evaluate_class_gmmT_evaluate_class_gmmEvaluateClassGmmEvaluateClassGmm (Operator)

Name

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

Signature

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

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

GMMHandleGMMHandleGMMHandleGMMHandleGMMHandle (input_control) class_gmm → (handle)

GMM handle.

FeaturesFeaturesFeaturesFeaturesfeatures (input_control) real-array → (real)

Feature vector.

ClassProbClassProbClassProbClassProbclassProb (output_control) real-array → (real)

A-posteriori probability of the classes.

DensityDensityDensityDensitydensity (output_control) real → (real)

Probability density of the feature vector.

KSigmaProbKSigmaProbKSigmaProbKSigmaProbKSigmaProb (output_control) real → (real)

Normalized k-sigma-probability for the feature vector.

Result

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

Alternatives

classify_class_gmmclassify_class_gmmClassifyClassGmmClassifyClassGmmClassifyClassGmm

References

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.

Module

Foundation

Operators