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tesseract/classify/cluster.cpp

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/******************************************************************************
** 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 "const.h"
#include "cluster.h"
#include "emalloc.h"
#include "genericheap.h"
#include "helpers.h"
#include "kdpair.h"
#include "matrix.h"
#include "tprintf.h"
#include "danerror.h"
#include <math.h>
#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;
};
typedef tesseract::KDPairInc<float, TEMPCLUSTER*> ClusterPair;
typedef tesseract::GenericHeap<ClusterPair> ClusterHeap;
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 occurrence histogram
FLOAT32 *ExpectedCount; // expected histogram
};
struct CHISTRUCT{
uinT16 DegreesOfFreedom;
FLOAT64 Alpha;
FLOAT64 ChiSquared;
};
// For use with KDWalk / MakePotentialClusters
struct ClusteringContext {
ClusterHeap *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--------------------------------------
/**
* This routine creates a new clusterer data structure,
* initializes it, and returns a pointer to it.
*
* @param SampleSize number of dimensions in feature space
* @param ParamDesc description of each dimension
* @return pointer to the new clusterer data structure
* @note Exceptions: None
* @note 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
/**
* 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.
*
* @param Clusterer clusterer data structure to add sample to
* @param Feature feature to be added to clusterer
* @param CharID unique ident. of char that sample came from
*
* @return Pointer to the new sample data structure
* @note Exceptions: ALREADYCLUSTERED MakeSample can't be called after
* ClusterSamples has been called
* @note 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
/**
* 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.
*
* @param Clusterer data struct containing samples to be clustered
* @param Config parameters which control clustering process
*
* @return Pointer to a list of prototypes
* @note Exceptions: None
* @note 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);
// We don't need the cluster pointers in the protos any more, so null them
// out, which makes it safe to delete the clusterer.
LIST proto_list = Clusterer->ProtoList;
iterate(proto_list) {
PROTOTYPE *proto = reinterpret_cast<PROTOTYPE *>(first_node(proto_list));
proto->Cluster = NULL;
}
return Clusterer->ProtoList;
} // ClusterSamples
/**
* 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.
* @param Clusterer pointer to data structure to be freed
* @return None
* @note Exceptions: None
* @note History: 6/6/89, DSJ, Created.
*/
void FreeClusterer(CLUSTERER *Clusterer) {
if (Clusterer != NULL) {
free(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]);
}
free(Clusterer);
}
} // FreeClusterer
/**
* 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.
* @param ProtoList pointer to list of prototypes to be freed
* @return None
* @note Exceptions: None
* @note History: 6/6/89, DSJ, Created.
*/
void FreeProtoList(LIST *ProtoList) {
destroy_nodes(*ProtoList, FreePrototype);
} // FreeProtoList
/**
* 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.
* @param arg prototype data structure to be deallocated
* @return None
* @note Exceptions: None
* @note 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
free(Prototype->Distrib);
free(Prototype->Mean);
if (Prototype->Style != spherical) {
free(Prototype->Variance.Elliptical);
free(Prototype->Magnitude.Elliptical);
free(Prototype->Weight.Elliptical);
}
free(Prototype);
} // FreePrototype
/**
* 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.
* @param SearchState ptr to list containing clusters to be searched
* @return Pointer to the next leaf cluster (sample) or NULL.
* @note Exceptions: None
* @note 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
/**
* This routine returns the mean of the specified
* prototype in the indicated dimension.
* @param Proto prototype to return mean of
* @param Dimension dimension whose mean is to be returned
* @return Mean of Prototype in Dimension
* @note Exceptions: none
* @note History: 7/6/89, DSJ, Created.
*/
FLOAT32 Mean(PROTOTYPE *Proto, uinT16 Dimension) {
return (Proto->Mean[Dimension]);
} // Mean
/**
* This routine returns the standard deviation of the
* prototype in the indicated dimension.
* @param Proto prototype to return standard deviation of
* @param Dimension dimension whose stddev is to be returned
* @return Standard deviation of Prototype in Dimension
* @note Exceptions: none
* @note 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
----------------------------------------------------------------------------*/
/**
* 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.
* @param Clusterer data structure holdings samples to be clustered
* @return None (the Clusterer data structure is changed)
* @note Exceptions: None
* @note History: 5/29/89, DSJ, Created.
*/
void CreateClusterTree(CLUSTERER *Clusterer) {
ClusteringContext context;
ClusterPair 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 = new ClusterHeap(Clusterer->NumberOfSamples);
KDWalk(context.tree, (void_proc)MakePotentialClusters, &context);
// form potential clusters into actual clusters - always do "best" first
while (context.heap->Pop(&HeapEntry)) {
PotentialCluster = 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) {
context.heap->Push(&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) {
context.heap->Push(&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;
delete context.heap;
free(context.candidates);
} // CreateClusterTree
/**
* 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.
* @param context ClusteringContext (see definition above)
* @param Cluster current cluster being visited in kd-tree walk
* @param Level level of this cluster in the kd-tree
*/
void MakePotentialClusters(ClusteringContext *context,
CLUSTER *Cluster, inT32 Level) {
ClusterPair HeapEntry;
int next = context->next;
context->candidates[next].Cluster = Cluster;
HeapEntry.data = &(context->candidates[next]);
context->candidates[next].Neighbor =
FindNearestNeighbor(context->tree,
context->candidates[next].Cluster,
&HeapEntry.key);
if (context->candidates[next].Neighbor != NULL) {
context->heap->Push(&HeapEntry);
context->next++;
}
} // MakePotentialClusters
/**
* 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.
* @param Tree kd-tree to search in for nearest neighbor
* @param Cluster cluster whose nearest neighbor is to be found
* @param Distance ptr to variable to report distance found
* @return Pointer to the nearest neighbor of Cluster, or NULL
* @note Exceptions: none
* @note 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
/**
* 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.
* @param Clusterer current clustering environment
* @param TempCluster potential cluster to make permanent
* @return Pointer to the new permanent cluster
* @note Exceptions: none
* @note 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
/**
* 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.
* @param N # of dimensions (size of arrays)
* @param ParamDesc array of dimension descriptions
* @param n1, n2 number of samples in each old cluster
* @param m array to hold mean of new cluster
* @param m1, m2 arrays containing means of old clusters
* @return The number of samples in the new cluster.
* @note Exceptions: None
* @note 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
/**
* 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.
* @param Clusterer data structure holding cluster tree
* @param Config parameters used to control prototype generation
* @return None
* @note Exceptions: None
* @note 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
/**
* 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.
* @param Clusterer data structure holding cluster tree
* @param Config parameters used to control prototype generation
* @param Cluster cluster to be made into a prototype
* @return Pointer to new prototype or NULL
* @note Exceptions: None
* @note 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
/**
* 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.
*
* @param N number of dimensions
* @param Cluster cluster being analyzed
* @param Statistics statistical info about cluster
* @param Style type of prototype to be generated
* @param MinSamples minimum number of samples in a cluster
* @return Pointer to degenerate prototype or NULL.
* @note Exceptions: None
* @note 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
/**
* 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.
* @param Clusterer data struct containing samples being clustered
* @param Config provides the magic number of samples that make a good cluster
* @param Cluster cluster to be made into an elliptical prototype
* @param Statistics statistical info about cluster
* @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 = static_cast<FLOAT32 *>(Emalloc(kMatrixSize));
FLOAT32 *Inverse = static_cast<FLOAT32 *>(Emalloc(kMatrixSize));
FLOAT32 *Delta = static_cast<FLOAT32 *>(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;
}
free(Covariance);
free(Inverse);
free(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;
}
/**
* 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.
* @param Clusterer data struct containing samples being clustered
* @param Cluster cluster to be made into a spherical prototype
* @param Statistics statistical info about cluster
* @param Buckets histogram struct used to analyze distribution
* @return Pointer to new spherical prototype or NULL.
* @note Exceptions: None
* @note 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
/**
* 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.
* @param Clusterer data struct containing samples being clustered
* @param Cluster cluster to be made into an elliptical prototype
* @param Statistics statistical info about cluster
* @param Buckets histogram struct used to analyze distribution
* @return Pointer to new elliptical prototype or NULL.
* @note Exceptions: None
* @note 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
/**
* 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.
* @param Clusterer data struct containing samples being clustered
* @param Cluster cluster to be made into a prototype
* @param Statistics statistical info about cluster
* @param NormalBuckets histogram struct used to analyze distribution
* @param Confidence confidence level for alternate distributions
* @return Pointer to new mixed prototype or NULL.
* @note Exceptions: None
* @note 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
/**
* This routine alters the ith dimension of the specified
* mixed prototype to be D_random.
* @param i index of dimension to be changed
* @param Proto prototype whose dimension is to be altered
* @param ParamDesc description of specified dimension
* @return None
* @note Exceptions: None
* @note 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
/**
* This routine alters the ith dimension of the specified
* mixed prototype to be uniform.
* @param i index of dimension to be changed
* @param Proto prototype whose dimension is to be altered
* @param Statistics statistical info about prototype
* @return None
* @note Exceptions: None
* @note 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
/**
* 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.
* @param N number of dimensions
* @param ParamDesc array of dimension descriptions
* @param Cluster cluster whose stats are to be computed
* @return Pointer to new data structure containing statistics
* @note Exceptions: None
* @note 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
free(Distance);
return (Statistics);
} // ComputeStatistics
/**
* 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.
* @param N number of dimensions
* @param Cluster cluster to be made into a spherical prototype
* @param Statistics statistical info about samples in cluster
* @return Pointer to a new spherical prototype data structure
* @note Exceptions: None
* @note 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
/**
* 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.
* @param N number of dimensions
* @param Cluster cluster to be made into an elliptical prototype
* @param Statistics statistical info about samples in cluster
* @return Pointer to a new elliptical prototype data structure
* @note Exceptions: None
* @note 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
/**
* 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.
* @param N number of dimensions
* @param Cluster cluster to be made into a mixed prototype
* @param Statistics statistical info about samples in cluster
* @return Pointer to a new mixed prototype data structure
* @note Exceptions: None
* @note 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
/**
* This routine allocates memory to hold a simple prototype
* data structure, i.e. one without independent distributions
* and variances for each dimension.
* @param N number of dimensions
* @param Cluster cluster to be made into a prototype
* @return Pointer to new simple prototype
* @note Exceptions: None
* @note 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
/**
* 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).
* @param ParamDesc descriptions of each feature space dimension
* @param N number of dimensions
* @param CoVariance ptr to a covariance matrix
* @param Independence max off-diagonal correlation coefficient
* @return TRUE if dimensions are independent, FALSE otherwise
* @note Exceptions: None
* @note 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
/**
* 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.
* @param clusterer which keeps a bucket_cache for us.
* @param Distribution type of probability distribution to test for
* @param SampleCount number of samples that are available
* @param Confidence probability of a Type I error
* @return Bucket data structure
* @note Exceptions: none
* @note 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
/**
* 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.
* @param Distribution type of probability distribution to test for
* @param SampleCount number of samples that are available
* @param Confidence probability of a Type I error
* @return Pointer to new histogram data structure
* @note Exceptions: None
* @note 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 = static_cast<BUCKETS *>(Emalloc(sizeof(BUCKETS)));
Buckets->NumberOfBuckets = OptimumNumberOfBuckets(SampleCount);
Buckets->SampleCount = SampleCount;
Buckets->Confidence = Confidence;
Buckets->Count =
static_cast<uinT32 *>(Emalloc(Buckets->NumberOfBuckets * sizeof(uinT32)));
Buckets->ExpectedCount = static_cast<FLOAT32 *>(
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
/**
* 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.
* @param SampleCount number of samples to be tested
* @return Optimum number of histogram buckets
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
uinT16 OptimumNumberOfBuckets(uinT32 SampleCount) {
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
/**
* 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.
* @param DegreesOfFreedom determines shape of distribution
* @param Alpha probability of right tail
* @return Desired chi-squared value
* @note Exceptions: none
* @note History: 6/5/89, DSJ, Created.
*/
FLOAT64
ComputeChiSquared (uinT16 DegreesOfFreedom, FLOAT64 Alpha)
#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
/**
* 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.
* @param x number to compute the normal probability density for
* @note Globals:
* kNormalMean mean of a discrete normal distribution
* kNormalVariance variance of a discrete normal distribution
* kNormalMagnitude magnitude of a discrete normal
*distribution
* @return The value of the normal distribution at x.
* @note Exceptions: None
* @note History: 6/4/89, DSJ, Created.
*/
FLOAT64 NormalDensity(inT32 x) {
FLOAT64 Distance;
Distance = x - kNormalMean;
return kNormalMagnitude * exp(-0.5 * Distance * Distance / kNormalVariance);
} // NormalDensity
/**
* 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.
* @param x number to compute the uniform probability density for
* @return The value of the uniform distribution at x.
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
FLOAT64 UniformDensity(inT32 x) {
static FLOAT64 UniformDistributionDensity = (FLOAT64) 1.0 / BUCKETTABLESIZE;
if ((x >= 0.0) && (x <= BUCKETTABLESIZE))
return UniformDistributionDensity;
else
return (FLOAT64) 0.0;
} // UniformDensity
/**
* This routine computes a trapezoidal approximation to the
* integral of a function over a small delta in x.
* @param f1 value of function at x1
* @param f2 value of function at x2
* @param Dx x2 - x1 (should always be positive)
* @return Approximation of the integral of the function from x1 to x2.
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
FLOAT64 Integral(FLOAT64 f1, FLOAT64 f2, FLOAT64 Dx) {
return (f1 + f2) * Dx / 2.0;
} // Integral
/**
* 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.
* @param Buckets histogram buckets to count samples
* @param Cluster cluster whose samples are being analyzed
* @param Dim dimension of samples which is being analyzed
* @param ParamDesc description of the dimension
* @param Mean "mean" of the distribution
* @param StdDev "standard deviation" of the distribution
* @return None (the Buckets data structure is filled in)
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
void FillBuckets(BUCKETS *Buckets,
CLUSTER *Cluster,
uinT16 Dim,
PARAM_DESC *ParamDesc,
FLOAT32 Mean,
FLOAT32 StdDev) {
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
/**
* 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.
* @param ParamDesc used to identify circular dimensions
* @param x value to be normalized
* @param Mean mean of normal distribution
* @param StdDev standard deviation of normal distribution
* @return Bucket number into which x falls
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
uinT16 NormalBucket(PARAM_DESC *ParamDesc,
FLOAT32 x,
FLOAT32 Mean,
FLOAT32 StdDev) {
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
/**
* 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.
* @param ParamDesc used to identify circular dimensions
* @param x value to be normalized
* @param Mean center of range of uniform distribution
* @param StdDev 1/2 the range of the uniform distribution
* @return Bucket number into which x falls
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
uinT16 UniformBucket(PARAM_DESC *ParamDesc,
FLOAT32 x,
FLOAT32 Mean,
FLOAT32 StdDev) {
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
/**
* 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.
* @param Buckets histogram data to perform chi-square test on
* @return TRUE if samples match distribution, FALSE otherwise
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
BOOL8 DistributionOK(BUCKETS *Buckets) {
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
/**
* This routine frees the memory used by the statistics
* data structure.
* @param Statistics pointer to data structure to be freed
* @return None
* @note Exceptions: None
* @note History: 6/5/89, DSJ, Created.
*/
void FreeStatistics(STATISTICS *Statistics) {
free(Statistics->CoVariance);
free(Statistics->Min);
free(Statistics->Max);
free(Statistics);
} // FreeStatistics
/**
* This routine properly frees the memory used by a BUCKETS.
*
* @param buckets pointer to data structure to be freed
*/
void FreeBuckets(BUCKETS *buckets) {
Efree(buckets->Count);
Efree(buckets->ExpectedCount);
Efree(buckets);
} // FreeBuckets
/**
* This routine frees the memory consumed by the specified
* cluster and all of its subclusters. This is done by
* recursive calls to FreeCluster().
*
* @param Cluster pointer to cluster to be freed
*
* @return None
*
* @note Exceptions: None
* @note History: 6/6/89, DSJ, Created.
*/
void FreeCluster(CLUSTER *Cluster) {
if (Cluster != NULL) {
FreeCluster (Cluster->Left);
FreeCluster (Cluster->Right);
free(Cluster);
}
} // FreeCluster
/**
* 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.
* @param Distribution distribution being tested for
* @param HistogramBuckets number of buckets in chi-square test
* @return The number of degrees of freedom for a chi-square test
* @note Exceptions: none
* @note History: Thu Aug 3 14:04:18 1989, DSJ, Created.
*/
uinT16 DegreesOfFreedom(DISTRIBUTION Distribution, uinT16 HistogramBuckets) {
static uinT8 DegreeOffsets[] = { 3, 3, 1 };
uinT16 AdjustedNumBuckets;
AdjustedNumBuckets = HistogramBuckets - DegreeOffsets[(int) Distribution];
if (Odd (AdjustedNumBuckets))
AdjustedNumBuckets++;
return (AdjustedNumBuckets);
} // DegreesOfFreedom
/**
* 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.
* @param arg1 current histogram being tested for a match
* @param arg2 match key
* @return TRUE if arg1 matches arg2
* @note Exceptions: none
* @note History: Thu Aug 3 14:17:33 1989, DSJ, Created.
*/
int NumBucketsMatch(void *arg1, // BUCKETS *Histogram,
void *arg2) { // uinT16 *DesiredNumberOfBuckets)
BUCKETS *Histogram = (BUCKETS *) arg1;
uinT16 *DesiredNumberOfBuckets = (uinT16 *) arg2;
return (*DesiredNumberOfBuckets == Histogram->NumberOfBuckets);
} // NumBucketsMatch
/**
* 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
* @note Exceptions: none
* @note History: Thu Aug 3 14:23:58 1989, DSJ, Created.
*/
int ListEntryMatch(void *arg1, //ListNode
void *arg2) { //Key
return (arg1 == arg2);
} // ListEntryMatch
/**
* This routine multiplies each ExpectedCount histogram entry
* by NewSampleCount/OldSampleCount so that the histogram
* is now adjusted to the new sample count.
* @param Buckets histogram data structure to adjust
* @param NewSampleCount new sample count to adjust to
* @return none
* @note Exceptions: none
* @note History: Thu Aug 3 14:31:14 1989, DSJ, Created.
*/
void AdjustBuckets(BUCKETS *Buckets, uinT32 NewSampleCount) {
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
/**
* This routine sets the bucket counts in the specified histogram
* to zero.
* @param Buckets histogram data structure to init
* @return none
* @note Exceptions: none
* @note History: Thu Aug 3 14:31:14 1989, DSJ, Created.
*/
void InitBuckets(BUCKETS *Buckets) {
int i;
for (i = 0; i < Buckets->NumberOfBuckets; i++) {
Buckets->Count[i] = 0;
}
} // InitBuckets
/**
* 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.
*
* @param arg1 chi-squared struct being tested for a match
* @param arg2 chi-squared struct that is the search key
* @return TRUE if ChiStruct's Alpha matches SearchKey's Alpha
* @note Exceptions: none
* @note History: Thu Aug 3 14:17:33 1989, DSJ, Created.
*/
int AlphaMatch(void *arg1, //CHISTRUCT *ChiStruct,
void *arg2) { //CHISTRUCT *SearchKey)
CHISTRUCT *ChiStruct = (CHISTRUCT *) arg1;
CHISTRUCT *SearchKey = (CHISTRUCT *) arg2;
return (ChiStruct->Alpha == SearchKey->Alpha);
} // AlphaMatch
/**
* 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.
*
* @param DegreesOfFreedom degrees of freedom for new chi value
* @param Alpha confidence level for new chi value
* @return none
* @note Exceptions: none
* @note History: Fri Aug 4 11:04:59 1989, DSJ, Created.
*/
CHISTRUCT *NewChiStruct(uinT16 DegreesOfFreedom, FLOAT64 Alpha) {
CHISTRUCT *NewChiStruct;
NewChiStruct = (CHISTRUCT *) Emalloc (sizeof (CHISTRUCT));
NewChiStruct->DegreesOfFreedom = DegreesOfFreedom;
NewChiStruct->Alpha = Alpha;
return (NewChiStruct);
} // NewChiStruct
/**
* 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.
*
* @param Function function whose zero is to be found
* @param FunctionParams arbitrary data to pass to function
* @param InitialGuess point to start solution search at
* @param Accuracy maximum allowed error
* @return Solution of function ( x for which f(x) = 0 ).
* @note Exceptions: none
* @note History: Fri Aug 4 11:08:59 1989, DSJ, Created.
*/
FLOAT64
Solve (SOLVEFUNC Function,
void *FunctionParams, FLOAT64 InitialGuess, FLOAT64 Accuracy)
#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
/**
* 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.
* @param ChiParams contains degrees of freedom and alpha
* @param x value of chi-squared to evaluate
* @return Error between actual and desired area under the chi curve.
* @note Exceptions: none
* @note History: Fri Aug 4 12:48:41 1989, DSJ, Created.
*/
FLOAT64 ChiArea(CHISTRUCT *ChiParams, FLOAT64 x) {
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
/**
* 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.
*
* @param Clusterer data structure holding cluster tree
* @param Cluster cluster containing samples to be tested
* @param MaxIllegal max percentage of samples allowed to have
* more than 1 feature in the cluster
* @return TRUE if the cluster should be split, FALSE otherwise.
* @note Exceptions: none
* @note History: Wed Aug 30 11:13:05 1989, DSJ, Created.
* 2/22/90, DSJ, Added MaxIllegal control rather than always
* splitting illegal clusters.
*/
BOOL8
MultipleCharSamples (CLUSTERER * Clusterer,
CLUSTER * Cluster, FLOAT32 MaxIllegal)
#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) {
free(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<double> U(size, size, 0.0);
GENERIC_2D_ARRAY<double> U_inv(size, size, 0.0);
GENERIC_2D_ARRAY<double> 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;
}
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