#include <map>
#include <iostream>
+/**
+ @defgroup ml Machine Learning
+ @{
+@defgroup ml_stat Statistical Models
+@defgroup ml_bayes Normal Bayes Classifier
+
+This simple classification model assumes that feature vectors from each class are normally
+distributed (though, not necessarily independently distributed). So, the whole data distribution
+function is assumed to be a Gaussian mixture, one component per class. Using the training data the
+algorithm estimates mean vectors and covariance matrices for every class, and then it uses them for
+prediction.
+
+@defgroup ml_knearest K-Nearest Neighbors
+
+The algorithm caches all training samples and predicts the response for a new sample by analyzing a
+certain number (**K**) of the nearest neighbors of the sample using voting, calculating weighted
+sum, and so on. The method is sometimes referred to as "learning by example" because for prediction
+it looks for the feature vector with a known response that is closest to the given vector.
+
+@defgroup ml_svm Support Vector Machines
+
+Originally, support vector machines (SVM) was a technique for building an optimal binary (2-class)
+classifier. Later the technique was extended to regression and clustering problems. SVM is a partial
+case of kernel-based methods. It maps feature vectors into a higher-dimensional space using a kernel
+function and builds an optimal linear discriminating function in this space or an optimal
+hyper-plane that fits into the training data. In case of SVM, the kernel is not defined explicitly.
+Instead, a distance between any 2 points in the hyper-space needs to be defined.
+
+The solution is optimal, which means that the margin between the separating hyper-plane and the
+nearest feature vectors from both classes (in case of 2-class classifier) is maximal. The feature
+vectors that are the closest to the hyper-plane are called *support vectors*, which means that the
+position of other vectors does not affect the hyper-plane (the decision function).
+
+SVM implementation in OpenCV is based on @cite LibSVM.
+
+Prediction with SVM
+-------------------
+
+StatModel::predict(samples, results, flags) should be used. Pass flags=StatModel::RAW\_OUTPUT to get
+the raw response from SVM (in the case of regression, 1-class or 2-class classification problem).
+
+@defgroup ml_decsiontrees Decision Trees
+
+The ML classes discussed in this section implement Classification and Regression Tree algorithms
+described in @cite Breiman84.
+
+The class cv::ml::DTrees represents a single decision tree or a collection of decision trees. It's
+also a base class for RTrees and Boost.
+
+A decision tree is a binary tree (tree where each non-leaf node has two child nodes). It can be used
+either for classification or for regression. For classification, each tree leaf is marked with a
+class label; multiple leaves may have the same label. For regression, a constant is also assigned to
+each tree leaf, so the approximation function is piecewise constant.
+
+Predicting with Decision Trees
+------------------------------
+
+To reach a leaf node and to obtain a response for the input feature vector, the prediction procedure
+starts with the root node. From each non-leaf node the procedure goes to the left (selects the left
+child node as the next observed node) or to the right based on the value of a certain variable whose
+index is stored in the observed node. The following variables are possible:
+
+- **Ordered variables.** The variable value is compared with a threshold that is also stored in
+ the node. If the value is less than the threshold, the procedure goes to the left. Otherwise, it
+ goes to the right. For example, if the weight is less than 1 kilogram, the procedure goes to the
+ left, else to the right.
+
+- **Categorical variables.** A discrete variable value is tested to see whether it belongs to a
+ certain subset of values (also stored in the node) from a limited set of values the variable
+ could take. If it does, the procedure goes to the left. Otherwise, it goes to the right. For
+ example, if the color is green or red, go to the left, else to the right.
+
+So, in each node, a pair of entities (variable\_index , `decision_rule (threshold/subset)` ) is
+used. This pair is called a *split* (split on the variable variable\_index ). Once a leaf node is
+reached, the value assigned to this node is used as the output of the prediction procedure.
+
+Sometimes, certain features of the input vector are missed (for example, in the darkness it is
+difficult to determine the object color), and the prediction procedure may get stuck in the certain
+node (in the mentioned example, if the node is split by color). To avoid such situations, decision
+trees use so-called *surrogate splits*. That is, in addition to the best "primary" split, every tree
+node may also be split to one or more other variables with nearly the same results.
+
+Training Decision Trees
+-----------------------
+
+The tree is built recursively, starting from the root node. All training data (feature vectors and
+responses) is used to split the root node. In each node the optimum decision rule (the best
+"primary" split) is found based on some criteria. In machine learning, gini "purity" criteria are
+used for classification, and sum of squared errors is used for regression. Then, if necessary, the
+surrogate splits are found. They resemble the results of the primary split on the training data. All
+the data is divided using the primary and the surrogate splits (like it is done in the prediction
+procedure) between the left and the right child node. Then, the procedure recursively splits both
+left and right nodes. At each node the recursive procedure may stop (that is, stop splitting the
+node further) in one of the following cases:
+
+- Depth of the constructed tree branch has reached the specified maximum value.
+- Number of training samples in the node is less than the specified threshold when it is not
+ statistically representative to split the node further.
+- All the samples in the node belong to the same class or, in case of regression, the variation is
+ too small.
+- The best found split does not give any noticeable improvement compared to a random choice.
+
+When the tree is built, it may be pruned using a cross-validation procedure, if necessary. That is,
+some branches of the tree that may lead to the model overfitting are cut off. Normally, this
+procedure is only applied to standalone decision trees. Usually tree ensembles build trees that are
+small enough and use their own protection schemes against overfitting.
+
+Variable Importance
+-------------------
+
+Besides the prediction that is an obvious use of decision trees, the tree can be also used for
+various data analyses. One of the key properties of the constructed decision tree algorithms is an
+ability to compute the importance (relative decisive power) of each variable. For example, in a spam
+filter that uses a set of words occurred in the message as a feature vector, the variable importance
+rating can be used to determine the most "spam-indicating" words and thus help keep the dictionary
+size reasonable.
+
+Importance of each variable is computed over all the splits on this variable in the tree, primary
+and surrogate ones. Thus, to compute variable importance correctly, the surrogate splits must be
+enabled in the training parameters, even if there is no missing data.
+
+@defgroup ml_boost Boosting
+
+A common machine learning task is supervised learning. In supervised learning, the goal is to learn
+the functional relationship \f$F: y = F(x)\f$ between the input \f$x\f$ and the output \f$y\f$ . Predicting the
+qualitative output is called *classification*, while predicting the quantitative output is called
+*regression*.
+
+Boosting is a powerful learning concept that provides a solution to the supervised classification
+learning task. It combines the performance of many "weak" classifiers to produce a powerful
+committee @cite HTF01. A weak classifier is only required to be better than chance, and thus can be
+very simple and computationally inexpensive. However, many of them smartly combine results to a
+strong classifier that often outperforms most "monolithic" strong classifiers such as SVMs and
+Neural Networks.
+
+Decision trees are the most popular weak classifiers used in boosting schemes. Often the simplest
+decision trees with only a single split node per tree (called stumps ) are sufficient.
+
+The boosted model is based on \f$N\f$ training examples \f${(x_i,y_i)}1N\f$ with \f$x_i \in{R^K}\f$ and
+\f$y_i \in{-1, +1}\f$ . \f$x_i\f$ is a \f$K\f$ -component vector. Each component encodes a feature relevant to
+the learning task at hand. The desired two-class output is encoded as -1 and +1.
+
+Different variants of boosting are known as Discrete Adaboost, Real AdaBoost, LogitBoost, and Gentle
+AdaBoost @cite FHT98. All of them are very similar in their overall structure. Therefore, this chapter
+focuses only on the standard two-class Discrete AdaBoost algorithm, outlined below. Initially the
+same weight is assigned to each sample (step 2). Then, a weak classifier \f$f_{m(x)}\f$ is trained on
+the weighted training data (step 3a). Its weighted training error and scaling factor \f$c_m\f$ is
+computed (step 3b). The weights are increased for training samples that have been misclassified
+(step 3c). All weights are then normalized, and the process of finding the next weak classifier
+continues for another \f$M\f$ -1 times. The final classifier \f$F(x)\f$ is the sign of the weighted sum over
+the individual weak classifiers (step 4).
+
+**Two-class Discrete AdaBoost Algorithm**
+
+- Set \f$N\f$ examples \f${(x_i,y_i)}1N\f$ with \f$x_i \in{R^K}, y_i \in{-1, +1}\f$ .
+
+- Assign weights as \f$w_i = 1/N, i = 1,...,N\f$ .
+
+- Repeat for \f$m = 1,2,...,M\f$ :
+
+ 3.1. Fit the classifier \f$f_m(x) \in{-1,1}\f$, using weights \f$w_i\f$ on the training data.
+
+ 3.2. Compute \f$err_m = E_w [1_{(y \neq f_m(x))}], c_m = log((1 - err_m)/err_m)\f$ .
+
+ 3.3. Set \f$w_i \Leftarrow w_i exp[c_m 1_{(y_i \neq f_m(x_i))}], i = 1,2,...,N,\f$ and renormalize
+ so that \f$\Sigma i w_i = 1\f$ .
+
+1. Classify new samples *x* using the formula: \f$\textrm{sign} (\Sigma m = 1M c_m f_m(x))\f$ .
+
+@note Similar to the classical boosting methods, the current implementation supports two-class
+classifiers only. For M \> 2 classes, there is the **AdaBoost.MH** algorithm (described in
+@cite FHT98) that reduces the problem to the two-class problem, yet with a much larger training set.
+To reduce computation time for boosted models without substantially losing accuracy, the influence
+trimming technique can be employed. As the training algorithm proceeds and the number of trees in
+the ensemble is increased, a larger number of the training samples are classified correctly and with
+increasing confidence, thereby those samples receive smaller weights on the subsequent iterations.
+Examples with a very low relative weight have a small impact on the weak classifier training. Thus,
+such examples may be excluded during the weak classifier training without having much effect on the
+induced classifier. This process is controlled with the weight\_trim\_rate parameter. Only examples
+with the summary fraction weight\_trim\_rate of the total weight mass are used in the weak
+classifier training. Note that the weights for **all** training examples are recomputed at each
+training iteration. Examples deleted at a particular iteration may be used again for learning some
+of the weak classifiers further @cite FHT98.
+
+Prediction with Boost
+---------------------
+StatModel::predict(samples, results, flags) should be used. Pass flags=StatModel::RAW\_OUTPUT to get
+the raw sum from Boost classifier.
+
+@defgroup ml_randomtrees Random Trees
+
+Random trees have been introduced by Leo Breiman and Adele Cutler:
+<http://www.stat.berkeley.edu/users/breiman/RandomForests/> . The algorithm can deal with both
+classification and regression problems. Random trees is a collection (ensemble) of tree predictors
+that is called *forest* further in this section (the term has been also introduced by L. Breiman).
+The classification works as follows: the random trees classifier takes the input feature vector,
+classifies it with every tree in the forest, and outputs the class label that received the majority
+of "votes". In case of a regression, the classifier response is the average of the responses over
+all the trees in the forest.
+
+All the trees are trained with the same parameters but on different training sets. These sets are
+generated from the original training set using the bootstrap procedure: for each training set, you
+randomly select the same number of vectors as in the original set ( =N ). The vectors are chosen
+with replacement. That is, some vectors will occur more than once and some will be absent. At each
+node of each trained tree, not all the variables are used to find the best split, but a random
+subset of them. With each node a new subset is generated. However, its size is fixed for all the
+nodes and all the trees. It is a training parameter set to \f$\sqrt{number\_of\_variables}\f$ by
+default. None of the built trees are pruned.
+
+In random trees there is no need for any accuracy estimation procedures, such as cross-validation or
+bootstrap, or a separate test set to get an estimate of the training error. The error is estimated
+internally during the training. When the training set for the current tree is drawn by sampling with
+replacement, some vectors are left out (so-called *oob (out-of-bag) data* ). The size of oob data is
+about N/3 . The classification error is estimated by using this oob-data as follows:
+
+- Get a prediction for each vector, which is oob relative to the i-th tree, using the very i-th
+ tree.
+
+- After all the trees have been trained, for each vector that has ever been oob, find the
+ class-*winner* for it (the class that has got the majority of votes in the trees where the
+ vector was oob) and compare it to the ground-truth response.
+
+- Compute the classification error estimate as a ratio of the number of misclassified oob vectors
+ to all the vectors in the original data. In case of regression, the oob-error is computed as the
+ squared error for oob vectors difference divided by the total number of vectors.
+
+For the random trees usage example, please, see letter\_recog.cpp sample in OpenCV distribution.
+
+**References:**
+
+- *Machine Learning*, Wald I, July 2002.
+<http://stat-www.berkeley.edu/users/breiman/wald2002-1.pdf>
+- *Looking Inside the Black Box*, Wald II, July 2002.
+<http://stat-www.berkeley.edu/users/breiman/wald2002-2.pdf>
+- *Software for the Masses*, Wald III, July 2002.
+<http://stat-www.berkeley.edu/users/breiman/wald2002-3.pdf>
+- And other articles from the web site
+<http://www.stat.berkeley.edu/users/breiman/RandomForests/cc_home.htm>
+
+@defgroup ml_em Expectation Maximization
+
+The Expectation Maximization(EM) algorithm estimates the parameters of the multivariate probability
+density function in the form of a Gaussian mixture distribution with a specified number of mixtures.
+
+Consider the set of the N feature vectors { \f$x_1, x_2,...,x_{N}\f$ } from a d-dimensional Euclidean
+space drawn from a Gaussian mixture:
+
+\f[p(x;a_k,S_k, \pi _k) = \sum _{k=1}^{m} \pi _kp_k(x), \quad \pi _k \geq 0, \quad \sum _{k=1}^{m} \pi _k=1,\f]
+
+\f[p_k(x)= \varphi (x;a_k,S_k)= \frac{1}{(2\pi)^{d/2}\mid{S_k}\mid^{1/2}} exp \left \{ - \frac{1}{2} (x-a_k)^TS_k^{-1}(x-a_k) \right \} ,\f]
+
+where \f$m\f$ is the number of mixtures, \f$p_k\f$ is the normal distribution density with the mean \f$a_k\f$
+and covariance matrix \f$S_k\f$, \f$\pi_k\f$ is the weight of the k-th mixture. Given the number of mixtures
+\f$M\f$ and the samples \f$x_i\f$, \f$i=1..N\f$ the algorithm finds the maximum-likelihood estimates (MLE) of
+all the mixture parameters, that is, \f$a_k\f$, \f$S_k\f$ and \f$\pi_k\f$ :
+
+\f[L(x, \theta )=logp(x, \theta )= \sum _{i=1}^{N}log \left ( \sum _{k=1}^{m} \pi _kp_k(x) \right ) \to \max _{ \theta \in \Theta },\f]
+
+\f[\Theta = \left \{ (a_k,S_k, \pi _k): a_k \in \mathbbm{R} ^d,S_k=S_k^T>0,S_k \in \mathbbm{R} ^{d \times d}, \pi _k \geq 0, \sum _{k=1}^{m} \pi _k=1 \right \} .\f]
+
+The EM algorithm is an iterative procedure. Each iteration includes two steps. At the first step
+(Expectation step or E-step), you find a probability \f$p_{i,k}\f$ (denoted \f$\alpha_{i,k}\f$ in the
+formula below) of sample i to belong to mixture k using the currently available mixture parameter
+estimates:
+
+\f[\alpha _{ki} = \frac{\pi_k\varphi(x;a_k,S_k)}{\sum\limits_{j=1}^{m}\pi_j\varphi(x;a_j,S_j)} .\f]
+
+At the second step (Maximization step or M-step), the mixture parameter estimates are refined using
+the computed probabilities:
+
+\f[\pi _k= \frac{1}{N} \sum _{i=1}^{N} \alpha _{ki}, \quad a_k= \frac{\sum\limits_{i=1}^{N}\alpha_{ki}x_i}{\sum\limits_{i=1}^{N}\alpha_{ki}} , \quad S_k= \frac{\sum\limits_{i=1}^{N}\alpha_{ki}(x_i-a_k)(x_i-a_k)^T}{\sum\limits_{i=1}^{N}\alpha_{ki}}\f]
+
+Alternatively, the algorithm may start with the M-step when the initial values for \f$p_{i,k}\f$ can be
+provided. Another alternative when \f$p_{i,k}\f$ are unknown is to use a simpler clustering algorithm to
+pre-cluster the input samples and thus obtain initial \f$p_{i,k}\f$ . Often (including machine learning)
+the k-means algorithm is used for that purpose.
+
+One of the main problems of the EM algorithm is a large number of parameters to estimate. The
+majority of the parameters reside in covariance matrices, which are \f$d \times d\f$ elements each where
+\f$d\f$ is the feature space dimensionality. However, in many practical problems, the covariance
+matrices are close to diagonal or even to \f$\mu_k*I\f$ , where \f$I\f$ is an identity matrix and \f$\mu_k\f$ is
+a mixture-dependent "scale" parameter. So, a robust computation scheme could start with harder
+constraints on the covariance matrices and then use the estimated parameters as an input for a less
+constrained optimization problem (often a diagonal covariance matrix is already a good enough
+approximation).
+
+References:
+- Bilmes98 J. A. Bilmes. *A Gentle Tutorial of the EM Algorithm and its Application to Parameter
+ Estimation for Gaussian Mixture and Hidden Markov Models*. Technical Report TR-97-021,
+ International Computer Science Institute and Computer Science Division, University of California
+ at Berkeley, April 1998.
+
+@defgroup ml_neural Neural Networks
+
+ML implements feed-forward artificial neural networks or, more particularly, multi-layer perceptrons
+(MLP), the most commonly used type of neural networks. MLP consists of the input layer, output
+layer, and one or more hidden layers. Each layer of MLP includes one or more neurons directionally
+linked with the neurons from the previous and the next layer. The example below represents a 3-layer
+perceptron with three inputs, two outputs, and the hidden layer including five neurons:
+
+
+
+All the neurons in MLP are similar. Each of them has several input links (it takes the output values
+from several neurons in the previous layer as input) and several output links (it passes the
+response to several neurons in the next layer). The values retrieved from the previous layer are
+summed up with certain weights, individual for each neuron, plus the bias term. The sum is
+transformed using the activation function \f$f\f$ that may be also different for different neurons.
+
+
+
+In other words, given the outputs \f$x_j\f$ of the layer \f$n\f$ , the outputs \f$y_i\f$ of the layer \f$n+1\f$ are
+computed as:
+
+\f[u_i = \sum _j (w^{n+1}_{i,j}*x_j) + w^{n+1}_{i,bias}\f]
+
+\f[y_i = f(u_i)\f]
+
+Different activation functions may be used. ML implements three standard functions:
+
+- Identity function ( ANN\_MLP::IDENTITY ): \f$f(x)=x\f$
+
+- Symmetrical sigmoid ( ANN\_MLP::SIGMOID\_SYM ): \f$f(x)=\beta*(1-e^{-\alpha x})/(1+e^{-\alpha x}\f$
+ ), which is the default choice for MLP. The standard sigmoid with \f$\beta =1, \alpha =1\f$ is shown
+ below:
+
+ 
+
+- Gaussian function ( ANN\_MLP::GAUSSIAN ): \f$f(x)=\beta e^{-\alpha x*x}\f$ , which is not completely
+ supported at the moment.
+
+In ML, all the neurons have the same activation functions, with the same free parameters (
+\f$\alpha, \beta\f$ ) that are specified by user and are not altered by the training algorithms.
+
+So, the whole trained network works as follows:
+
+1. Take the feature vector as input. The vector size is equal to the size of the input layer.
+2. Pass values as input to the first hidden layer.
+3. Compute outputs of the hidden layer using the weights and the activation functions.
+4. Pass outputs further downstream until you compute the output layer.
+
+So, to compute the network, you need to know all the weights \f$w^{n+1)}_{i,j}\f$ . The weights are
+computed by the training algorithm. The algorithm takes a training set, multiple input vectors with
+the corresponding output vectors, and iteratively adjusts the weights to enable the network to give
+the desired response to the provided input vectors.
+
+The larger the network size (the number of hidden layers and their sizes) is, the more the potential
+network flexibility is. The error on the training set could be made arbitrarily small. But at the
+same time the learned network also "learns" the noise present in the training set, so the error on
+the test set usually starts increasing after the network size reaches a limit. Besides, the larger
+networks are trained much longer than the smaller ones, so it is reasonable to pre-process the data,
+using PCA::operator() or similar technique, and train a smaller network on only essential features.
+
+Another MLP feature is an inability to handle categorical data as is. However, there is a
+workaround. If a certain feature in the input or output (in case of n -class classifier for \f$n>2\f$ )
+layer is categorical and can take \f$M>2\f$ different values, it makes sense to represent it as a binary
+tuple of M elements, where the i -th element is 1 if and only if the feature is equal to the i -th
+value out of M possible. It increases the size of the input/output layer but speeds up the training
+algorithm convergence and at the same time enables "fuzzy" values of such variables, that is, a
+tuple of probabilities instead of a fixed value.
+
+ML implements two algorithms for training MLP's. The first algorithm is a classical random
+sequential back-propagation algorithm. The second (default) one is a batch RPROP algorithm.
+
+@defgroup ml_lr Logistic Regression
+
+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 @cite BatchDesWiki).
+Logistic Regression is a discriminative classifier (see @cite LogRegTomMitch for more details).
+Logistic Regression is implemented as a C++ class in LogisticRegression.
+
+In Logistic Regression, we try to optimize the training paramater \f$\theta\f$ such that the hypothesis
+\f$0 \leq h_\theta(x) \leq 1\f$ is acheived. We have \f$h_\theta(x) = g(h_\theta(x))\f$ and
+\f$g(z) = \frac{1}{1+e^{-z}}\f$ as the logistic or sigmoid function. The term "Logistic" in Logistic
+Regression refers to this function. For given data of a binary classification problem of classes 0
+and 1, one can determine that the given data instance belongs to class 1 if \f$h_\theta(x) \geq 0.5\f$
+or class 0 if \f$h_\theta(x) < 0.5\f$ .
+
+In Logistic Regression, choosing the right parameters is of utmost importance for reducing the
+training error and ensuring high training accuracy. LogisticRegression::Params is the structure that
+defines parameters that are required to train a Logistic Regression classifier. The learning rate is
+determined by LogisticRegression::Params.alpha. It determines how faster we approach the solution.
+It is a positive real number. Optimization algorithms like Batch Gradient Descent and Mini-Batch
+Gradient Descent are supported in LogisticRegression. It is important that we mention the number of
+iterations these optimization algorithms have to run. The number of iterations are mentioned by
+LogisticRegression::Params.num\_iters. 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.
+
+A sample set of training parameters for the Logistic Regression classifier can be initialized as
+follows:
+@code
+ LogisticRegression::Params params;
+ params.alpha = 0.5;
+ params.num_iters = 10000;
+ params.norm = LogisticRegression::REG_L2;
+ params.regularized = 1;
+ params.train_method = LogisticRegression::MINI_BATCH;
+ params.mini_batch_size = 10;
+@endcode
+
+@defgroup ml_data Training Data
+
+In machine learning algorithms there is notion of training data. Training data includes several
+components:
+
+- A set of training samples. Each training sample is a vector of values (in Computer Vision it's
+ sometimes referred to as feature vector). Usually all the vectors have the same number of
+ components (features); OpenCV ml module assumes that. Each feature can be ordered (i.e. its
+ values are floating-point numbers that can be compared with each other and strictly ordered,
+ i.e. sorted) or categorical (i.e. its value belongs to a fixed set of values that can be
+ integers, strings etc.).
+- Optional set of responses corresponding to the samples. Training data with no responses is used
+ in unsupervised learning algorithms that learn structure of the supplied data based on distances
+ between different samples. Training data with responses is used in supervised learning
+ algorithms, which learn the function mapping samples to responses. Usually the responses are
+ scalar values, ordered (when we deal with regression problem) or categorical (when we deal with
+ classification problem; in this case the responses are often called "labels"). Some algorithms,
+ most noticeably Neural networks, can handle not only scalar, but also multi-dimensional or
+ vector responses.
+- Another optional component is the mask of missing measurements. Most algorithms require all the
+ components in all the training samples be valid, but some other algorithms, such as decision
+ tress, can handle the cases of missing measurements.
+- In the case of classification problem user may want to give different weights to different
+ classes. This is useful, for example, when
+ - user wants to shift prediction accuracy towards lower false-alarm rate or higher hit-rate.
+ - user wants to compensate for significantly different amounts of training samples from
+ different classes.
+- In addition to that, each training sample may be given a weight, if user wants the algorithm to
+ pay special attention to certain training samples and adjust the training model accordingly.
+- Also, user may wish not to use the whole training data at once, but rather use parts of it, e.g.
+ to do parameter optimization via cross-validation procedure.
+
+As you can see, training data can have rather complex structure; besides, it may be very big and/or
+not entirely available, so there is need to make abstraction for this concept. In OpenCV ml there is
+cv::ml::TrainData class for that.
+
+ @}
+ */
+
namespace cv
{
namespace ml
{
+//! @addtogroup ml
+//! @{
+
/* Variable type */
enum
{
COL_SAMPLE = 1
};
+//! @addtogroup ml_svm
+//! @{
+
+/** @brief The structure represents the logarithmic grid range of statmodel parameters.
+
+It is used for optimizing statmodel accuracy by varying model parameters, the accuracy estimate
+being computed by cross-validation.
+- member double ParamGrid::minVal
+Minimum value of the statmodel parameter.
+- member double ParamGrid::maxVal
+Maximum value of the statmodel parameter.
+- member double ParamGrid::logStep
+Logarithmic step for iterating the statmodel parameter.
+The grid determines the following iteration sequence of the statmodel parameter values:
+
+\f[(minVal, minVal*step, minVal*{step}^2, \dots, minVal*{logStep}^n),\f]
+
+where \f$n\f$ is the maximal index satisfying
+
+\f[\texttt{minVal} * \texttt{logStep} ^n < \texttt{maxVal}\f]
+
+The grid is logarithmic, so logStep must always be greater then 1.
+ */
class CV_EXPORTS_W_MAP ParamGrid
{
public:
+ /** @brief The constructors.
+
+ The full constructor initializes corresponding members. The default constructor creates a dummy
+ grid:
+ @code
+ ParamGrid::ParamGrid()
+ {
+ minVal = maxVal = 0;
+ logStep = 1;
+ }
+ @endcode
+ */
ParamGrid();
ParamGrid(double _minVal, double _maxVal, double _logStep);
CV_PROP_RW double logStep;
};
+//! @} ml_svm
+
+//! @addtogroup ml_data
+//! @{
+
+/** @brief Class encapsulating training data.
+
+Please note that the class only specifies the interface of training data, but not implementation.
+All the statistical model classes in ml take Ptr\<TrainData\>. In other words, you can create your
+own class derived from TrainData and supply smart pointer to the instance of this class into
+StatModel::train.
+ */
class CV_EXPORTS TrainData
{
public:
virtual void getSample(InputArray varIdx, int sidx, float* buf) const = 0;
virtual Mat getSamples() const = 0;
virtual Mat getMissing() const = 0;
+
+ /** @brief Returns matrix of train samples
+
+ @param layout The requested layout. If it's different from the initial one, the matrix is
+ transposed.
+ @param compressSamples if true, the function returns only the training samples (specified by
+ sampleIdx)
+ @param compressVars if true, the function returns the shorter training samples, containing only
+ the active variables.
+
+ In current implementation the function tries to avoid physical data copying and returns the matrix
+ stored inside TrainData (unless the transposition or compression is needed).
+ */
virtual Mat getTrainSamples(int layout=ROW_SAMPLE,
bool compressSamples=true,
bool compressVars=true) const = 0;
+
+ /** @brief Returns the vector of responses
+
+ The function returns ordered or the original categorical responses. Usually it's used in regression
+ algorithms.
+ */
virtual Mat getTrainResponses() const = 0;
+
+ /** @brief Returns the vector of normalized categorical responses
+
+ The function returns vector of responses. Each response is integer from 0 to \<number of
+ classes\>-1. The actual label value can be retrieved then from the class label vector, see
+ TrainData::getClassLabels.
+ */
virtual Mat getTrainNormCatResponses() const = 0;
virtual Mat getTestResponses() const = 0;
virtual Mat getTestNormCatResponses() const = 0;
virtual Mat getDefaultSubstValues() const = 0;
virtual int getCatCount(int vi) const = 0;
+
+ /** @brief Returns the vector of class labels
+
+ The function returns vector of unique labels occurred in the responses.
+ */
virtual Mat getClassLabels() const = 0;
virtual Mat getCatOfs() const = 0;
virtual Mat getCatMap() const = 0;
virtual void setTrainTestSplit(int count, bool shuffle=true) = 0;
+
+ /** @brief Splits the training data into the training and test parts
+
+ The function selects a subset of specified relative size and then returns it as the training set. If
+ the function is not called, all the data is used for training. Please, note that for each of
+ TrainData::getTrain\* there is corresponding TrainData::getTest\*, so that the test subset can be
+ retrieved and processed as well.
+ */
virtual void setTrainTestSplitRatio(double ratio, bool shuffle=true) = 0;
virtual void shuffleTrainTest() = 0;
static Mat getSubVector(const Mat& vec, const Mat& idx);
+
+ /** @brief Reads the dataset from a .csv file and returns the ready-to-use training data.
+
+ @param filename The input file name
+ @param headerLineCount The number of lines in the beginning to skip; besides the header, the
+ function also skips empty lines and lines staring with '\#'
+ @param responseStartIdx Index of the first output variable. If -1, the function considers the last
+ variable as the response
+ @param responseEndIdx Index of the last output variable + 1. If -1, then there is single response
+ variable at responseStartIdx.
+ @param varTypeSpec The optional text string that specifies the variables' types. It has the format ord[n1-n2,n3,n4-n5,...]cat[n6,n7-n8,...]. That is, variables from n1 to n2 (inclusive range), n3, n4 to n5 ... are considered ordered and n6, n7 to n8 ... are considered as categorical. The range [n1..n2] + [n3] + [n4..n5] + ... + [n6] + [n7..n8] should cover all the variables. If varTypeSpec is not specified, then algorithm uses the following rules:
+ # all input variables are considered ordered by default. If some column contains has
+ non-numerical values, e.g. 'apple', 'pear', 'apple', 'apple', 'mango', the corresponding
+ variable is considered categorical.
+ # if there are several output variables, they are all considered as ordered. Error is
+ reported when non-numerical values are used.
+ # if there is a single output variable, then if its values are non-numerical or are all
+ integers, then it's considered categorical. Otherwise, it's considered ordered.
+ @param delimiter The character used to separate values in each line.
+ @param missch The character used to specify missing measurements. It should not be a digit.
+ Although it's a non-numerical value, it surely does not affect the decision of whether the
+ variable ordered or categorical.
+ */
static Ptr<TrainData> loadFromCSV(const String& filename,
int headerLineCount,
int responseStartIdx=-1,
const String& varTypeSpec=String(),
char delimiter=',',
char missch='?');
+ /** @brief Creates training data from in-memory arrays.
+
+ @param samples matrix of samples. It should have CV\_32F type.
+ @param layout it's either ROW\_SAMPLE, which means that each training sample is a row of samples,
+ or COL\_SAMPLE, which means that each training sample occupies a column of samples.
+ @param responses matrix of responses. If the responses are scalar, they should be stored as a
+ single row or as a single column. The matrix should have type CV\_32F or CV\_32S (in the former
+ case the responses are considered as ordered by default; in the latter case - as categorical)
+ @param varIdx vector specifying which variables to use for training. It can be an integer vector
+ (CV\_32S) containing 0-based variable indices or byte vector (CV\_8U) containing a mask of active
+ variables.
+ @param sampleIdx vector specifying which samples to use for training. It can be an integer vector
+ (CV\_32S) containing 0-based sample indices or byte vector (CV\_8U) containing a mask of training
+ samples.
+ @param sampleWeights optional vector with weights for each sample. It should have CV\_32F type.
+ @param varType optional vector of type CV\_8U and size \<number\_of\_variables\_in\_samples\> +
+ \<number\_of\_variables\_in\_responses\>, containing types of each input and output variable. The
+ ordered variables are denoted by value VAR\_ORDERED, and categorical - by VAR\_CATEGORICAL.
+ */
static Ptr<TrainData> create(InputArray samples, int layout, InputArray responses,
InputArray varIdx=noArray(), InputArray sampleIdx=noArray(),
InputArray sampleWeights=noArray(), InputArray varType=noArray());
};
+//! @} ml_data
+//! @addtogroup ml_stat
+//! @{
+
+/** @brief Base class for statistical models in OpenCV ML.
+ */
class CV_EXPORTS_W StatModel : public Algorithm
{
public:
enum { UPDATE_MODEL = 1, RAW_OUTPUT=1, COMPRESSED_INPUT=2, PREPROCESSED_INPUT=4 };
virtual void clear();
+ /** @brief Returns the number of variables in training samples
+
+ The method must be overwritten in the derived classes.
+ */
virtual int getVarCount() const = 0;
+ /** @brief Returns true if the model is trained
+
+ The method must be overwritten in the derived classes.
+ */
virtual bool isTrained() const = 0;
+ /** @brief Returns true if the model is classifier
+
+ The method must be overwritten in the derived classes.
+ */
virtual bool isClassifier() const = 0;
+ /** @brief Trains the statistical model
+
+ @param trainData training data that can be loaded from file using TrainData::loadFromCSV or
+ created with TrainData::create.
+ @param flags optional flags, depending on the model. Some of the models can be updated with the
+ new training samples, not completely overwritten (such as NormalBayesClassifier or ANN\_MLP).
+
+ There are 2 instance methods and 2 static (class) template methods. The first two train the already
+ created model (the very first method must be overwritten in the derived classes). And the latter two
+ variants are convenience methods that construct empty model and then call its train method.
+ */
virtual bool train( const Ptr<TrainData>& trainData, int flags=0 );
+ /** @overload
+ @param samples training samples
+ @param layout ROW\_SAMPLE (training samples are the matrix rows) or COL\_SAMPLE (training samples
+ are the matrix columns)
+ @param responses vector of responses associated with the training samples.
+ */
virtual bool train( InputArray samples, int layout, InputArray responses );
+
+ /** @brief Computes error on the training or test dataset
+
+ @param data the training data
+ @param test if true, the error is computed over the test subset of the data, otherwise it's
+ computed over the training subset of the data. Please note that if you loaded a completely
+ different dataset to evaluate already trained classifier, you will probably want not to set the
+ test subset at all with TrainData::setTrainTestSplitRatio and specify test=false, so that the
+ error is computed for the whole new set. Yes, this sounds a bit confusing.
+ @param resp the optional output responses.
+
+ The method uses StatModel::predict to compute the error. For regression models the error is computed
+ as RMS, for classifiers - as a percent of missclassified samples (0%-100%).
+ */
virtual float calcError( const Ptr<TrainData>& data, bool test, OutputArray resp ) const;
+
+ /** @brief Predicts response(s) for the provided sample(s)
+
+ @param samples The input samples, floating-point matrix
+ @param results The optional output matrix of results.
+ @param flags The optional flags, model-dependent. Some models, such as Boost, SVM recognize
+ StatModel::RAW\_OUTPUT flag, which makes the method return the raw results (the sum), not the
+ class label.
+ */
virtual float predict( InputArray samples, OutputArray results=noArray(), int flags=0 ) const = 0;
+ /** @brief Loads model from the file
+
+ This is static template method of StatModel. It's usage is following (in the case of SVM): :
+
+ Ptr<SVM> svm = StatModel::load<SVM>("my_svm_model.xml");
+
+ In order to make this method work, the derived class must overwrite
+ Algorithm::read(const FileNode& fn).
+ */
template<typename _Tp> static Ptr<_Tp> load(const String& filename)
{
FileStorage fs(filename, FileStorage::READ);
return !model.empty() && model->train(TrainData::create(samples, layout, responses), flags) ? model : Ptr<_Tp>();
}
+ /** @brief Saves the model to a file.
+
+ In order to make this method work, the derived class must overwrite
+ Algorithm::write(FileStorage& fs).
+ */
virtual void save(const String& filename) const;
virtual String getDefaultModelName() const = 0;
};
+//! @} ml_stat
+
/****************************************************************************************\
* Normal Bayes Classifier *
\****************************************************************************************/
-/* The structure, representing the grid range of statmodel parameters.
- It is used for optimizing statmodel accuracy by varying model parameters,
- the accuracy estimate being computed by cross-validation.
- The grid is logarithmic, so <step> must be greater then 1. */
+//! @addtogroup ml_bayes
+//! @{
+/** @brief Bayes classifier for normally distributed data.
+ */
class CV_EXPORTS_W NormalBayesClassifier : public StatModel
{
public:
public:
Params();
};
+ /** @brief Predicts the response for sample(s).
+
+ The method estimates the most probable classes for input vectors. Input vectors (one or more) are
+ stored as rows of the matrix inputs. In case of multiple input vectors, there should be one output
+ vector outputs. The predicted class for a single input vector is returned by the method. The vector
+ outputProbs contains the output probabilities corresponding to each element of result.
+ */
virtual float predictProb( InputArray inputs, OutputArray outputs,
OutputArray outputProbs, int flags=0 ) const = 0;
virtual void setParams(const Params& params) = 0;
virtual Params getParams() const = 0;
+ /** @brief Creates empty model
+
+ @param params The model parameters. There is none so far, the structure is used as a placeholder
+ for possible extensions.
+
+ Use StatModel::train to train the model,
+ StatModel::train\<NormalBayesClassifier\>(traindata, params) to create and train the model,
+ StatModel::load\<NormalBayesClassifier\>(filename) to load the pre-trained model.
+ */
static Ptr<NormalBayesClassifier> create(const Params& params=Params());
};
+//! @} ml_bayes
+
/****************************************************************************************\
* K-Nearest Neighbour Classifier *
\****************************************************************************************/
-// k Nearest Neighbors
+//! @addtogroup ml_knearest
+//! @{
+
+/** @brief The class implements K-Nearest Neighbors model as described in the beginning of this section.
+
+@note
+ - (Python) An example of digit recognition using KNearest can be found at
+ opencv\_source/samples/python2/digits.py
+ - (Python) An example of grid search digit recognition using KNearest can be found at
+ opencv\_source/samples/python2/digits\_adjust.py
+ - (Python) An example of video digit recognition using KNearest can be found at
+ opencv\_source/samples/python2/digits\_video.py
+ */
class CV_EXPORTS_W KNearest : public StatModel
{
public:
};
virtual void setParams(const Params& p) = 0;
virtual Params getParams() const = 0;
+
+ /** @brief Finds the neighbors and predicts responses for input vectors.
+
+ @param samples Input samples stored by rows. It is a single-precision floating-point matrix of
+ \<number\_of\_samples\> \* k size.
+ @param k Number of used nearest neighbors. Should be greater than 1.
+ @param results Vector with results of prediction (regression or classification) for each input
+ sample. It is a single-precision floating-point vector with \<number\_of\_samples\> elements.
+ @param neighborResponses Optional output values for corresponding neighbors. It is a
+ single-precision floating-point matrix of \<number\_of\_samples\> \* k size.
+ @param dist Optional output distances from the input vectors to the corresponding neighbors. It is
+ a single-precision floating-point matrix of \<number\_of\_samples\> \* k size.
+
+ For each input vector (a row of the matrix samples), the method finds the k nearest neighbors. In
+ case of regression, the predicted result is a mean value of the particular vector's neighbor
+ responses. In case of classification, the class is determined by voting.
+
+ For each input vector, the neighbors are sorted by their distances to the vector.
+
+ In case of C++ interface you can use output pointers to empty matrices and the function will
+ allocate memory itself.
+
+ If only a single input vector is passed, all output matrices are optional and the predicted value is
+ returned by the method.
+
+ The function is parallelized with the TBB library.
+ */
virtual float findNearest( InputArray samples, int k,
OutputArray results,
OutputArray neighborResponses=noArray(),
enum { BRUTE_FORCE=1, KDTREE=2 };
+ /** @brief Creates the empty model
+
+ @param params The model parameters: default number of neighbors to use in predict method (in
+ KNearest::findNearest this number must be passed explicitly) and the flag on whether
+ classification or regression model should be trained.
+
+ The static method creates empty KNearest classifier. It should be then trained using train method
+ (see StatModel::train). Alternatively, you can load boost model from file using
+ StatModel::load\<KNearest\>(filename).
+ */
static Ptr<KNearest> create(const Params& params=Params());
};
+//! @} ml_knearest
+
/****************************************************************************************\
* Support Vector Machines *
\****************************************************************************************/
-// SVM model
+//! @addtogroup ml_svm
+//! @{
+
+/** @brief Support Vector Machines.
+
+@note
+ - (Python) An example of digit recognition using SVM can be found at
+ opencv\_source/samples/python2/digits.py
+ - (Python) An example of grid search digit recognition using SVM can be found at
+ opencv\_source/samples/python2/digits\_adjust.py
+ - (Python) An example of video digit recognition using SVM can be found at
+ opencv\_source/samples/python2/digits\_video.py
+ */
class CV_EXPORTS_W SVM : public StatModel
{
public:
+ /** @brief SVM training parameters.
+
+ The structure must be initialized and passed to the training method of SVM.
+ */
class CV_EXPORTS_W_MAP Params
{
public:
Params();
+ /** @brief The constructors
+
+ @param svm_type Type of a SVM formulation. Possible values are:
+ - **SVM::C\_SVC** C-Support Vector Classification. n-class classification (n \f$\geq\f$ 2), allows
+ imperfect separation of classes with penalty multiplier C for outliers.
+ - **SVM::NU\_SVC** \f$\nu\f$-Support Vector Classification. n-class classification with possible
+ imperfect separation. Parameter \f$\nu\f$ (in the range 0..1, the larger the value, the smoother
+ the decision boundary) is used instead of C.
+ - **SVM::ONE\_CLASS** Distribution Estimation (One-class SVM). All the training data are from
+ the same class, SVM builds a boundary that separates the class from the rest of the feature
+ space.
+ - **SVM::EPS\_SVR** \f$\epsilon\f$-Support Vector Regression. The distance between feature vectors
+ from the training set and the fitting hyper-plane must be less than p. For outliers the
+ penalty multiplier C is used.
+ - **SVM::NU\_SVR** \f$\nu\f$-Support Vector Regression. \f$\nu\f$ is used instead of p.
+ See @cite LibSVM for details.
+ @param kernel_type Type of a SVM kernel. Possible values are:
+ - **SVM::LINEAR** Linear kernel. No mapping is done, linear discrimination (or regression) is
+ done in the original feature space. It is the fastest option. \f$K(x_i, x_j) = x_i^T x_j\f$.
+ - **SVM::POLY** Polynomial kernel:
+ \f$K(x_i, x_j) = (\gamma x_i^T x_j + coef0)^{degree}, \gamma > 0\f$.
+ - **SVM::RBF** Radial basis function (RBF), a good choice in most cases.
+ \f$K(x_i, x_j) = e^{-\gamma ||x_i - x_j||^2}, \gamma > 0\f$.
+ - **SVM::SIGMOID** Sigmoid kernel: \f$K(x_i, x_j) = \tanh(\gamma x_i^T x_j + coef0)\f$.
+ - **SVM::CHI2** Exponential Chi2 kernel, similar to the RBF kernel:
+ \f$K(x_i, x_j) = e^{-\gamma \chi^2(x_i,x_j)}, \chi^2(x_i,x_j) = (x_i-x_j)^2/(x_i+x_j), \gamma > 0\f$.
+ - **SVM::INTER** Histogram intersection kernel. A fast kernel. \f$K(x_i, x_j) = min(x_i,x_j)\f$.
+ @param degree Parameter degree of a kernel function (POLY).
+ @param gamma Parameter \f$\gamma\f$ of a kernel function (POLY / RBF / SIGMOID / CHI2).
+ @param coef0 Parameter coef0 of a kernel function (POLY / SIGMOID).
+ @param Cvalue Parameter C of a SVM optimization problem (C\_SVC / EPS\_SVR / NU\_SVR).
+ @param nu Parameter \f$\nu\f$ of a SVM optimization problem (NU\_SVC / ONE\_CLASS / NU\_SVR).
+ @param p Parameter \f$\epsilon\f$ of a SVM optimization problem (EPS\_SVR).
+ @param classWeights Optional weights in the C\_SVC problem , assigned to particular classes. They
+ are multiplied by C so the parameter C of class \#i becomes classWeights(i) \* C. Thus these
+ weights affect the misclassification penalty for different classes. The larger weight, the larger
+ penalty on misclassification of data from the corresponding class.
+ @param termCrit Termination criteria of the iterative SVM training procedure which solves a
+ partial case of constrained quadratic optimization problem. You can specify tolerance and/or the
+ maximum number of iterations.
+
+ The default constructor initialize the structure with following values:
+ @code
+ SVMParams::SVMParams() :
+ svmType(SVM::C_SVC), kernelType(SVM::RBF), degree(0),
+ gamma(1), coef0(0), C(1), nu(0), p(0), classWeights(0)
+ {
+ termCrit = TermCriteria( TermCriteria::MAX_ITER+TermCriteria::EPS, 1000, FLT_EPSILON );
+ }
+ @endcode
+ A comparison of different kernels on the following 2D test case with four classes. Four C\_SVC SVMs
+ have been trained (one against rest) with auto\_train. Evaluation on three different kernels (CHI2,
+ INTER, RBF). The color depicts the class with max score. Bright means max-score \> 0, dark means
+ max-score \< 0.
+
+ 
+ */
Params( int svm_type, int kernel_type,
double degree, double gamma, double coef0,
double Cvalue, double nu, double p,
// SVM params type
enum { C=0, GAMMA=1, P=2, NU=3, COEF=4, DEGREE=5 };
+ /** @brief Trains an SVM with optimal parameters.
+
+ @param data the training data that can be constructed using TrainData::create or
+ TrainData::loadFromCSV.
+ @param kFold Cross-validation parameter. The training set is divided into kFold subsets. One
+ subset is used to test the model, the others form the train set. So, the SVM algorithm is executed
+ kFold times.
+ @param Cgrid
+ @param gammaGrid
+ @param pGrid
+ @param nuGrid
+ @param coeffGrid
+ @param degreeGrid Iteration grid for the corresponding SVM parameter.
+ @param balanced If true and the problem is 2-class classification then the method creates more
+ balanced cross-validation subsets that is proportions between classes in subsets are close to such
+ proportion in the whole train dataset.
+
+ The method trains the SVM model automatically by choosing the optimal parameters C, gamma, p, nu,
+ coef0, degree from SVM::Params. Parameters are considered optimal when the cross-validation estimate
+ of the test set error is minimal.
+
+ If there is no need to optimize a parameter, the corresponding grid step should be set to any value
+ less than or equal to 1. For example, to avoid optimization in gamma, set gammaGrid.step = 0,
+ gammaGrid.minVal, gamma\_grid.maxVal as arbitrary numbers. In this case, the value params.gamma is
+ taken for gamma.
+
+ And, finally, if the optimization in a parameter is required but the corresponding grid is unknown,
+ you may call the function SVM::getDefaulltGrid. To generate a grid, for example, for gamma, call
+ SVM::getDefaulltGrid(SVM::GAMMA).
+
+ This function works for the classification (params.svmType=SVM::C\_SVC or
+ params.svmType=SVM::NU\_SVC) as well as for the regression (params.svmType=SVM::EPS\_SVR or
+ params.svmType=SVM::NU\_SVR). If params.svmType=SVM::ONE\_CLASS, no optimization is made and the
+ usual SVM with parameters specified in params is executed.
+ */
virtual bool trainAuto( const Ptr<TrainData>& data, int kFold = 10,
ParamGrid Cgrid = SVM::getDefaultGrid(SVM::C),
ParamGrid gammaGrid = SVM::getDefaultGrid(SVM::GAMMA),
ParamGrid degreeGrid = SVM::getDefaultGrid(SVM::DEGREE),
bool balanced=false) = 0;
+ /** @brief Retrieves all the support vectors
+
+ The method returns all the support vector as floating-point matrix, where support vectors are stored
+ as matrix rows.
+ */
CV_WRAP virtual Mat getSupportVectors() const = 0;
virtual void setParams(const Params& p, const Ptr<Kernel>& customKernel=Ptr<Kernel>()) = 0;
+
+ /** @brief Returns the current SVM parameters.
+
+ This function may be used to get the optimal parameters obtained while automatically training
+ SVM::trainAuto.
+ */
virtual Params getParams() const = 0;
virtual Ptr<Kernel> getKernel() const = 0;
+
+ /** @brief Retrieves the decision function
+
+ @param i the index of the decision function. If the problem solved is regression, 1-class or
+ 2-class classification, then there will be just one decision function and the index should always
+ be 0. Otherwise, in the case of N-class classification, there will be N\*(N-1)/2 decision
+ functions.
+ @param alpha the optional output vector for weights, corresponding to different support vectors.
+ In the case of linear SVM all the alpha's will be 1's.
+ @param svidx the optional output vector of indices of support vectors within the matrix of support
+ vectors (which can be retrieved by SVM::getSupportVectors). In the case of linear SVM each
+ decision function consists of a single "compressed" support vector.
+
+ The method returns rho parameter of the decision function, a scalar subtracted from the weighted sum
+ of kernel responses.
+ */
virtual double getDecisionFunction(int i, OutputArray alpha, OutputArray svidx) const = 0;
+ /** @brief Generates a grid for SVM parameters.
+
+ @param param\_id SVM parameters IDs that must be one of the following:
+ - **SVM::C**
+ - **SVM::GAMMA**
+ - **SVM::P**
+ - **SVM::NU**
+ - **SVM::COEF**
+ - **SVM::DEGREE**
+ The grid is generated for the parameter with this ID.
+
+ The function generates a grid for the specified parameter of the SVM algorithm. The grid may be
+ passed to the function SVM::trainAuto.
+ */
static ParamGrid getDefaultGrid( int param_id );
+
+ /** @brief Creates empty model
+
+ @param p SVM parameters
+ @param customKernel the optional custom kernel to use. It must implement SVM::Kernel interface.
+
+ Use StatModel::train to train the model, StatModel::train\<RTrees\>(traindata, params) to create and
+ train the model, StatModel::load\<RTrees\>(filename) to load the pre-trained model. Since SVM has
+ several parameters, you may want to find the best parameters for your problem. It can be done with
+ SVM::trainAuto.
+ */
static Ptr<SVM> create(const Params& p=Params(), const Ptr<Kernel>& customKernel=Ptr<Kernel>());
};
+//! @} ml_svm
+
/****************************************************************************************\
* Expectation - Maximization *
\****************************************************************************************/
+
+//! @addtogroup ml_em
+//! @{
+
+/** @brief The class implements the EM algorithm as described in the beginning of this section.
+ */
class CV_EXPORTS_W EM : public StatModel
{
public:
// The initial step
enum {START_E_STEP=1, START_M_STEP=2, START_AUTO_STEP=0};
+ /** @brief The class describes EM training parameters.
+ */
class CV_EXPORTS_W_MAP Params
{
public:
+ /** @brief The constructor
+
+ @param nclusters The number of mixture components in the Gaussian mixture model. Default value of
+ the parameter is EM::DEFAULT\_NCLUSTERS=5. Some of EM implementation could determine the optimal
+ number of mixtures within a specified value range, but that is not the case in ML yet.
+ @param covMatType Constraint on covariance matrices which defines type of matrices. Possible
+ values are:
+ - **EM::COV\_MAT\_SPHERICAL** A scaled identity matrix \f$\mu_k * I\f$. There is the only
+ parameter \f$\mu_k\f$ to be estimated for each matrix. The option may be used in special cases,
+ when the constraint is relevant, or as a first step in the optimization (for example in case
+ when the data is preprocessed with PCA). The results of such preliminary estimation may be
+ passed again to the optimization procedure, this time with
+ covMatType=EM::COV\_MAT\_DIAGONAL.
+ - **EM::COV\_MAT\_DIAGONAL** A diagonal matrix with positive diagonal elements. The number of
+ free parameters is d for each matrix. This is most commonly used option yielding good
+ estimation results.
+ - **EM::COV\_MAT\_GENERIC** A symmetric positively defined matrix. The number of free
+ parameters in each matrix is about \f$d^2/2\f$. It is not recommended to use this option, unless
+ there is pretty accurate initial estimation of the parameters and/or a huge number of
+ training samples.
+ @param termCrit The termination criteria of the EM algorithm. The EM algorithm can be terminated
+ by the number of iterations termCrit.maxCount (number of M-steps) or when relative change of
+ likelihood logarithm is less than termCrit.epsilon. Default maximum number of iterations is
+ EM::DEFAULT\_MAX\_ITERS=100.
+ */
explicit Params(int nclusters=DEFAULT_NCLUSTERS, int covMatType=EM::COV_MAT_DIAGONAL,
const TermCriteria& termCrit=TermCriteria(TermCriteria::COUNT+TermCriteria::EPS,
EM::DEFAULT_MAX_ITERS, 1e-6));
virtual void setParams(const Params& p) = 0;
virtual Params getParams() const = 0;
+ /** @brief Returns weights of the mixtures
+
+ Returns vector with the number of elements equal to the number of mixtures.
+ */
virtual Mat getWeights() const = 0;
+ /** @brief Returns the cluster centers (means of the Gaussian mixture)
+
+ Returns matrix with the number of rows equal to the number of mixtures and number of columns equal
+ to the space dimensionality.
+ */
virtual Mat getMeans() const = 0;
+ /** @brief Returns covariation matrices
+
+ Returns vector of covariation matrices. Number of matrices is the number of gaussian mixtures, each
+ matrix is a square floating-point matrix NxN, where N is the space dimensionality.
+ */
virtual void getCovs(std::vector<Mat>& covs) const = 0;
+ /** @brief Returns a likelihood logarithm value and an index of the most probable mixture component for the
+ given sample.
+
+ @param sample A sample for classification. It should be a one-channel matrix of \f$1 \times dims\f$ or
+ \f$dims \times 1\f$ size.
+ @param probs Optional output matrix that contains posterior probabilities of each component given
+ the sample. It has \f$1 \times nclusters\f$ size and CV\_64FC1 type.
+
+ The method returns a two-element double vector. Zero element is a likelihood logarithm value for the
+ sample. First element is an index of the most probable mixture component for the given sample.
+ */
CV_WRAP virtual Vec2d predict2(InputArray sample, OutputArray probs) const = 0;
virtual bool train( const Ptr<TrainData>& trainData, int flags=0 ) = 0;
+ /** @brief Static methods that estimate the Gaussian mixture parameters from a samples set
+
+ @param samples Samples from which the Gaussian mixture model will be estimated. It should be a
+ one-channel matrix, each row of which is a sample. If the matrix does not have CV\_64F type it
+ will be converted to the inner matrix of such type for the further computing.
+ @param logLikelihoods The optional output matrix that contains a likelihood logarithm value for
+ each sample. It has \f$nsamples \times 1\f$ size and CV\_64FC1 type.
+ @param labels The optional output "class label" for each sample:
+ \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable mixture
+ component for each sample). It has \f$nsamples \times 1\f$ size and CV\_32SC1 type.
+ @param probs The optional output matrix that contains posterior probabilities of each Gaussian
+ mixture component given the each sample. It has \f$nsamples \times nclusters\f$ size and CV\_64FC1
+ type.
+ @param params The Gaussian mixture params, see EM::Params description
+ @return true if the Gaussian mixture model was trained successfully, otherwise it returns
+ false.
+
+ Starts with Expectation step. Initial values of the model parameters will be estimated by the
+ k-means algorithm.
+
+ Unlike many of the ML models, EM is an unsupervised learning algorithm and it does not take
+ responses (class labels or function values) as input. Instead, it computes the *Maximum Likelihood
+ Estimate* of the Gaussian mixture parameters from an input sample set, stores all the parameters
+ inside the structure: \f$p_{i,k}\f$ in probs, \f$a_k\f$ in means , \f$S_k\f$ in covs[k], \f$\pi_k\f$ in weights ,
+ and optionally computes the output "class label" for each sample:
+ \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable mixture
+ component for each sample).
+
+ The trained model can be used further for prediction, just like any other classifier. The trained
+ model is similar to the NormalBayesClassifier.
+ */
static Ptr<EM> train(InputArray samples,
OutputArray logLikelihoods=noArray(),
OutputArray labels=noArray(),
OutputArray probs=noArray(),
const Params& params=Params());
+ /** Starts with Expectation step. You need to provide initial means \f$a_k\f$ of mixture
+ components. Optionally you can pass initial weights \f$\pi_k\f$ and covariance matrices
+ \f$S_k\f$ of mixture components.
+
+ @param samples Samples from which the Gaussian mixture model will be estimated. It should be a
+ one-channel matrix, each row of which is a sample. If the matrix does not have CV\_64F type it
+ will be converted to the inner matrix of such type for the further computing.
+ @param means0 Initial means \f$a_k\f$ of mixture components. It is a one-channel matrix of
+ \f$nclusters \times dims\f$ size. If the matrix does not have CV\_64F type it will be converted to the
+ inner matrix of such type for the further computing.
+ @param covs0 The vector of initial covariance matrices \f$S_k\f$ of mixture components. Each of
+ covariance matrices is a one-channel matrix of \f$dims \times dims\f$ size. If the matrices do not
+ have CV\_64F type they will be converted to the inner matrices of such type for the further
+ computing.
+ @param weights0 Initial weights \f$\pi_k\f$ of mixture components. It should be a one-channel
+ floating-point matrix with \f$1 \times nclusters\f$ or \f$nclusters \times 1\f$ size.
+ @param logLikelihoods The optional output matrix that contains a likelihood logarithm value for
+ each sample. It has \f$nsamples \times 1\f$ size and CV\_64FC1 type.
+ @param labels The optional output "class label" for each sample:
+ \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable mixture
+ component for each sample). It has \f$nsamples \times 1\f$ size and CV\_32SC1 type.
+ @param probs The optional output matrix that contains posterior probabilities of each Gaussian
+ mixture component given the each sample. It has \f$nsamples \times nclusters\f$ size and CV\_64FC1
+ type.
+ @param params The Gaussian mixture params, see EM::Params description
+ */
static Ptr<EM> train_startWithE(InputArray samples, InputArray means0,
InputArray covs0=noArray(),
InputArray weights0=noArray(),
OutputArray probs=noArray(),
const Params& params=Params());
+ /** Starts with Maximization step. You need to provide initial probabilities \f$p_{i,k}\f$ to
+ use this option.
+
+ @param samples Samples from which the Gaussian mixture model will be estimated. It should be a
+ one-channel matrix, each row of which is a sample. If the matrix does not have CV\_64F type it
+ will be converted to the inner matrix of such type for the further computing.
+ @param probs0
+ @param logLikelihoods The optional output matrix that contains a likelihood logarithm value for
+ each sample. It has \f$nsamples \times 1\f$ size and CV\_64FC1 type.
+ @param labels The optional output "class label" for each sample:
+ \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable mixture
+ component for each sample). It has \f$nsamples \times 1\f$ size and CV\_32SC1 type.
+ @param probs The optional output matrix that contains posterior probabilities of each Gaussian
+ mixture component given the each sample. It has \f$nsamples \times nclusters\f$ size and CV\_64FC1
+ type.
+ @param params The Gaussian mixture params, see EM::Params description
+ */
static Ptr<EM> train_startWithM(InputArray samples, InputArray probs0,
OutputArray logLikelihoods=noArray(),
OutputArray labels=noArray(),
OutputArray probs=noArray(),
const Params& params=Params());
+
+ /** @brief Creates empty EM model
+
+ @param params EM parameters
+
+ The model should be trained then using StatModel::train(traindata, flags) method. Alternatively, you
+ can use one of the EM::train\* methods or load it from file using StatModel::load\<EM\>(filename).
+ */
static Ptr<EM> create(const Params& params=Params());
};
+//! @} ml_em
/****************************************************************************************\
* Decision Tree *
\****************************************************************************************/
+//! @addtogroup ml_decsiontrees
+//! @{
+
+/** @brief The class represents a single decision tree or a collection of decision trees. The current public
+interface of the class allows user to train only a single decision tree, however the class is
+capable of storing multiple decision trees and using them for prediction (by summing responses or
+using a voting schemes), and the derived from DTrees classes (such as RTrees and Boost) use this
+capability to implement decision tree ensembles.
+ */
class CV_EXPORTS_W DTrees : public StatModel
{
public:
enum { PREDICT_AUTO=0, PREDICT_SUM=(1<<8), PREDICT_MAX_VOTE=(2<<8), PREDICT_MASK=(3<<8) };
+ /** @brief The structure contains all the decision tree training parameters. You can initialize it by default
+ constructor and then override any parameters directly before training, or the structure may be fully
+ initialized using the advanced variant of the constructor.
+ */
class CV_EXPORTS_W_MAP Params
{
public:
Params();
+ /** @brief The constructors
+
+ @param maxDepth The maximum possible depth of the tree. That is the training algorithms attempts
+ to split a node while its depth is less than maxDepth. The root node has zero depth. The actual
+ depth may be smaller if the other termination criteria are met (see the outline of the training
+ procedure in the beginning of the section), and/or if the tree is pruned.
+ @param minSampleCount If the number of samples in a node is less than this parameter then the node
+ will not be split.
+ @param regressionAccuracy Termination criteria for regression trees. If all absolute differences
+ between an estimated value in a node and values of train samples in this node are less than this
+ parameter then the node will not be split further.
+ @param useSurrogates If true then surrogate splits will be built. These splits allow to work with
+ missing data and compute variable importance correctly.
+
+ @note currently it's not implemented.
+
+ @param maxCategories Cluster possible values of a categorical variable into K\<=maxCategories
+ clusters to find a suboptimal split. If a discrete variable, on which the training procedure
+ tries to make a split, takes more than maxCategories values, the precise best subset estimation
+ may take a very long time because the algorithm is exponential. Instead, many decision trees
+ engines (including our implementation) try to find sub-optimal split in this case by clustering
+ all the samples into maxCategories clusters that is some categories are merged together. The
+ clustering is applied only in n \> 2-class classification problems for categorical variables
+ with N \> max\_categories possible values. In case of regression and 2-class classification the
+ optimal split can be found efficiently without employing clustering, thus the parameter is not
+ used in these cases.
+
+ @param CVFolds If CVFolds \> 1 then algorithms prunes the built decision tree using K-fold
+ cross-validation procedure where K is equal to CVFolds.
+
+ @param use1SERule If true then a pruning will be harsher. This will make a tree more compact and
+ more resistant to the training data noise but a bit less accurate.
+
+ @param truncatePrunedTree If true then pruned branches are physically removed from the tree.
+ Otherwise they are retained and it is possible to get results from the original unpruned (or
+ pruned less aggressively) tree.
+
+ @param priors The array of a priori class probabilities, sorted by the class label value. The
+ parameter can be used to tune the decision tree preferences toward a certain class. For example,
+ if you want to detect some rare anomaly occurrence, the training base will likely contain much
+ more normal cases than anomalies, so a very good classification performance will be achieved
+ just by considering every case as normal. To avoid this, the priors can be specified, where the
+ anomaly probability is artificially increased (up to 0.5 or even greater), so the weight of the
+ misclassified anomalies becomes much bigger, and the tree is adjusted properly. You can also
+ think about this parameter as weights of prediction categories which determine relative weights
+ that you give to misclassification. That is, if the weight of the first category is 1 and the
+ weight of the second category is 10, then each mistake in predicting the second category is
+ equivalent to making 10 mistakes in predicting the first category.
+
+ The default constructor initializes all the parameters with the default values tuned for the
+ standalone classification tree:
+ @code
+ DTrees::Params::Params()
+ {
+ maxDepth = INT_MAX;
+ minSampleCount = 10;
+ regressionAccuracy = 0.01f;
+ useSurrogates = false;
+ maxCategories = 10;
+ CVFolds = 10;
+ use1SERule = true;
+ truncatePrunedTree = true;
+ priors = Mat();
+ }
+ @endcode
+ */
Params( int maxDepth, int minSampleCount,
double regressionAccuracy, bool useSurrogates,
int maxCategories, int CVFolds,
CV_PROP_RW Mat priors;
};
+ /** @brief The class represents a decision tree node. It has public members:
+ - member double value
+ Value at the node: a class label in case of classification or estimated function value in case
+ of regression.
+ - member int classIdx
+ Class index normalized to 0..class\_count-1 range and assigned to the node. It is used
+ internally in classification trees and tree ensembles.
+ - member int parent
+ Index of the parent node
+ - member int left
+ Index of the left child node
+ - member int right
+ Index of right child node.
+ - member int defaultDir
+ Default direction where to go (-1: left or +1: right). It helps in the case of missing values.
+ - member int split
+ Index of the first split
+ */
class CV_EXPORTS Node
{
public:
int split;
};
+ /** @brief The class represents split in a decision tree. It has public members:
+ - member int varIdx
+ Index of variable on which the split is created.
+ - member bool inversed
+ If true, then the inverse split rule is used (i.e. left and right branches are exchanged in
+ the rule expressions below).
+ - member float quality
+ The split quality, a positive number. It is used to choose the best split.
+ - member int next
+ Index of the next split in the list of splits for the node
+ - member float c
+ The threshold value in case of split on an ordered variable. The rule is: :
+ if var_value < c
+ then next_node<-left
+ else next_node<-right
+ - member int subsetOfs
+ Offset of the bitset used by the split on a categorical variable. The rule is: :
+ if bitset[var_value] == 1
+ then next_node <- left
+ else next_node <- right
+ */
class CV_EXPORTS Split
{
public:
int subsetOfs;
};
+ /** @brief Sets the training parameters
+
+ @param p Training parameters of type DTrees::Params.
+
+ The method sets the training parameters.
+ */
virtual void setDParams(const Params& p);
+ /** @brief Returns the training parameters
+
+ The method returns the training parameters.
+ */
virtual Params getDParams() const;
+ /** @brief Returns indices of root nodes
+ */
virtual const std::vector<int>& getRoots() const = 0;
+ /** @brief Returns all the nodes
+
+ all the node indices, mentioned above (left, right, parent, root indices) are indices in the
+ returned vector
+ */
virtual const std::vector<Node>& getNodes() const = 0;
+ /** @brief Returns all the splits
+
+ all the split indices, mentioned above (split, next etc.) are indices in the returned vector
+ */
virtual const std::vector<Split>& getSplits() const = 0;
+ /** @brief Returns all the bitsets for categorical splits
+
+ Split::subsetOfs is an offset in the returned vector
+ */
virtual const std::vector<int>& getSubsets() const = 0;
+ /** @brief Creates the empty model
+
+ The static method creates empty decision tree with the specified parameters. It should be then
+ trained using train method (see StatModel::train). Alternatively, you can load the model from file
+ using StatModel::load\<DTrees\>(filename).
+ */
static Ptr<DTrees> create(const Params& params=Params());
};
+//! @} ml_decsiontrees
+
/****************************************************************************************\
* Random Trees Classifier *
\****************************************************************************************/
+//! @addtogroup ml_randomtrees
+//! @{
+
+/** @brief The class implements the random forest predictor as described in the beginning of this section.
+ */
class CV_EXPORTS_W RTrees : public DTrees
{
public:
+ /** @brief The set of training parameters for the forest is a superset of the training
+ parameters for a single tree.
+
+ However, random trees do not need all the functionality/features of decision trees. Most
+ noticeably, the trees are not pruned, so the cross-validation parameters are not used.
+ */
class CV_EXPORTS_W_MAP Params : public DTrees::Params
{
public:
Params();
+ /** @brief The constructors
+
+ @param maxDepth the depth of the tree. A low value will likely underfit and conversely a high
+ value will likely overfit. The optimal value can be obtained using cross validation or other
+ suitable methods.
+ @param minSampleCount minimum samples required at a leaf node for it to be split. A reasonable
+ value is a small percentage of the total data e.g. 1%.
+ @param regressionAccuracy
+ @param useSurrogates
+ @param maxCategories Cluster possible values of a categorical variable into K \<= maxCategories
+ clusters to find a suboptimal split. If a discrete variable, on which the training procedure tries
+ to make a split, takes more than max\_categories values, the precise best subset estimation may
+ take a very long time because the algorithm is exponential. Instead, many decision trees engines
+ (including ML) try to find sub-optimal split in this case by clustering all the samples into
+ maxCategories clusters that is some categories are merged together. The clustering is applied only
+ in n\>2-class classification problems for categorical variables with N \> max\_categories possible
+ values. In case of regression and 2-class classification the optimal split can be found
+ efficiently without employing clustering, thus the parameter is not used in these cases.
+ @param priors
+ @param calcVarImportance If true then variable importance will be calculated and then it can be
+ retrieved by RTrees::getVarImportance.
+ @param nactiveVars The size of the randomly selected subset of features at each tree node and that
+ are used to find the best split(s). If you set it to 0 then the size will be set to the square
+ root of the total number of features.
+ @param termCrit The termination criteria that specifies when the training algorithm stops - either
+ when the specified number of trees is trained and added to the ensemble or when sufficient
+ accuracy (measured as OOB error) is achieved. Typically the more trees you have the better the
+ accuracy. However, the improvement in accuracy generally diminishes and asymptotes pass a certain
+ number of trees. Also to keep in mind, the number of tree increases the prediction time linearly.
+
+ The default constructor sets all parameters to default values which are different from default
+ values of `DTrees::Params`:
+ @code
+ RTrees::Params::Params() : DTrees::Params( 5, 10, 0, false, 10, 0, false, false, Mat() ),
+ calcVarImportance(false), nactiveVars(0)
+ {
+ termCrit = cvTermCriteria( TermCriteria::MAX_ITERS + TermCriteria::EPS, 50, 0.1 );
+ }
+ @endcode
+ */
Params( int maxDepth, int minSampleCount,
double regressionAccuracy, bool useSurrogates,
int maxCategories, const Mat& priors,
virtual void setRParams(const Params& p) = 0;
virtual Params getRParams() const = 0;
+ /** @brief Returns the variable importance array.
+
+ The method returns the variable importance vector, computed at the training stage when
+ RTParams::calcVarImportance is set to true. If this flag was set to false, the empty matrix is
+ returned.
+ */
virtual Mat getVarImportance() const = 0;
+ /** @brief Creates the empty model
+
+ Use StatModel::train to train the model, StatModel::train to create and
+ train the model, StatModel::load to load the pre-trained model.
+ */
static Ptr<RTrees> create(const Params& params=Params());
};
+//! @} ml_randomtrees
+
/****************************************************************************************\
* Boosted tree classifier *
\****************************************************************************************/
+//! @addtogroup ml_boost
+//! @{
+
+/** @brief Boosted tree classifier derived from DTrees
+ */
class CV_EXPORTS_W Boost : public DTrees
{
public:
+ /** @brief The structure is derived from DTrees::Params but not all of the decision tree parameters are
+ supported. In particular, cross-validation is not supported.
+
+ All parameters are public. You can initialize them by a constructor and then override some of them
+ directly if you want.
+ */
class CV_EXPORTS_W_MAP Params : public DTrees::Params
{
public:
CV_PROP_RW double weightTrimRate;
Params();
+ /** @brief The constructors.
+
+ @param boostType Type of the boosting algorithm. Possible values are:
+ - **Boost::DISCRETE** Discrete AdaBoost.
+ - **Boost::REAL** Real AdaBoost. It is a technique that utilizes confidence-rated predictions
+ and works well with categorical data.
+ - **Boost::LOGIT** LogitBoost. It can produce good regression fits.
+ - **Boost::GENTLE** Gentle AdaBoost. It puts less weight on outlier data points and for that
+ reason is often good with regression data.
+ Gentle AdaBoost and Real AdaBoost are often the preferable choices.
+ @param weakCount The number of weak classifiers.
+ @param weightTrimRate A threshold between 0 and 1 used to save computational time. Samples
+ with summary weight \f$\leq 1 - weight\_trim\_rate\f$ do not participate in the *next* iteration of
+ training. Set this parameter to 0 to turn off this functionality.
+ @param maxDepth
+ @param useSurrogates
+ @param priors
+
+ See DTrees::Params for description of other parameters.
+
+ Default parameters are:
+ @code
+ Boost::Params::Params()
+ {
+ boostType = Boost::REAL;
+ weakCount = 100;
+ weightTrimRate = 0.95;
+ CVFolds = 0;
+ maxDepth = 1;
+ }
+ @endcode
+ */
Params( int boostType, int weakCount, double weightTrimRate,
int maxDepth, bool useSurrogates, const Mat& priors );
};
// Boosting type
enum { DISCRETE=0, REAL=1, LOGIT=2, GENTLE=3 };
+ /** @brief Returns the boosting parameters
+
+ The method returns the training parameters.
+ */
virtual Params getBParams() const = 0;
+ /** @brief Sets the boosting parameters
+
+ @param p Training parameters of type Boost::Params.
+
+ The method sets the training parameters.
+ */
virtual void setBParams(const Params& p) = 0;
+ /** @brief Creates the empty model
+
+ Use StatModel::train to train the model, StatModel::train\<Boost\>(traindata, params) to create and
+ train the model, StatModel::load\<Boost\>(filename) to load the pre-trained model.
+ */
static Ptr<Boost> create(const Params& params=Params());
};
+//! @} ml_boost
+
/****************************************************************************************\
* Gradient Boosted Trees *
\****************************************************************************************/
/////////////////////////////////// Multi-Layer Perceptrons //////////////////////////////
+//! @addtogroup ml_neural
+//! @{
+
+/** @brief MLP model.
+
+Unlike many other models in ML that are constructed and trained at once, in the MLP model these
+steps are separated. First, a network with the specified topology is created using the non-default
+constructor or the method ANN\_MLP::create. All the weights are set to zeros. Then, the network is
+trained using a set of input and output vectors. The training procedure can be repeated more than
+once, that is, the weights can be adjusted based on the new training data.
+ */
class CV_EXPORTS_W ANN_MLP : public StatModel
{
public:
+ /** @brief Parameters of the MLP and of the training algorithm.
+
+ You can initialize the structure by a constructor or the individual parameters can be adjusted
+ after the structure is created.
+ The network structure:
+ - member Mat layerSizes
+ The number of elements in each layer of network. The very first element specifies the number
+ of elements in the input layer. The last element - number of elements in the output layer.
+ - member int activateFunc
+ The activation function. Currently the only fully supported activation function is
+ ANN\_MLP::SIGMOID\_SYM.
+ - member double fparam1
+ The first parameter of activation function, 0 by default.
+ - member double fparam2
+ The second parameter of the activation function, 0 by default.
+ @note
+ If you are using the default ANN\_MLP::SIGMOID\_SYM activation function with the default
+ parameter values fparam1=0 and fparam2=0 then the function used is y = 1.7159\*tanh(2/3 \* x),
+ so the output will range from [-1.7159, 1.7159], instead of [0,1].
+
+ The back-propagation algorithm parameters:
+ - member double bpDWScale
+ Strength of the weight gradient term. The recommended value is about 0.1.
+ - member double bpMomentScale
+ Strength of the momentum term (the difference between weights on the 2 previous iterations).
+ This parameter provides some inertia to smooth the random fluctuations of the weights. It
+ can vary from 0 (the feature is disabled) to 1 and beyond. The value 0.1 or so is good
+ enough
+ The RPROP algorithm parameters (see @cite RPROP93 for details):
+ - member double prDW0
+ Initial value \f$\Delta_0\f$ of update-values \f$\Delta_{ij}\f$.
+ - member double rpDWPlus
+ Increase factor \f$\eta^+\f$. It must be \>1.
+ - member double rpDWMinus
+ Decrease factor \f$\eta^-\f$. It must be \<1.
+ - member double rpDWMin
+ Update-values lower limit \f$\Delta_{min}\f$. It must be positive.
+ - member double rpDWMax
+ Update-values upper limit \f$\Delta_{max}\f$. It must be \>1.
+ */
struct CV_EXPORTS_W_MAP Params
{
Params();
+ /** @brief Construct the parameter structure
+
+ @param layerSizes Integer vector specifying the number of neurons in each layer including the
+ input and output layers.
+ @param activateFunc Parameter specifying the activation function for each neuron: one of
+ ANN\_MLP::IDENTITY, ANN\_MLP::SIGMOID\_SYM, and ANN\_MLP::GAUSSIAN.
+ @param fparam1 The first parameter of the activation function, \f$\alpha\f$. See the formulas in the
+ introduction section.
+ @param fparam2 The second parameter of the activation function, \f$\beta\f$. See the formulas in the
+ introduction section.
+ @param termCrit Termination criteria of the training algorithm. You can specify the maximum number
+ of iterations (maxCount) and/or how much the error could change between the iterations to make the
+ algorithm continue (epsilon).
+ @param trainMethod Training method of the MLP. Possible values are:
+ - **ANN\_MLP\_TrainParams::BACKPROP** The back-propagation algorithm.
+ - **ANN\_MLP\_TrainParams::RPROP** The RPROP algorithm.
+ @param param1 Parameter of the training method. It is rp\_dw0 for RPROP and bp\_dw\_scale for
+ BACKPROP.
+ @param param2 Parameter of the training method. It is rp\_dw\_min for RPROP and bp\_moment\_scale
+ for BACKPROP.
+
+ By default the RPROP algorithm is used:
+ @code
+ ANN_MLP_TrainParams::ANN_MLP_TrainParams()
+ {
+ layerSizes = Mat();
+ activateFun = SIGMOID_SYM;
+ fparam1 = fparam2 = 0;
+ term_crit = TermCriteria( TermCriteria::MAX_ITER + TermCriteria::EPS, 1000, 0.01 );
+ train_method = RPROP;
+ bpDWScale = bpMomentScale = 0.1;
+ rpDW0 = 0.1; rpDWPlus = 1.2; rpDWMinus = 0.5;
+ rpDWMin = FLT_EPSILON; rpDWMax = 50.;
+ }
+ @endcode
+ */
Params( const Mat& layerSizes, int activateFunc, double fparam1, double fparam2,
TermCriteria termCrit, int trainMethod, double param1, double param2=0 );
enum { UPDATE_WEIGHTS = 1, NO_INPUT_SCALE = 2, NO_OUTPUT_SCALE = 4 };
virtual Mat getWeights(int layerIdx) const = 0;
+
+ /** @brief Sets the new network parameters
+
+ @param p The new parameters
+
+ The existing network, if any, will be destroyed and new empty one will be created. It should be
+ re-trained after that.
+ */
virtual void setParams(const Params& p) = 0;
+
+ /** @brief Retrieves the current network parameters
+ */
virtual Params getParams() const = 0;
+ /** @brief Creates empty model
+
+ Use StatModel::train to train the model, StatModel::train\<ANN\_MLP\>(traindata, params) to create
+ and train the model, StatModel::load\<ANN\_MLP\>(filename) to load the pre-trained model. Note that
+ the train method has optional flags, and the following flags are handled by \`ANN\_MLP\`:
+
+ - **UPDATE\_WEIGHTS** Algorithm updates the network weights, rather than computes them from
+ scratch. In the latter case the weights are initialized using the Nguyen-Widrow algorithm.
+ - **NO\_INPUT\_SCALE** Algorithm does not normalize the input vectors. If this flag is not set,
+ the training algorithm normalizes each input feature independently, shifting its mean value to
+ 0 and making the standard deviation equal to 1. If the network is assumed to be updated
+ frequently, the new training data could be much different from original one. In this case, you
+ should take care of proper normalization.
+ - **NO\_OUTPUT\_SCALE** Algorithm does not normalize the output vectors. If the flag is not set,
+ the training algorithm normalizes each output feature independently, by transforming it to the
+ certain range depending on the used activation function.
+ */
static Ptr<ANN_MLP> create(const Params& params=Params());
};
+//! @} ml_neural
+
/****************************************************************************************\
* Logistic Regression *
\****************************************************************************************/
+//! @addtogroup ml_lr
+//! @{
+
+/** @brief Implements Logistic Regression classifier.
+ */
class CV_EXPORTS LogisticRegression : public StatModel
{
public:
class CV_EXPORTS Params
{
public:
+ /** @brief The constructors
+
+ @param learning\_rate Specifies the learning rate.
+ @param iters Specifies the number of iterations.
+ @param 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 reg To enable or disable regularization. Set to positive integer (greater than zero) to
+ enable and to 0 to disable.
+ @param 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.
+
+ By initializing this structure, one can set all the parameters required for Logistic Regression
+ classifier.
+ */
Params(double learning_rate = 0.001,
int iters = 1000,
int method = LogisticRegression::BATCH,
- int normlization = LogisticRegression::REG_L2,
+ int normalization = LogisticRegression::REG_L2,
int reg = 1,
int batch_size = 1);
double alpha;
enum { REG_L1 = 0, REG_L2 = 1};
enum { BATCH = 0, MINI_BATCH = 1};
- // Algorithm interface
+ /** @brief This function writes the trained LogisticRegression clasifier to disk.
+ */
virtual void write( FileStorage &fs ) const = 0;
+ /** @brief This function reads the trained LogisticRegression clasifier from disk.
+ */
virtual void read( const FileNode &fn ) = 0;
- // StatModel interface
+ /** @brief Trains the Logistic Regression classifier and returns true if successful.
+
+ @param trainData Instance of ml::TrainData class holding learning data.
+ @param flags Not used.
+ */
virtual bool train( const Ptr<TrainData>& trainData, int flags=0 ) = 0;
+ /** @brief Predicts responses for input samples and returns a float type.
+
+ @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.
+ @param results Predicted labels as a column matrix of type CV\_32S.
+ @param flags Not used.
+ */
virtual float predict( InputArray samples, OutputArray results=noArray(), int flags=0 ) const = 0;
virtual void clear() = 0;
+ /** @brief This function returns the trained paramters arranged across rows.
+
+ For a two class classifcation problem, it returns a row matrix.
+ It returns learnt paramters of the Logistic Regression as a matrix of type CV\_32F.
+ */
virtual Mat get_learnt_thetas() const = 0;
+ /** @brief Creates empty model.
+
+ @param params The training parameters for the classifier of type LogisticRegression::Params.
+
+ Creates Logistic Regression model with parameters given.
+ */
static Ptr<LogisticRegression> create( const Params& params = Params() );
};
+//! @} ml_lr
+
/****************************************************************************************\
* Auxilary functions declarations *
\****************************************************************************************/
-/* Generates <sample> from multivariate normal distribution, where <mean> - is an
- average row vector, <cov> - symmetric covariation matrix */
+/** Generates `sample` from multivariate normal distribution, where `mean` - is an
+ average row vector, `cov` - symmetric covariation matrix */
CV_EXPORTS void randMVNormal( InputArray mean, InputArray cov, int nsamples, OutputArray samples);
-/* Generates sample from gaussian mixture distribution */
+/** Generates sample from gaussian mixture distribution */
CV_EXPORTS void randGaussMixture( InputArray means, InputArray covs, InputArray weights,
int nsamples, OutputArray samples, OutputArray sampClasses );
-/* creates test set */
+/** creates test set */
CV_EXPORTS void createConcentricSpheresTestSet( int nsamples, int nfeatures, int nclasses,
OutputArray samples, OutputArray responses);
+//! @} ml
+
}
}
projects / platform / upstream / opencv.git / commitdiff