evaluate_class_gmmT_evaluate_class_gmmEvaluateClassGmmEvaluateClassGmm (Operator)


evaluate_class_gmmT_evaluate_class_gmmEvaluateClassGmmEvaluateClassGmm — Evaluate a feature vector by a Gaussian Mixture Model.


evaluate_class_gmm( : : GMMHandle, Features : ClassProb, Density, KSigmaProb)

Herror T_evaluate_class_gmm(const Htuple GMMHandle, const Htuple Features, Htuple* ClassProb, Htuple* Density, Htuple* KSigmaProb)

void EvaluateClassGmm(const HTuple& GMMHandle, const HTuple& Features, HTuple* ClassProb, HTuple* Density, HTuple* KSigmaProb)

HTuple HClassGmm::EvaluateClassGmm(const HTuple& Features, double* Density, double* KSigmaProb) const

static void HOperatorSet.EvaluateClassGmm(HTuple GMMHandle, HTuple features, out HTuple classProb, out HTuple density, out HTuple KSigmaProb)

HTuple HClassGmm.EvaluateClassGmm(HTuple features, out double density, out double KSigmaProb)


evaluate_class_gmmevaluate_class_gmmEvaluateClassGmmEvaluateClassGmmEvaluateClassGmm computes three different probability values for a feature vector FeaturesFeaturesFeaturesFeaturesfeatures with the Gaussian Mixture Model (GMM) GMMHandleGMMHandleGMMHandleGMMHandleGMMHandle.

The a-posteriori probability of class i for the sample FeaturesFeaturesFeaturesFeaturesfeatures(x) is computed as and returned for each class in ClassProbClassProbClassProbClassProbclassProb. The formulas for the calculation of the center density function p(x|j) are described with create_class_gmmcreate_class_gmmCreateClassGmmCreateClassGmmCreateClassGmm.

The probability density of the feature vector is computed as a sum of the posterior class probabilities and is returned in DensityDensityDensityDensitydensity. Here, Pr(i) are the prior classes probabilities as computed by train_class_gmmtrain_class_gmmTrainClassGmmTrainClassGmmTrainClassGmm. DensityDensityDensityDensitydensity can be used for novelty detection, i.e., to reject feature vectors that do not belong to any of the trained classes. However, since DensityDensityDensityDensitydensity depends on the scaling of the feature vectors and since DensityDensityDensityDensitydensity is a probability density, and consequently does not need to lie between 0 and 1, the novelty detection can typically be performed more easily with KSigmaProbKSigmaProbKSigmaProbKSigmaProbKSigmaProb (see below).

A k-sigma error ellipsoid is defined as a locus of points for which In the one dimensional case this is the interval . For any 1D Gaussian distribution, it is true that approximately 65% of the occurrences of the random variable are within this range for k=1, approximately 95% for k=2, approximately 99% for k=3, etc. Hence, the probability that a Gaussian distribution will generate a random variable outside this range is approximately 35%, 5%, and 1%, respectively. This probability is called k-sigma probability and is denoted by P[k]. P[k] can be computed numerically for univariate as well as for multivariate Gaussian distributions, where it should be noted that for the same values of k, (here N and (N+1) denote dimensions). For Gaussian mixture models the k-sigma probability is computed as: They are weighted with the class priors and then normalized. The maximum value of all classes is returned in KSigmaProbKSigmaProbKSigmaProbKSigmaProbKSigmaProb, such that

KSigmaProbKSigmaProbKSigmaProbKSigmaProbKSigmaProb can be used for novelty detection. Typically, feature vectors having values below 0.0001 should be rejected. Note that the rejection threshold defined by the parameter RejectionThresholdRejectionThresholdRejectionThresholdRejectionThresholdrejectionThreshold in classify_image_class_gmmclassify_image_class_gmmClassifyImageClassGmmClassifyImageClassGmmClassifyImageClassGmm refers to the KSigmaProbKSigmaProbKSigmaProbKSigmaProbKSigmaProb values.

Before calling evaluate_class_gmmevaluate_class_gmmEvaluateClassGmmEvaluateClassGmmEvaluateClassGmm, the GMM must be trained with train_class_gmmtrain_class_gmmTrainClassGmmTrainClassGmmTrainClassGmm.

The position of the maximum value of ClassProbClassProbClassProbClassProbclassProb is usually interpreted as the class of the feature vector and the corresponding value as the probability of the class. In this case, classify_class_gmmclassify_class_gmmClassifyClassGmmClassifyClassGmmClassifyClassGmm should be used instead of evaluate_class_gmmevaluate_class_gmmEvaluateClassGmmEvaluateClassGmmEvaluateClassGmm, because classify_class_gmmclassify_class_gmmClassifyClassGmmClassifyClassGmmClassifyClassGmm directly returns the class and corresponding probability.

Execution Information


GMMHandleGMMHandleGMMHandleGMMHandleGMMHandle (input_control)  class_gmm HClassGmm, HTupleHTupleHtuple (handle) (IntPtr) (HHandle) (handle)

GMM handle.

FeaturesFeaturesFeaturesFeaturesfeatures (input_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

Feature vector.

ClassProbClassProbClassProbClassProbclassProb (output_control)  real-array HTupleHTupleHtuple (real) (double) (double) (double)

A-posteriori probability of the classes.

DensityDensityDensityDensitydensity (output_control)  real HTupleHTupleHtuple (real) (double) (double) (double)

Probability density of the feature vector.

KSigmaProbKSigmaProbKSigmaProbKSigmaProbKSigmaProb (output_control)  real HTupleHTupleHtuple (real) (double) (double) (double)

Normalized k-sigma-probability for the feature vector.


If the parameters are valid, the operator evaluate_class_gmmevaluate_class_gmmEvaluateClassGmmEvaluateClassGmmEvaluateClassGmm returns the value 2 (H_MSG_TRUE). If necessary an exception is raised.

Possible Predecessors

train_class_gmmtrain_class_gmmTrainClassGmmTrainClassGmmTrainClassGmm, read_class_gmmread_class_gmmReadClassGmmReadClassGmmReadClassGmm



See also



Christopher M. Bishop: “Neural Networks for Pattern Recognition”; Oxford University Press, Oxford; 1995.
Mario A.T. Figueiredo: “Unsupervised Learning of Finite Mixture Models”; IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 3; March 2002.