created. 7/12/89, DSJ, Changed name and added check for 0 stddev. 8/8/89, DSJ, Removed check for 0 stddev (handled elsewhere). ********************************************************************************/ PROTOTYPE *MakeDegenerateProto( //this was MinSample uinT16 N, CLUSTER *Cluster, STATISTICS *Statistics, PROTOSTYLE Style, inT32 MinSamples) { PROTOTYPE *Proto = NULL; if (MinSamples < MINSAMPLESNEEDED) MinSamples = MINSAMPLESNEEDED; if (Cluster->SampleCount < MinSamples) { switch (Style) { case spherical: Proto = NewSphericalProto (N, Cluster, Statistics); break; case elliptical: case automatic: Proto = NewEllipticalProto (N, Cluster, Statistics); break; case mixed: Proto = NewMixedProto (N, Cluster, Statistics); break; } Proto->Significant = FALSE; } return (Proto); } // MakeDegenerateProto /** TestEllipticalProto **************************************************** Parameters: Clusterer data struct containing samples being clustered Config provides the magic number of samples that make a good cluster Cluster cluster to be made into an elliptical prototype Statistics statistical info about cluster Operation: This routine tests the specified cluster to see if ** * there is a statistically significant difference between * the sub-clusters that would be made if the cluster were to * be split. If not, then a new prototype is formed and * returned to the caller. If there is, then NULL is returned * to the caller. Return: Pointer to new elliptical prototype or NULL. ****************************************************************************/ PROTOTYPE *TestEllipticalProto(CLUSTERER *Clusterer, CLUSTERCONFIG *Config, CLUSTER *Cluster, STATISTICS *Statistics) { // Fraction of the number of samples used as a range around 1 within // which a cluster has the magic size that allows a boost to the // FTable by kFTableBoostMargin, thus allowing clusters near the // magic size (equal to the number of sample characters) to be more // likely to stay together. const double kMagicSampleMargin = 0.0625; const double kFTableBoostMargin = 2.0; int N = Clusterer->SampleSize; CLUSTER* Left = Cluster->Left; CLUSTER* Right = Cluster->Right; if (Left == NULL || Right == NULL) return NULL; int TotalDims = Left->SampleCount + Right->SampleCount; if (TotalDims < N + 1 || TotalDims < 2) return NULL; const int kMatrixSize = N * N * sizeof(FLOAT32); FLOAT32* Covariance = reinterpret_cast(Emalloc(kMatrixSize)); FLOAT32* Inverse = reinterpret_cast(Emalloc(kMatrixSize)); FLOAT32* Delta = reinterpret_cast(Emalloc(N * sizeof(FLOAT32))); // Compute a new covariance matrix that only uses essential features. for (int i = 0; i < N; ++i) { int row_offset = i * N; if (!Clusterer->ParamDesc[i].NonEssential) { for (int j = 0; j < N; ++j) { if (!Clusterer->ParamDesc[j].NonEssential) Covariance[j + row_offset] = Statistics->CoVariance[j + row_offset]; else Covariance[j + row_offset] = 0.0f; } } else { for (int j = 0; j < N; ++j) { if (i == j) Covariance[j + row_offset] = 1.0f; else Covariance[j + row_offset] = 0.0f; } } } double err = InvertMatrix(Covariance, N, Inverse); if (err > 1) { tprintf("Clustering error: Matrix inverse failed with error %g\n", err); } int EssentialN = 0; for (int dim = 0; dim < N; ++dim) { if (!Clusterer->ParamDesc[dim].NonEssential) { Delta[dim] = Left->Mean[dim] - Right->Mean[dim]; ++EssentialN; } else { Delta[dim] = 0.0f; } } // Compute Hotelling's T-squared. double Tsq = 0.0; for (int x = 0; x < N; ++x) { double temp = 0.0; for (int y = 0; y < N; ++y) { temp += Inverse[y + N*x] * Delta[y]; } Tsq += Delta[x] * temp; } memfree(Covariance); memfree(Inverse); memfree(Delta); // Changed this function to match the formula in // Statistical Methods in Medical Research p 473 // By Peter Armitage, Geoffrey Berry, J. N. S. Matthews. // Tsq *= Left->SampleCount * Right->SampleCount / TotalDims; double F = Tsq * (TotalDims - EssentialN - 1) / ((TotalDims - 2)*EssentialN); int Fx = EssentialN; if (Fx > FTABLE_X) Fx = FTABLE_X; --Fx; int Fy = TotalDims - EssentialN - 1; if (Fy > FTABLE_Y) Fy = FTABLE_Y; --Fy; double FTarget = FTable[Fy][Fx]; if (Config->MagicSamples > 0 && TotalDims >= Config->MagicSamples * (1.0 - kMagicSampleMargin) && TotalDims <= Config->MagicSamples * (1.0 + kMagicSampleMargin)) { // Give magic-sized clusters a magic FTable boost. FTarget += kFTableBoostMargin; } if (F < FTarget) { return NewEllipticalProto (Clusterer->SampleSize, Cluster, Statistics); } return NULL; } /* MakeSphericalProto ******************************************************* Parameters: Clusterer data struct containing samples being clustered Cluster cluster to be made into a spherical prototype Statistics statistical info about cluster Buckets histogram struct used to analyze distribution Operation: This routine tests the specified cluster to see if it can be approximated by a spherical normal distribution. If it can be, then a new prototype is formed and returned to the caller. If it can't be, then NULL is returned to the caller. Return: Pointer to new spherical prototype or NULL. Exceptions: None History: 6/1/89, DSJ, Created. ******************************************************************************/ PROTOTYPE *MakeSphericalProto(CLUSTERER *Clusterer, CLUSTER *Cluster, STATISTICS *Statistics, BUCKETS *Buckets) { PROTOTYPE *Proto = NULL; int i; // check that each dimension is a normal distribution for (i = 0; i < Clusterer->SampleSize; i++) { if (Clusterer->ParamDesc[i].NonEssential) continue; FillBuckets (Buckets, Cluster, i, &(Clusterer->ParamDesc[i]), Cluster->Mean[i], sqrt ((FLOAT64) (Statistics->AvgVariance))); if (!DistributionOK (Buckets)) break; } // if all dimensions matched a normal distribution, make a proto if (i >= Clusterer->SampleSize) Proto = NewSphericalProto (Clusterer->SampleSize, Cluster, Statistics); return (Proto); } // MakeSphericalProto /** MakeEllipticalProto **************************************************** Parameters: Clusterer data struct containing samples being clustered Cluster cluster to be made into an elliptical prototype Statistics statistical info about cluster Buckets histogram struct used to analyze distribution Operation: This routine tests the specified cluster to see if it can be approximated by an elliptical normal distribution. If it can be, then a new prototype is formed and returned to the caller. If it can't be, then NULL is returned to the caller. Return: Pointer to new elliptical prototype or NULL. Exceptions: None History: 6/12/89, DSJ, Created. ****************************************************************************/ PROTOTYPE *MakeEllipticalProto(CLUSTERER *Clusterer, CLUSTER *Cluster, STATISTICS *Statistics, BUCKETS *Buckets) { PROTOTYPE *Proto = NULL; int i; // check that each dimension is a normal distribution for (i = 0; i < Clusterer->SampleSize; i++) { if (Clusterer->ParamDesc[i].NonEssential) continue; FillBuckets (Buckets, Cluster, i, &(Clusterer->ParamDesc[i]), Cluster->Mean[i], sqrt ((FLOAT64) Statistics-> CoVariance[i * (Clusterer->SampleSize + 1)])); if (!DistributionOK (Buckets)) break; } // if all dimensions matched a normal distribution, make a proto if (i >= Clusterer->SampleSize) Proto = NewEllipticalProto (Clusterer->SampleSize, Cluster, Statistics); return (Proto); } // MakeEllipticalProto /** MakeMixedProto *********************************************************** Parameters: Clusterer data struct containing samples being clustered Cluster cluster to be made into a prototype Statistics statistical info about cluster NormalBuckets histogram struct used to analyze distribution Confidence confidence level for alternate distributions Operation: This routine tests each dimension of the specified cluster to see what distribution would best approximate that dimension. Each dimension is compared to the following distributions in order: normal, random, uniform. If each dimension can be represented by one of these distributions, then a new prototype is formed and returned to the caller. If it can't be, then NULL is returned to the caller. Return: Pointer to new mixed prototype or NULL. Exceptions: None History: 6/12/89, DSJ, Created. ********************************************************************************/ PROTOTYPE *MakeMixedProto(CLUSTERER *Clusterer, CLUSTER *Cluster, STATISTICS *Statistics, BUCKETS *NormalBuckets, FLOAT64 Confidence) { PROTOTYPE *Proto; int i; BUCKETS *UniformBuckets = NULL; BUCKETS *RandomBuckets = NULL; // create a mixed proto to work on - initially assume all dimensions normal*/ Proto = NewMixedProto (Clusterer->SampleSize, Cluster, Statistics); // find the proper distribution for each dimension for (i = 0; i < Clusterer->SampleSize; i++) { if (Clusterer->ParamDesc[i].NonEssential) continue; FillBuckets (NormalBuckets, Cluster, i, &(Clusterer->ParamDesc[i]), Proto->Mean[i], sqrt ((FLOAT64) Proto->Variance.Elliptical[i])); if (DistributionOK (NormalBuckets)) continue; if (RandomBuckets == NULL) RandomBuckets = GetBuckets(Clusterer, D_random, Cluster->SampleCount, Confidence); MakeDimRandom (i, Proto, &(Clusterer->ParamDesc[i])); FillBuckets (RandomBuckets, Cluster, i, &(Clusterer->ParamDesc[i]), Proto->Mean[i], Proto->Variance.Elliptical[i]); if (DistributionOK (RandomBuckets)) continue; if (UniformBuckets == NULL) UniformBuckets = GetBuckets(Clusterer, uniform, Cluster->SampleCount, Confidence); MakeDimUniform(i, Proto, Statistics); FillBuckets (UniformBuckets, Cluster, i, &(Clusterer->ParamDesc[i]), Proto->Mean[i], Proto->Variance.Elliptical[i]); if (DistributionOK (UniformBuckets)) continue; break; } // if any dimension failed to match a distribution, discard the proto if (i < Clusterer->SampleSize) { FreePrototype(Proto); Proto = NULL; } return (Proto); } // MakeMixedProto /* MakeDimRandom ************************************************************* Parameters: i index of dimension to be changed Proto prototype whose dimension is to be altered ParamDesc description of specified dimension Operation: This routine alters the ith dimension of the specified mixed prototype to be D_random. Return: None Exceptions: None History: 6/20/89, DSJ, Created. ******************************************************************************/ void MakeDimRandom(uinT16 i, PROTOTYPE *Proto, PARAM_DESC *ParamDesc) { Proto->Distrib[i] = D_random; Proto->Mean[i] = ParamDesc->MidRange; Proto->Variance.Elliptical[i] = ParamDesc->HalfRange; // subtract out the previous magnitude of this dimension from the total Proto->TotalMagnitude /= Proto->Magnitude.Elliptical[i]; Proto->Magnitude.Elliptical[i] = 1.0 / ParamDesc->Range; Proto->TotalMagnitude *= Proto->Magnitude.Elliptical[i]; Proto->LogMagnitude = log ((double) Proto->TotalMagnitude); // note that the proto Weight is irrelevant for D_random protos } // MakeDimRandom /** MakeDimUniform *********************************************************** Parameters: i index of dimension to be changed Proto prototype whose dimension is to be altered Statistics statistical info about prototype Operation: This routine alters the ith dimension of the specified mixed prototype to be uniform. Return: None Exceptions: None History: 6/20/89, DSJ, Created. ******************************************************************************/ void MakeDimUniform(uinT16 i, PROTOTYPE *Proto, STATISTICS *Statistics) { Proto->Distrib[i] = uniform; Proto->Mean[i] = Proto->Cluster->Mean[i] + (Statistics->Min[i] + Statistics->Max[i]) / 2; Proto->Variance.Elliptical[i] = (Statistics->Max[i] - Statistics->Min[i]) / 2; if (Proto->Variance.Elliptical[i] < MINVARIANCE) Proto->Variance.Elliptical[i] = MINVARIANCE; // subtract out the previous magnitude of this dimension from the total Proto->TotalMagnitude /= Proto->Magnitude.Elliptical[i]; Proto->Magnitude.Elliptical[i] = 1.0 / (2.0 * Proto->Variance.Elliptical[i]); Proto->TotalMagnitude *= Proto->Magnitude.Elliptical[i]; Proto->LogMagnitude = log ((double) Proto->TotalMagnitude); // note that the proto Weight is irrelevant for uniform protos } // MakeDimUniform /** ComputeStatistics ********************************************************* Parameters: N number of dimensions ParamDesc array of dimension descriptions Cluster cluster whose stats are to be computed Operation: This routine searches the cluster tree for all leaf nodes which are samples in the specified cluster. It computes a full covariance matrix for these samples as well as keeping track of the ranges (min and max) for each dimension. A special data structure is allocated to return this information to the caller. An incremental algorithm for computing statistics is not used because it will not work with circular dimensions. Return: Pointer to new data structure containing statistics Exceptions: None History: 6/2/89, DSJ, Created. *********************************************************************************/ STATISTICS * ComputeStatistics (inT16 N, PARAM_DESC ParamDesc[], CLUSTER * Cluster) { STATISTICS *Statistics; int i, j; FLOAT32 *CoVariance; FLOAT32 *Distance; LIST SearchState; SAMPLE *Sample; uinT32 SampleCountAdjustedForBias; // allocate memory to hold the statistics results Statistics = (STATISTICS *) Emalloc (sizeof (STATISTICS)); Statistics->CoVariance = (FLOAT32 *) Emalloc (N * N * sizeof (FLOAT32)); Statistics->Min = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); Statistics->Max = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); // allocate temporary memory to hold the sample to mean distances Distance = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); // initialize the statistics Statistics->AvgVariance = 1.0; CoVariance = Statistics->CoVariance; for (i = 0; i < N; i++) { Statistics->Min[i] = 0.0; Statistics->Max[i] = 0.0; for (j = 0; j < N; j++, CoVariance++) *CoVariance = 0; } // find each sample in the cluster and merge it into the statistics InitSampleSearch(SearchState, Cluster); while ((Sample = NextSample (&SearchState)) != NULL) { for (i = 0; i < N; i++) { Distance[i] = Sample->Mean[i] - Cluster->Mean[i]; if (ParamDesc[i].Circular) { if (Distance[i] > ParamDesc[i].HalfRange) Distance[i] -= ParamDesc[i].Range; if (Distance[i] < -ParamDesc[i].HalfRange) Distance[i] += ParamDesc[i].Range; } if (Distance[i] < Statistics->Min[i]) Statistics->Min[i] = Distance[i]; if (Distance[i] > Statistics->Max[i]) Statistics->Max[i] = Distance[i]; } CoVariance = Statistics->CoVariance; for (i = 0; i < N; i++) for (j = 0; j < N; j++, CoVariance++) *CoVariance += Distance[i] * Distance[j]; } // normalize the variances by the total number of samples // use SampleCount-1 instead of SampleCount to get an unbiased estimate // also compute the geometic mean of the diagonal variances // ensure that clusters with only 1 sample are handled correctly if (Cluster->SampleCount > 1) SampleCountAdjustedForBias = Cluster->SampleCount - 1; else SampleCountAdjustedForBias = 1; CoVariance = Statistics->CoVariance; for (i = 0; i < N; i++) for (j = 0; j < N; j++, CoVariance++) { *CoVariance /= SampleCountAdjustedForBias; if (j == i) { if (*CoVariance < MINVARIANCE) *CoVariance = MINVARIANCE; Statistics->AvgVariance *= *CoVariance; } } Statistics->AvgVariance = (float)pow((double)Statistics->AvgVariance, 1.0 / N); // release temporary memory and return memfree(Distance); return (Statistics); } // ComputeStatistics /** NewSpericalProto ********************************************************* Parameters: N number of dimensions Cluster cluster to be made into a spherical prototype Statistics statistical info about samples in cluster Operation: This routine creates a spherical prototype data structure to approximate the samples in the specified cluster. Spherical prototypes have a single variance which is common across all dimensions. All dimensions are normally distributed and independent. Return: Pointer to a new spherical prototype data structure Exceptions: None History: 6/19/89, DSJ, Created. ******************************************************************************/ PROTOTYPE *NewSphericalProto(uinT16 N, CLUSTER *Cluster, STATISTICS *Statistics) { PROTOTYPE *Proto; Proto = NewSimpleProto (N, Cluster); Proto->Variance.Spherical = Statistics->AvgVariance; if (Proto->Variance.Spherical < MINVARIANCE) Proto->Variance.Spherical = MINVARIANCE; Proto->Magnitude.Spherical = 1.0 / sqrt ((double) (2.0 * PI * Proto->Variance.Spherical)); Proto->TotalMagnitude = (float)pow((double)Proto->Magnitude.Spherical, (double) N); Proto->Weight.Spherical = 1.0 / Proto->Variance.Spherical; Proto->LogMagnitude = log ((double) Proto->TotalMagnitude); return (Proto); } // NewSphericalProto /** NewEllipticalProto ******************************************************* Parameters: N number of dimensions Cluster cluster to be made into an elliptical prototype Statistics statistical info about samples in cluster Operation: This routine creates an elliptical prototype data structure to approximate the samples in the specified cluster. Elliptical prototypes have a variance for each dimension. All dimensions are normally distributed and independent. Return: Pointer to a new elliptical prototype data structure Exceptions: None History: 6/19/89, DSJ, Created. *******************************************************************************/ PROTOTYPE *NewEllipticalProto(inT16 N, CLUSTER *Cluster, STATISTICS *Statistics) { PROTOTYPE *Proto; FLOAT32 *CoVariance; int i; Proto = NewSimpleProto (N, Cluster); Proto->Variance.Elliptical = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); Proto->Magnitude.Elliptical = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); Proto->Weight.Elliptical = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); CoVariance = Statistics->CoVariance; Proto->TotalMagnitude = 1.0; for (i = 0; i < N; i++, CoVariance += N + 1) { Proto->Variance.Elliptical[i] = *CoVariance; if (Proto->Variance.Elliptical[i] < MINVARIANCE) Proto->Variance.Elliptical[i] = MINVARIANCE; Proto->Magnitude.Elliptical[i] = 1.0 / sqrt ((double) (2.0 * PI * Proto->Variance.Elliptical[i])); Proto->Weight.Elliptical[i] = 1.0 / Proto->Variance.Elliptical[i]; Proto->TotalMagnitude *= Proto->Magnitude.Elliptical[i]; } Proto->LogMagnitude = log ((double) Proto->TotalMagnitude); Proto->Style = elliptical; return (Proto); } // NewEllipticalProto /** MewMixedProto ************************************************************ Parameters: N number of dimensions Cluster cluster to be made into a mixed prototype Statistics statistical info about samples in cluster Operation: This routine creates a mixed prototype data structure to approximate the samples in the specified cluster. Mixed prototypes can have different distributions for each dimension. All dimensions are independent. The structure is initially filled in as though it were an elliptical prototype. The actual distributions of the dimensions can be altered by other routines. Return: Pointer to a new mixed prototype data structure Exceptions: None History: 6/19/89, DSJ, Created. ********************************************************************************/ PROTOTYPE *NewMixedProto(inT16 N, CLUSTER *Cluster, STATISTICS *Statistics) { PROTOTYPE *Proto; int i; Proto = NewEllipticalProto (N, Cluster, Statistics); Proto->Distrib = (DISTRIBUTION *) Emalloc (N * sizeof (DISTRIBUTION)); for (i = 0; i < N; i++) { Proto->Distrib[i] = normal; } Proto->Style = mixed; return (Proto); } // NewMixedProto /** NewSimpleProto *********************************************************** Parameters: N number of dimensions Cluster cluster to be made into a prototype Operation: This routine allocates memory to hold a simple prototype data structure, i.e. one without independent distributions and variances for each dimension. Return: Pointer to new simple prototype Exceptions: None History: 6/19/89, DSJ, Created. *******************************************************************************/ PROTOTYPE *NewSimpleProto(inT16 N, CLUSTER *Cluster) { PROTOTYPE *Proto; int i; Proto = (PROTOTYPE *) Emalloc (sizeof (PROTOTYPE)); Proto->Mean = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32)); for (i = 0; i < N; i++) Proto->Mean[i] = Cluster->Mean[i]; Proto->Distrib = NULL; Proto->Significant = TRUE; Proto->Merged = FALSE; Proto->Style = spherical; Proto->NumSamples = Cluster->SampleCount; Proto->Cluster = Cluster; Proto->Cluster->Prototype = TRUE; return (Proto); } // NewSimpleProto /** Independent *************************************************************** Parameters: ParamDesc descriptions of each feature space dimension N number of dimensions CoVariance ptr to a covariance matrix Independence max off-diagonal correlation coefficient Operation: This routine returns TRUE if the specified covariance matrix indicates that all N dimensions are independent of one another. One dimension is judged to be independent of another when the magnitude of the corresponding correlation coefficient is less than the specified Independence factor. The correlation coefficient is calculated as: (see Duda and Hart, pg. 247) coeff[ij] = stddev[ij] / sqrt (stddev[ii] * stddev[jj]) The covariance matrix is assumed to be symmetric (which should always be true). Return: TRUE if dimensions are independent, FALSE otherwise Exceptions: None History: 6/4/89, DSJ, Created. *******************************************************************************/ BOOL8 Independent (PARAM_DESC ParamDesc[], inT16 N, FLOAT32 * CoVariance, FLOAT32 Independence) { int i, j; FLOAT32 *VARii; // points to ith on-diagonal element FLOAT32 *VARjj; // points to jth on-diagonal element FLOAT32 CorrelationCoeff; VARii = CoVariance; for (i = 0; i < N; i++, VARii += N + 1) { if (ParamDesc[i].NonEssential) continue; VARjj = VARii + N + 1; CoVariance = VARii + 1; for (j = i + 1; j < N; j++, CoVariance++, VARjj += N + 1) { if (ParamDesc[j].NonEssential) continue; if ((*VARii == 0.0) || (*VARjj == 0.0)) CorrelationCoeff = 0.0; else CorrelationCoeff = sqrt (sqrt (*CoVariance * *CoVariance / (*VARii * *VARjj))); if (CorrelationCoeff > Independence) return (FALSE); } } return (TRUE); } // Independent /** GetBuckets ************************************************************** Parameters: Clusterer which keeps a bucket_cache for us. Distribution type of probability distribution to test for SampleCount number of samples that are available Confidence probability of a Type I error Operation: This routine returns a histogram data structure which can be used by other routines to place samples into histogram buckets, and then apply a goodness of fit test to the histogram data to determine if the samples belong to the specified probability distribution. The routine keeps a list of bucket data structures which have already been created so that it minimizes the computation time needed to create a new bucket. Return: Bucket data structure Exceptions: none History: Thu Aug 3 12:58:10 1989, DSJ, Created. *****************************************************************************/ BUCKETS *GetBuckets(CLUSTERER* clusterer, DISTRIBUTION Distribution, uinT32 SampleCount, FLOAT64 Confidence) { // Get an old bucket structure with the same number of buckets. uinT16 NumberOfBuckets = OptimumNumberOfBuckets(SampleCount); BUCKETS *Buckets = clusterer->bucket_cache[Distribution][NumberOfBuckets - MINBUCKETS]; // If a matching bucket structure is not found, make one and save it. if (Buckets == NULL) { Buckets = MakeBuckets(Distribution, SampleCount, Confidence); clusterer->bucket_cache[Distribution][NumberOfBuckets - MINBUCKETS] = Buckets; } else { // Just adjust the existing buckets. if (SampleCount != Buckets->SampleCount) AdjustBuckets(Buckets, SampleCount); if (Confidence != Buckets->Confidence) { Buckets->Confidence = Confidence; Buckets->ChiSquared = ComputeChiSquared( DegreesOfFreedom(Distribution, Buckets->NumberOfBuckets), Confidence); } InitBuckets(Buckets); } return Buckets; } // GetBuckets /** Makebuckets ************************************************************* Parameters: Distribution type of probability distribution to test for SampleCount number of samples that are available Confidence probability of a Type I error Operation: This routine creates a histogram data structure which can be used by other routines to place samples into histogram buckets, and then apply a goodness of fit test to the histogram data to determine if the samples belong to the specified probability distribution. The buckets are allocated in such a way that the expected frequency of samples in each bucket is approximately the same. In order to make this possible, a mapping table is computed which maps "normalized" samples into the appropriate bucket. Return: Pointer to new histogram data structure Exceptions: None History: 6/4/89, DSJ, Created. *****************************************************************************/ BUCKETS *MakeBuckets(DISTRIBUTION Distribution, uinT32 SampleCount, FLOAT64 Confidence) { const DENSITYFUNC DensityFunction[] = { NormalDensity, UniformDensity, UniformDensity }; int i, j; BUCKETS *Buckets; FLOAT64 BucketProbability; FLOAT64 NextBucketBoundary; FLOAT64 Probability; FLOAT64 ProbabilityDelta; FLOAT64 LastProbDensity; FLOAT64 ProbDensity; uinT16 CurrentBucket; BOOL8 Symmetrical; // allocate memory needed for data structure Buckets = reinterpret_cast(Emalloc(sizeof(BUCKETS))); Buckets->NumberOfBuckets = OptimumNumberOfBuckets(SampleCount); Buckets->SampleCount = SampleCount; Buckets->Confidence = Confidence; Buckets->Count = reinterpret_cast( Emalloc(Buckets->NumberOfBuckets * sizeof(uinT32))); Buckets->ExpectedCount = reinterpret_cast( Emalloc(Buckets->NumberOfBuckets * sizeof(FLOAT32))); // initialize simple fields Buckets->Distribution = Distribution; for (i = 0; i < Buckets->NumberOfBuckets; i++) { Buckets->Count[i] = 0; Buckets->ExpectedCount[i] = 0.0; } // all currently defined distributions are symmetrical Symmetrical = TRUE; Buckets->ChiSquared = ComputeChiSquared( DegreesOfFreedom(Distribution, Buckets->NumberOfBuckets), Confidence); if (Symmetrical) { // allocate buckets so that all have approx. equal probability BucketProbability = 1.0 / (FLOAT64) (Buckets->NumberOfBuckets); // distribution is symmetric so fill in upper half then copy CurrentBucket = Buckets->NumberOfBuckets / 2; if (Odd (Buckets->NumberOfBuckets)) NextBucketBoundary = BucketProbability / 2; else NextBucketBoundary = BucketProbability; Probability = 0.0; LastProbDensity = (*DensityFunction[(int) Distribution]) (BUCKETTABLESIZE / 2); for (i = BUCKETTABLESIZE / 2; i < BUCKETTABLESIZE; i++) { ProbDensity = (*DensityFunction[(int) Distribution]) (i + 1); ProbabilityDelta = Integral (LastProbDensity, ProbDensity, 1.0); Probability += ProbabilityDelta; if (Probability > NextBucketBoundary) { if (CurrentBucket < Buckets->NumberOfBuckets - 1) CurrentBucket++; NextBucketBoundary += BucketProbability; } Buckets->Bucket[i] = CurrentBucket; Buckets->ExpectedCount[CurrentBucket] += (FLOAT32) (ProbabilityDelta * SampleCount); LastProbDensity = ProbDensity; } // place any leftover probability into the last bucket Buckets->ExpectedCount[CurrentBucket] += (FLOAT32) ((0.5 - Probability) * SampleCount); // copy upper half of distribution to lower half for (i = 0, j = BUCKETTABLESIZE - 1; i < j; i++, j--) Buckets->Bucket[i] = Mirror(Buckets->Bucket[j], Buckets->NumberOfBuckets); // copy upper half of expected counts to lower half for (i = 0, j = Buckets->NumberOfBuckets - 1; i <= j; i++, j--) Buckets->ExpectedCount[i] += Buckets->ExpectedCount[j]; } return Buckets; } // MakeBuckets //--------------------------------------------------------------------------- uinT16 OptimumNumberOfBuckets(uinT32 SampleCount) { /* ** Parameters: ** SampleCount number of samples to be tested ** Operation: ** This routine computes the optimum number of histogram ** buckets that should be used in a chi-squared goodness of ** fit test for the specified number of samples. The optimum ** number is computed based on Table 4.1 on pg. 147 of ** "Measurement and Analysis of Random Data" by Bendat & Piersol. ** Linear interpolation is used to interpolate between table ** values. The table is intended for a 0.05 level of ** significance (alpha). This routine assumes that it is ** equally valid for other alpha's, which may not be true. ** Return: ** Optimum number of histogram buckets ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ uinT8 Last, Next; FLOAT32 Slope; if (SampleCount < kCountTable[0]) return kBucketsTable[0]; for (Last = 0, Next = 1; Next < LOOKUPTABLESIZE; Last++, Next++) { if (SampleCount <= kCountTable[Next]) { Slope = (FLOAT32) (kBucketsTable[Next] - kBucketsTable[Last]) / (FLOAT32) (kCountTable[Next] - kCountTable[Last]); return ((uinT16) (kBucketsTable[Last] + Slope * (SampleCount - kCountTable[Last]))); } } return kBucketsTable[Last]; } // OptimumNumberOfBuckets //--------------------------------------------------------------------------- FLOAT64 ComputeChiSquared (uinT16 DegreesOfFreedom, FLOAT64 Alpha) /* ** Parameters: ** DegreesOfFreedom determines shape of distribution ** Alpha probability of right tail ** Operation: ** This routine computes the chi-squared value which will ** leave a cumulative probability of Alpha in the right tail ** of a chi-squared distribution with the specified number of ** degrees of freedom. Alpha must be between 0 and 1. ** DegreesOfFreedom must be even. The routine maintains an ** array of lists. Each list corresponds to a different ** number of degrees of freedom. Each entry in the list ** corresponds to a different alpha value and its corresponding ** chi-squared value. Therefore, once a particular chi-squared ** value is computed, it is stored in the list and never ** needs to be computed again. ** Return: Desired chi-squared value ** Exceptions: none ** History: 6/5/89, DSJ, Created. */ #define CHIACCURACY 0.01 #define MINALPHA (1e-200) { static LIST ChiWith[MAXDEGREESOFFREEDOM + 1]; CHISTRUCT *OldChiSquared; CHISTRUCT SearchKey; // limit the minimum alpha that can be used - if alpha is too small // it may not be possible to compute chi-squared. Alpha = ClipToRange(Alpha, MINALPHA, 1.0); if (Odd (DegreesOfFreedom)) DegreesOfFreedom++; /* find the list of chi-squared values which have already been computed for the specified number of degrees of freedom. Search the list for the desired chi-squared. */ SearchKey.Alpha = Alpha; OldChiSquared = (CHISTRUCT *) first_node (search (ChiWith[DegreesOfFreedom], &SearchKey, AlphaMatch)); if (OldChiSquared == NULL) { OldChiSquared = NewChiStruct (DegreesOfFreedom, Alpha); OldChiSquared->ChiSquared = Solve (ChiArea, OldChiSquared, (FLOAT64) DegreesOfFreedom, (FLOAT64) CHIACCURACY); ChiWith[DegreesOfFreedom] = push (ChiWith[DegreesOfFreedom], OldChiSquared); } else { // further optimization might move OldChiSquared to front of list } return (OldChiSquared->ChiSquared); } // ComputeChiSquared //--------------------------------------------------------------------------- FLOAT64 NormalDensity(inT32 x) { /* ** Parameters: ** x number to compute the normal probability density for ** Globals: ** kNormalMean mean of a discrete normal distribution ** kNormalVariance variance of a discrete normal distribution ** kNormalMagnitude magnitude of a discrete normal distribution ** Operation: ** This routine computes the probability density function ** of a discrete normal distribution defined by the global ** variables kNormalMean, kNormalVariance, and kNormalMagnitude. ** Normal magnitude could, of course, be computed in terms of ** the normal variance but it is precomputed for efficiency. ** Return: ** The value of the normal distribution at x. ** Exceptions: ** None ** History: ** 6/4/89, DSJ, Created. */ FLOAT64 Distance; Distance = x - kNormalMean; return kNormalMagnitude * exp(-0.5 * Distance * Distance / kNormalVariance); } // NormalDensity //--------------------------------------------------------------------------- FLOAT64 UniformDensity(inT32 x) { /* ** Parameters: ** x number to compute the uniform probability density for ** Operation: ** This routine computes the probability density function ** of a uniform distribution at the specified point. The ** range of the distribution is from 0 to BUCKETTABLESIZE. ** Return: ** The value of the uniform distribution at x. ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ static FLOAT64 UniformDistributionDensity = (FLOAT64) 1.0 / BUCKETTABLESIZE; if ((x >= 0.0) && (x <= BUCKETTABLESIZE)) return UniformDistributionDensity; else return (FLOAT64) 0.0; } // UniformDensity //--------------------------------------------------------------------------- FLOAT64 Integral(FLOAT64 f1, FLOAT64 f2, FLOAT64 Dx) { /* ** Parameters: ** f1 value of function at x1 ** f2 value of function at x2 ** Dx x2 - x1 (should always be positive) ** Operation: ** This routine computes a trapezoidal approximation to the ** integral of a function over a small delta in x. ** Return: ** Approximation of the integral of the function from x1 to x2. ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ return (f1 + f2) * Dx / 2.0; } // Integral //--------------------------------------------------------------------------- void FillBuckets(BUCKETS *Buckets, CLUSTER *Cluster, uinT16 Dim, PARAM_DESC *ParamDesc, FLOAT32 Mean, FLOAT32 StdDev) { /* ** Parameters: ** Buckets histogram buckets to count samples ** Cluster cluster whose samples are being analyzed ** Dim dimension of samples which is being analyzed ** ParamDesc description of the dimension ** Mean "mean" of the distribution ** StdDev "standard deviation" of the distribution ** Operation: ** This routine counts the number of cluster samples which ** fall within the various histogram buckets in Buckets. Only ** one dimension of each sample is examined. The exact meaning ** of the Mean and StdDev parameters depends on the ** distribution which is being analyzed (this info is in the ** Buckets data structure). For normal distributions, Mean ** and StdDev have the expected meanings. For uniform and ** random distributions the Mean is the center point of the ** range and the StdDev is 1/2 the range. A dimension with ** zero standard deviation cannot be statistically analyzed. ** In this case, a pseudo-analysis is used. ** Return: ** None (the Buckets data structure is filled in) ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ uinT16 BucketID; int i; LIST SearchState; SAMPLE *Sample; // initialize the histogram bucket counts to 0 for (i = 0; i < Buckets->NumberOfBuckets; i++) Buckets->Count[i] = 0; if (StdDev == 0.0) { /* if the standard deviation is zero, then we can't statistically analyze the cluster. Use a pseudo-analysis: samples exactly on the mean are distributed evenly across all buckets. Samples greater than the mean are placed in the last bucket; samples less than the mean are placed in the first bucket. */ InitSampleSearch(SearchState, Cluster); i = 0; while ((Sample = NextSample (&SearchState)) != NULL) { if (Sample->Mean[Dim] > Mean) BucketID = Buckets->NumberOfBuckets - 1; else if (Sample->Mean[Dim] < Mean) BucketID = 0; else BucketID = i; Buckets->Count[BucketID] += 1; i++; if (i >= Buckets->NumberOfBuckets) i = 0; } } else { // search for all samples in the cluster and add to histogram buckets InitSampleSearch(SearchState, Cluster); while ((Sample = NextSample (&SearchState)) != NULL) { switch (Buckets->Distribution) { case normal: BucketID = NormalBucket (ParamDesc, Sample->Mean[Dim], Mean, StdDev); break; case D_random: case uniform: BucketID = UniformBucket (ParamDesc, Sample->Mean[Dim], Mean, StdDev); break; default: BucketID = 0; } Buckets->Count[Buckets->Bucket[BucketID]] += 1; } } } // FillBuckets //---------------------------------------------------------------------------*/ uinT16 NormalBucket(PARAM_DESC *ParamDesc, FLOAT32 x, FLOAT32 Mean, FLOAT32 StdDev) { /* ** Parameters: ** ParamDesc used to identify circular dimensions ** x value to be normalized ** Mean mean of normal distribution ** StdDev standard deviation of normal distribution ** Operation: ** This routine determines which bucket x falls into in the ** discrete normal distribution defined by kNormalMean ** and kNormalStdDev. x values which exceed the range of ** the discrete distribution are clipped. ** Return: ** Bucket number into which x falls ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ FLOAT32 X; // wraparound circular parameters if necessary if (ParamDesc->Circular) { if (x - Mean > ParamDesc->HalfRange) x -= ParamDesc->Range; else if (x - Mean < -ParamDesc->HalfRange) x += ParamDesc->Range; } X = ((x - Mean) / StdDev) * kNormalStdDev + kNormalMean; if (X < 0) return 0; if (X > BUCKETTABLESIZE - 1) return ((uinT16) (BUCKETTABLESIZE - 1)); return (uinT16) floor((FLOAT64) X); } // NormalBucket //--------------------------------------------------------------------------- uinT16 UniformBucket(PARAM_DESC *ParamDesc, FLOAT32 x, FLOAT32 Mean, FLOAT32 StdDev) { /* ** Parameters: ** ParamDesc used to identify circular dimensions ** x value to be normalized ** Mean center of range of uniform distribution ** StdDev 1/2 the range of the uniform distribution ** Operation: ** This routine determines which bucket x falls into in the ** discrete uniform distribution defined by ** BUCKETTABLESIZE. x values which exceed the range of ** the discrete distribution are clipped. ** Return: ** Bucket number into which x falls ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ FLOAT32 X; // wraparound circular parameters if necessary if (ParamDesc->Circular) { if (x - Mean > ParamDesc->HalfRange) x -= ParamDesc->Range; else if (x - Mean < -ParamDesc->HalfRange) x += ParamDesc->Range; } X = ((x - Mean) / (2 * StdDev) * BUCKETTABLESIZE + BUCKETTABLESIZE / 2.0); if (X < 0) return 0; if (X > BUCKETTABLESIZE - 1) return (uinT16) (BUCKETTABLESIZE - 1); return (uinT16) floor((FLOAT64) X); } // UniformBucket //--------------------------------------------------------------------------- BOOL8 DistributionOK(BUCKETS *Buckets) { /* ** Parameters: ** Buckets histogram data to perform chi-square test on ** Operation: ** This routine performs a chi-square goodness of fit test ** on the histogram data in the Buckets data structure. TRUE ** is returned if the histogram matches the probability ** distribution which was specified when the Buckets ** structure was originally created. Otherwise FALSE is ** returned. ** Return: ** TRUE if samples match distribution, FALSE otherwise ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ FLOAT32 FrequencyDifference; FLOAT32 TotalDifference; int i; // compute how well the histogram matches the expected histogram TotalDifference = 0.0; for (i = 0; i < Buckets->NumberOfBuckets; i++) { FrequencyDifference = Buckets->Count[i] - Buckets->ExpectedCount[i]; TotalDifference += (FrequencyDifference * FrequencyDifference) / Buckets->ExpectedCount[i]; } // test to see if the difference is more than expected if (TotalDifference > Buckets->ChiSquared) return FALSE; else return TRUE; } // DistributionOK //--------------------------------------------------------------------------- void FreeStatistics(STATISTICS *Statistics) { /* ** Parameters: ** Statistics pointer to data structure to be freed ** Operation: ** This routine frees the memory used by the statistics ** data structure. ** Return: ** None ** Exceptions: ** None ** History: ** 6/5/89, DSJ, Created. */ memfree (Statistics->CoVariance); memfree (Statistics->Min); memfree (Statistics->Max); memfree(Statistics); } // FreeStatistics //--------------------------------------------------------------------------- void FreeBuckets(BUCKETS *buckets) { /* ** Parameters: ** buckets pointer to data structure to be freed ** Operation: ** This routine properly frees the memory used by a BUCKETS. */ Efree(buckets->Count); Efree(buckets->ExpectedCount); Efree(buckets); } // FreeBuckets //--------------------------------------------------------------------------- void FreeCluster(CLUSTER *Cluster) { /* ** Parameters: ** Cluster pointer to cluster to be freed ** Operation: ** This routine frees the memory consumed by the specified ** cluster and all of its subclusters. This is done by ** recursive calls to FreeCluster(). ** Return: ** None ** Exceptions: ** None ** History: ** 6/6/89, DSJ, Created. */ if (Cluster != NULL) { FreeCluster (Cluster->Left); FreeCluster (Cluster->Right); memfree(Cluster); } } // FreeCluster //--------------------------------------------------------------------------- uinT16 DegreesOfFreedom(DISTRIBUTION Distribution, uinT16 HistogramBuckets) { /* ** Parameters: ** Distribution distribution being tested for ** HistogramBuckets number of buckets in chi-square test ** Operation: ** This routine computes the degrees of freedom that should ** be used in a chi-squared test with the specified number of ** histogram buckets. The result is always rounded up to ** the next even number so that the value of chi-squared can be ** computed more easily. This will cause the value of ** chi-squared to be higher than the optimum value, resulting ** in the chi-square test being more lenient than optimum. ** Return: The number of degrees of freedom for a chi-square test ** Exceptions: none ** History: Thu Aug 3 14:04:18 1989, DSJ, Created. */ static uinT8 DegreeOffsets[] = { 3, 3, 1 }; uinT16 AdjustedNumBuckets; AdjustedNumBuckets = HistogramBuckets - DegreeOffsets[(int) Distribution]; if (Odd (AdjustedNumBuckets)) AdjustedNumBuckets++; return (AdjustedNumBuckets); } // DegreesOfFreedom //--------------------------------------------------------------------------- int NumBucketsMatch(void *arg1, // BUCKETS *Histogram, void *arg2) { // uinT16 *DesiredNumberOfBuckets) /* ** Parameters: ** Histogram current histogram being tested for a match ** DesiredNumberOfBuckets match key ** Operation: ** This routine is used to search a list of histogram data ** structures to find one with the specified number of ** buckets. It is called by the list search routines. ** Return: TRUE if Histogram matches DesiredNumberOfBuckets ** Exceptions: none ** History: Thu Aug 3 14:17:33 1989, DSJ, Created. */ BUCKETS *Histogram = (BUCKETS *) arg1; uinT16 *DesiredNumberOfBuckets = (uinT16 *) arg2; return (*DesiredNumberOfBuckets == Histogram->NumberOfBuckets); } // NumBucketsMatch //--------------------------------------------------------------------------- int ListEntryMatch(void *arg1, //ListNode void *arg2) { //Key /* ** Parameters: none ** Operation: ** This routine is used to search a list for a list node ** whose contents match Key. It is called by the list ** delete_d routine. ** Return: TRUE if ListNode matches Key ** Exceptions: none ** History: Thu Aug 3 14:23:58 1989, DSJ, Created. */ return (arg1 == arg2); } // ListEntryMatch //--------------------------------------------------------------------------- void AdjustBuckets(BUCKETS *Buckets, uinT32 NewSampleCount) { /* ** Parameters: ** Buckets histogram data structure to adjust ** NewSampleCount new sample count to adjust to ** Operation: ** This routine multiplies each ExpectedCount histogram entry ** by NewSampleCount/OldSampleCount so that the histogram ** is now adjusted to the new sample count. ** Return: none ** Exceptions: none ** History: Thu Aug 3 14:31:14 1989, DSJ, Created. */ int i; FLOAT64 AdjustFactor; AdjustFactor = (((FLOAT64) NewSampleCount) / ((FLOAT64) Buckets->SampleCount)); for (i = 0; i < Buckets->NumberOfBuckets; i++) { Buckets->ExpectedCount[i] *= AdjustFactor; } Buckets->SampleCount = NewSampleCount; } // AdjustBuckets //--------------------------------------------------------------------------- void InitBuckets(BUCKETS *Buckets) { /* ** Parameters: ** Buckets histogram data structure to init ** Operation: ** This routine sets the bucket counts in the specified histogram ** to zero. ** Return: none ** Exceptions: none ** History: Thu Aug 3 14:31:14 1989, DSJ, Created. */ int i; for (i = 0; i < Buckets->NumberOfBuckets; i++) { Buckets->Count[i] = 0; } } // InitBuckets //--------------------------------------------------------------------------- int AlphaMatch(void *arg1, //CHISTRUCT *ChiStruct, void *arg2) { //CHISTRUCT *SearchKey) /* ** Parameters: ** ChiStruct chi-squared struct being tested for a match ** SearchKey chi-squared struct that is the search key ** Operation: ** This routine is used to search a list of structures which ** hold pre-computed chi-squared values for a chi-squared ** value whose corresponding alpha field matches the alpha ** field of SearchKey. ** It is called by the list search routines. ** Return: TRUE if ChiStruct's Alpha matches SearchKey's Alpha ** Exceptions: none ** History: Thu Aug 3 14:17:33 1989, DSJ, Created. */ CHISTRUCT *ChiStruct = (CHISTRUCT *) arg1; CHISTRUCT *SearchKey = (CHISTRUCT *) arg2; return (ChiStruct->Alpha == SearchKey->Alpha); } // AlphaMatch //--------------------------------------------------------------------------- CHISTRUCT *NewChiStruct(uinT16 DegreesOfFreedom, FLOAT64 Alpha) { /* ** Parameters: ** DegreesOfFreedom degrees of freedom for new chi value ** Alpha confidence level for new chi value ** Operation: ** This routine allocates a new data structure which is used ** to hold a chi-squared value along with its associated ** number of degrees of freedom and alpha value. ** Return: none ** Exceptions: none ** History: Fri Aug 4 11:04:59 1989, DSJ, Created. */ CHISTRUCT *NewChiStruct; NewChiStruct = (CHISTRUCT *) Emalloc (sizeof (CHISTRUCT)); NewChiStruct->DegreesOfFreedom = DegreesOfFreedom; NewChiStruct->Alpha = Alpha; return (NewChiStruct); } // NewChiStruct //--------------------------------------------------------------------------- FLOAT64 Solve (SOLVEFUNC Function, void *FunctionParams, FLOAT64 InitialGuess, FLOAT64 Accuracy) /* ** Parameters: ** Function function whose zero is to be found ** FunctionParams arbitrary data to pass to function ** InitialGuess point to start solution search at ** Accuracy maximum allowed error ** Operation: ** This routine attempts to find an x value at which Function ** goes to zero (i.e. a root of the function ). It will only ** work correctly if a solution actually exists and there ** are no extrema between the solution and the InitialGuess. ** The algorithms used are extremely primitive. ** Return: Solution of function ( x for which f(x) = 0 ). ** Exceptions: none ** History: Fri Aug 4 11:08:59 1989, DSJ, Created. */ #define INITIALDELTA 0.1 #define DELTARATIO 0.1 { FLOAT64 x; FLOAT64 f; FLOAT64 Slope; FLOAT64 Delta; FLOAT64 NewDelta; FLOAT64 xDelta; FLOAT64 LastPosX, LastNegX; x = InitialGuess; Delta = INITIALDELTA; LastPosX = MAX_FLOAT32; LastNegX = -MAX_FLOAT32; f = (*Function) ((CHISTRUCT *) FunctionParams, x); while (Abs (LastPosX - LastNegX) > Accuracy) { // keep track of outer bounds of current estimate if (f < 0) LastNegX = x; else LastPosX = x; // compute the approx. slope of f(x) at the current point Slope = ((*Function) ((CHISTRUCT *) FunctionParams, x + Delta) - f) / Delta; // compute the next solution guess */ xDelta = f / Slope; x -= xDelta; // reduce the delta used for computing slope to be a fraction of //the amount moved to get to the new guess NewDelta = Abs (xDelta) * DELTARATIO; if (NewDelta < Delta) Delta = NewDelta; // compute the value of the function at the new guess f = (*Function) ((CHISTRUCT *) FunctionParams, x); } return (x); } // Solve //--------------------------------------------------------------------------- FLOAT64 ChiArea(CHISTRUCT *ChiParams, FLOAT64 x) { /* ** Parameters: ** ChiParams contains degrees of freedom and alpha ** x value of chi-squared to evaluate ** Operation: ** This routine computes the area under a chi density curve ** from 0 to x, minus the desired area under the curve. The ** number of degrees of freedom of the chi curve is specified ** in the ChiParams structure. The desired area is also ** specified in the ChiParams structure as Alpha ( or 1 minus ** the desired area ). This routine is intended to be passed ** to the Solve() function to find the value of chi-squared ** which will yield a desired area under the right tail of ** the chi density curve. The function will only work for ** even degrees of freedom. The equations are based on ** integrating the chi density curve in parts to obtain ** a series that can be used to compute the area under the ** curve. ** Return: Error between actual and desired area under the chi curve. ** Exceptions: none ** History: Fri Aug 4 12:48:41 1989, DSJ, Created. */ int i, N; FLOAT64 SeriesTotal; FLOAT64 Denominator; FLOAT64 PowerOfx; N = ChiParams->DegreesOfFreedom / 2 - 1; SeriesTotal = 1; Denominator = 1; PowerOfx = 1; for (i = 1; i <= N; i++) { Denominator *= 2 * i; PowerOfx *= x; SeriesTotal += PowerOfx / Denominator; } return ((SeriesTotal * exp (-0.5 * x)) - ChiParams->Alpha); } // ChiArea //--------------------------------------------------------------------------- BOOL8 MultipleCharSamples (CLUSTERER * Clusterer, CLUSTER * Cluster, FLOAT32 MaxIllegal) /* ** Parameters: ** Clusterer data structure holding cluster tree ** Cluster cluster containing samples to be tested ** MaxIllegal max percentage of samples allowed to have ** more than 1 feature in the cluster ** Operation: ** This routine looks at all samples in the specified cluster. ** It computes a running estimate of the percentage of the ** charaters which have more than 1 sample in the cluster. ** When this percentage exceeds MaxIllegal, TRUE is returned. ** Otherwise FALSE is returned. The CharID ** fields must contain integers which identify the training ** characters which were used to generate the sample. One ** integer is used for each sample. The NumChar field in ** the Clusterer must contain the number of characters in the ** training set. All CharID fields must be between 0 and ** NumChar-1. The main function of this routine is to help ** identify clusters which need to be split further, i.e. if ** numerous training characters have 2 or more features which are ** contained in the same cluster, then the cluster should be ** split. ** Return: TRUE if the cluster should be split, FALSE otherwise. ** Exceptions: none ** History: Wed Aug 30 11:13:05 1989, DSJ, Created. ** 2/22/90, DSJ, Added MaxIllegal control rather than always ** splitting illegal clusters. */ #define ILLEGAL_CHAR 2 { static BOOL8 *CharFlags = NULL; static inT32 NumFlags = 0; int i; LIST SearchState; SAMPLE *Sample; inT32 CharID; inT32 NumCharInCluster; inT32 NumIllegalInCluster; FLOAT32 PercentIllegal; // initial estimate assumes that no illegal chars exist in the cluster NumCharInCluster = Cluster->SampleCount; NumIllegalInCluster = 0; if (Clusterer->NumChar > NumFlags) { if (CharFlags != NULL) memfree(CharFlags); NumFlags = Clusterer->NumChar; CharFlags = (BOOL8 *) Emalloc (NumFlags * sizeof (BOOL8)); } for (i = 0; i < NumFlags; i++) CharFlags[i] = FALSE; // find each sample in the cluster and check if we have seen it before InitSampleSearch(SearchState, Cluster); while ((Sample = NextSample (&SearchState)) != NULL) { CharID = Sample->CharID; if (CharFlags[CharID] == FALSE) { CharFlags[CharID] = TRUE; } else { if (CharFlags[CharID] == TRUE) { NumIllegalInCluster++; CharFlags[CharID] = ILLEGAL_CHAR; } NumCharInCluster--; PercentIllegal = (FLOAT32) NumIllegalInCluster / NumCharInCluster; if (PercentIllegal > MaxIllegal) { destroy(SearchState); return (TRUE); } } } return (FALSE); } // MultipleCharSamples // Compute the inverse of a matrix using LU decomposition with partial pivoting. // The return value is the sum of norms of the off-diagonal terms of the // product of a and inv. (A measure of the error.) double InvertMatrix(const float* input, int size, float* inv) { // Allocate memory for the 2D arrays. GENERIC_2D_ARRAY U(size, size, 0.0); GENERIC_2D_ARRAY U_inv(size, size, 0.0); GENERIC_2D_ARRAY L(size, size, 0.0); // Initialize the working matrices. U starts as input, L as I and U_inv as O. int row; int col; for (row = 0; row < size; row++) { for (col = 0; col < size; col++) { U[row][col] = input[row*size + col]; L[row][col] = row == col ? 1.0 : 0.0; U_inv[row][col] = 0.0; } } // Compute forward matrix by inversion by LU decomposition of input. for (col = 0; col < size; ++col) { // Find best pivot int best_row = 0; double best_pivot = -1.0; for (row = col; row < size; ++row) { if (Abs(U[row][col]) > best_pivot) { best_pivot = Abs(U[row][col]); best_row = row; } } // Exchange pivot rows. if (best_row != col) { for (int k = 0; k < size; ++k) { double tmp = U[best_row][k]; U[best_row][k] = U[col][k]; U[col][k] = tmp; tmp = L[best_row][k]; L[best_row][k] = L[col][k]; L[col][k] = tmp; } } // Now do the pivot itself. for (row = col + 1; row < size; ++row) { double ratio = -U[row][col] / U[col][col]; for (int j = col; j < size; ++j) { U[row][j] += U[col][j] * ratio; } for (int k = 0; k < size; ++k) { L[row][k] += L[col][k] * ratio; } } } // Next invert U. for (col = 0; col < size; ++col) { U_inv[col][col] = 1.0 / U[col][col]; for (row = col - 1; row >= 0; --row) { double total = 0.0; for (int k = col; k > row; --k) { total += U[row][k] * U_inv[k][col]; } U_inv[row][col] = -total / U[row][row]; } } // Now the answer is U_inv.L. for (row = 0; row < size; row++) { for (col = 0; col < size; col++) { double sum = 0.0; for (int k = row; k < size; ++k) { sum += U_inv[row][k] * L[k][col]; } inv[row*size + col] = sum; } } // Check matrix product. double error_sum = 0.0; for (row = 0; row < size; row++) { for (col = 0; col < size; col++) { double sum = 0.0; for (int k = 0; k < size; ++k) { sum += input[row*size + k] * inv[k *size + col]; } if (row != col) { error_sum += Abs(sum); } } } return error_sum; }