ML implements logistic regression, which is a probabilistic classification technique. Logistic Regression is a binary classification algorithm which is closely related to Support Vector Machines (SVM).
Like SVM, Logistic Regression can be extended to work on multi-class classification problems like digit recognition (i.e. recognizing digitis like 0,1 2, 3,... from the given images).
This version of Logistic Regression supports both binary and multi-class classifications (for multi-class it creates a multiple 2-class classifiers).
In order to train the logistic regression classifier, Batch Gradient Descent and Mini-Batch Gradient Descent algorithms are used (see [BatchDesWiki]_).
Logistic Regression is a discriminative classifier (see [LogRegTomMitch]_ for more details). Logistic Regression is implemented as a C++ class in ``LogisticRegression``.
It is a positive real number. Optimization algorithms like Batch Gradient Descent and Mini-Batch Gradient Descent are supported in ``LogisticRegression``.
The number of iterations can be thought as number of steps taken and learning rate specifies if it is a long step or a short step. These two parameters define how fast we arrive at a possible solution.
In order to compensate for overfitting regularization is performed, which can be enabled by setting ``LogisticRegression::Params.regularized`` to a positive integer (greater than zero).
One can specify what kind of regularization has to be performed by setting ``LogisticRegression::Params.norm`` to ``LogisticRegression::REG_L1`` or ``LogisticRegression::REG_L2`` values.
``LogisticRegression`` provides a choice of 2 training methods with Batch Gradient Descent or the Mini-Batch Gradient Descent. To specify this, set ``LogisticRegression::Params.train_method`` to either ``LogisticRegression::BATCH`` or ``LogisticRegression::MINI_BATCH``.
If ``LogisticRegression::Params`` is set to ``LogisticRegression::MINI_BATCH``, the size of the mini batch has to be to a postive integer using ``LogisticRegression::Params.mini_batch_size``.
..[LogRegWiki] http://en.wikipedia.org/wiki/Logistic_regression. Wikipedia article about the Logistic Regression algorithm.
..[RenMalik2003] Learning a Classification Model for Segmentation. Proc. CVPR, Nice, France (2003).
..[LogRegTomMitch] http://www.cs.cmu.edu/~tom/NewChapters.html. "Generative and Discriminative Classifiers: Naive Bayes and Logistic Regression" in Machine Learning, Tom Mitchell.
Parameters of the Logistic Regression training algorithm. You can initialize the structure using a constructor or declaring the variable and initializing the the individual parameters.
The training parameters for Logistic Regression:
..ocv:member:: double alpha
The learning rate of the optimization algorithm. The higher the value, faster the rate and vice versa. If the value is too high, the learning algorithm may overshoot the optimal parameters and result in lower training accuracy. If the value is too low, the learning algorithm converges towards the optimal parameters very slowly. The value must a be a positive real number. You can experiment with different values with small increments as in 0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, ... and select the learning rate with less training error.
..ocv:member:: int num_iters
The number of iterations required for the learing algorithm (Gradient Descent or Mini Batch Gradient Descent). It has to be a positive integer. You can try different number of iterations like in 100, 1000, 2000, 3000, 5000, 10000, .. so on.
The kind of training method used to train the classifier. It should be set to either ``LogisticRegression::BATCH`` or ``LogisticRegression::MINI_BATCH``.
If the training method is set to LogisticRegression::MINI_BATCH, it has to be set to positive integer. It can range from 1 to number of training samples.
..ocv:function:: LogisticRegression::Params::Params(double learning_rate = 0.001, int iters = 1000, int method = LogisticRegression::BATCH, int normlization = LogisticRegression::REG_L2, int reg = 1, int batch_size = 1)
:param train_method:Specifies the kind of training method used. It should be set to either ``LogisticRegression::BATCH`` or ``LogisticRegression::MINI_BATCH``. If using ``LogisticRegression::MINI_BATCH``, set ``LogisticRegression::Params.mini_batch_size`` to a positive integer.
:param normalization:Specifies the kind of regularization to be applied. ``LogisticRegression::REG_L1`` or ``LogisticRegression::REG_L2`` (L1 norm or L2 norm). To use this, set ``LogisticRegression::Params.regularized`` to a integer greater than zero.
:param mini_batch_size:Specifies the number of training samples taken in each step of Mini-Batch Gradient Descent. Will only be used if using ``LogisticRegression::MINI_BATCH`` training algorithm. It has to take values less than the total number of training samples.
:param samples:The input data for the prediction algorithm. Matrix [m x n], where each row contains variables (features) of one object being classified. Should have data type ``CV_32F``.
