Name
create_class_gmm create_class_gmm CreateClassGmm create_class_gmm CreateClassGmm CreateClassGmm — Create a Gaussian Mixture Model for classification
Herror create_class_gmm (const Hlong NumDim , const Hlong NumClasses , const Hlong NumCenters , const char* CovarType , const char* Preprocessing , const Hlong NumComponents , const Hlong RandSeed , Hlong* GMMHandle )
Herror T_create_class_gmm (const Htuple NumDim , const Htuple NumClasses , const Htuple NumCenters , const Htuple CovarType , const Htuple Preprocessing , const Htuple NumComponents , const Htuple RandSeed , Htuple* GMMHandle )
Herror create_class_gmm (const HTuple& NumDim , const HTuple& NumClasses , const HTuple& NumCenters , const HTuple& CovarType , const HTuple& Preprocessing , const HTuple& NumComponents , const HTuple& RandSeed , Hlong* GMMHandle )
void HClassGmm ::CreateClassGmm (const HTuple& NumDim , const HTuple& NumClasses , const HTuple& NumCenters , const HTuple& CovarType , const HTuple& Preprocessing , const HTuple& NumComponents , const HTuple& RandSeed )
void CreateClassGmm (const HTuple& NumDim , const HTuple& NumClasses , const HTuple& NumCenters , const HTuple& CovarType , const HTuple& Preprocessing , const HTuple& NumComponents , const HTuple& RandSeed , HTuple* GMMHandle )
void HClassGmm ::HClassGmm (Hlong NumDim , Hlong NumClasses , const HTuple& NumCenters , const HString& CovarType , const HString& Preprocessing , Hlong NumComponents , Hlong RandSeed )
void HClassGmm ::HClassGmm (Hlong NumDim , Hlong NumClasses , Hlong NumCenters , const HString& CovarType , const HString& Preprocessing , Hlong NumComponents , Hlong RandSeed )
void HClassGmm ::HClassGmm (Hlong NumDim , Hlong NumClasses , Hlong NumCenters , const char* CovarType , const char* Preprocessing , Hlong NumComponents , Hlong RandSeed )
void HClassGmm ::CreateClassGmm (Hlong NumDim , Hlong NumClasses , const HTuple& NumCenters , const HString& CovarType , const HString& Preprocessing , Hlong NumComponents , Hlong RandSeed )
void HClassGmm ::CreateClassGmm (Hlong NumDim , Hlong NumClasses , Hlong NumCenters , const HString& CovarType , const HString& Preprocessing , Hlong NumComponents , Hlong RandSeed )
void HClassGmm ::CreateClassGmm (Hlong NumDim , Hlong NumClasses , Hlong NumCenters , const char* CovarType , const char* Preprocessing , Hlong NumComponents , Hlong RandSeed )
void HOperatorSetX .CreateClassGmm ( [in] VARIANT NumDim , [in] VARIANT NumClasses , [in] VARIANT NumCenters , [in] VARIANT CovarType , [in] VARIANT Preprocessing , [in] VARIANT NumComponents , [in] VARIANT RandSeed , [out] VARIANT* GMMHandle )
void HClassGmmX .CreateClassGmm ( [in] Hlong NumDim , [in] Hlong NumClasses , [in] VARIANT NumCenters , [in] BSTR CovarType , [in] BSTR Preprocessing , [in] Hlong NumComponents , [in] Hlong RandSeed )
static void HOperatorSet .CreateClassGmm (HTuple numDim , HTuple numClasses , HTuple numCenters , HTuple covarType , HTuple preprocessing , HTuple numComponents , HTuple randSeed , out HTuple GMMHandle )
public HClassGmm (int numDim , int numClasses , HTuple numCenters , string covarType , string preprocessing , int numComponents , int randSeed )
public HClassGmm (int numDim , int numClasses , int numCenters , string covarType , string preprocessing , int numComponents , int randSeed )
void HClassGmm .CreateClassGmm (int numDim , int numClasses , HTuple numCenters , string covarType , string preprocessing , int numComponents , int randSeed )
void HClassGmm .CreateClassGmm (int numDim , int numClasses , int numCenters , string covarType , string preprocessing , int numComponents , int randSeed )
create_class_gmm create_class_gmm CreateClassGmm create_class_gmm CreateClassGmm CreateClassGmm creates a Gaussian Mixture Model (GMM) for
classification. NumDim NumDim NumDim NumDim NumDim numDim specifies the number of dimensions
of the feature space, NumClasses NumClasses NumClasses NumClasses NumClasses numClasses specifies the number of
classes. A GMM consists of NumCenters NumCenters NumCenters NumCenters NumCenters numCenters Gaussian
centers per class. NumCenters NumCenters NumCenters NumCenters NumCenters numCenters can not only be the exact
number of centers to be used, but, depending on the number of
parameters, can specify upper and lower bounds for the number of
centers:
exactly one parameter:
The parameter determines the exact
number of centers to be used for all classes.
exactly two parameters:
The first parameter determines the
mimimum number of centers, the second determines the maximum
number of centers for all classes.
exactly
parameters:
Alternatingly every first parameter determines the minimum number of
centers per class and every second parameters determines the maximum
number of centers per class.
When upper and lower bounds are specified, the optimum number of
centers will be determined with the help of the Mimimum Message
Length Criterion (MML). In general, we recommend to start the
training with (too) many centers as maximum and the
expected number of centers as minimum.
Each center is described by the parameters center
, covariance matrix
, and mixing
coefficient
. These parameters are calculated from
the training data by means of the Expectation Maximization (EM)
algorithm. A GMM can approximate an arbitrary probability density,
provided that enough centers are being used. The covariance matrices
have the dimensions NumDim NumDim NumDim NumDim NumDim numDim
x NumDim NumDim NumDim NumDim NumDim numDim (NumComponents NumComponents NumComponents NumComponents NumComponents numComponents
x NumComponents NumComponents NumComponents NumComponents NumComponents numComponents if preprocessing is used) and
are symmetric. Further constraints can be given by
CovarType CovarType CovarType CovarType CovarType covarType :
For CovarType CovarType CovarType CovarType CovarType covarType = 'spherical' "spherical" "spherical" "spherical" "spherical" "spherical" ,
is a scalar multiple of the identity matrix
. The center density
function p(x|j) is
For CovarType CovarType CovarType CovarType CovarType covarType = 'diag' "diag" "diag" "diag" "diag" "diag" ,
is a diagonal matrix
. The
center density function p(x|j) is
For CovarType CovarType CovarType CovarType CovarType covarType = 'full' "full" "full" "full" "full" "full" ,
is a positive definite matrix. The center density function
p(x|j) is
The complexity of the calculations increases from CovarType CovarType CovarType CovarType CovarType covarType
= 'spherical' "spherical" "spherical" "spherical" "spherical" "spherical" over CovarType CovarType CovarType CovarType CovarType covarType = 'diag' "diag" "diag" "diag" "diag" "diag"
to CovarType CovarType CovarType CovarType CovarType covarType = 'full' "full" "full" "full" "full" "full" . At the same time the
flexibility of the centers increases. In general,
'spherical' "spherical" "spherical" "spherical" "spherical" "spherical" therefore needs higher values for
NumCenters NumCenters NumCenters NumCenters NumCenters numCenters than 'full' "full" "full" "full" "full" "full" .
The procedure to use GMM is as follows: First, a GMM is created by
create_class_gmm create_class_gmm CreateClassGmm create_class_gmm CreateClassGmm CreateClassGmm . Then, training vectors are added by
add_sample_class_gmm add_sample_class_gmm AddSampleClassGmm add_sample_class_gmm AddSampleClassGmm AddSampleClassGmm , afterwards they can be written to disk
with write_samples_class_gmm write_samples_class_gmm WriteSamplesClassGmm write_samples_class_gmm WriteSamplesClassGmm WriteSamplesClassGmm . With train_class_gmm train_class_gmm TrainClassGmm train_class_gmm TrainClassGmm TrainClassGmm
the classifier center parameters (defined above) are determined.
Furthermore, they can be saved with write_class_gmm write_class_gmm WriteClassGmm write_class_gmm WriteClassGmm WriteClassGmm for
later classifications.
From the mixing probabilities
and the
center density function p(x|j), the probability
density function p(x) can be calculated by:
The probability density function p(x) can be
evaluated with evaluate_class_gmm evaluate_class_gmm EvaluateClassGmm evaluate_class_gmm EvaluateClassGmm EvaluateClassGmm for a feature
vector x. classify_class_gmm classify_class_gmm ClassifyClassGmm classify_class_gmm ClassifyClassGmm ClassifyClassGmm sorts the
p(x) and therefore discovers the most probable
class of the feature vector.
The parameters Preprocessing Preprocessing Preprocessing Preprocessing Preprocessing preprocessing and NumComponents NumComponents NumComponents NumComponents NumComponents numComponents can
be used to preprocess the training data and reduce its dimensions.
These parameters are explained in the description of the operator
create_class_mlp create_class_mlp CreateClassMlp create_class_mlp CreateClassMlp CreateClassMlp .
create_class_gmm create_class_gmm CreateClassGmm create_class_gmm CreateClassGmm CreateClassGmm initializes the coordinates of the centers
with random numbers. To ensure that the results of training the
classifier with train_class_gmm train_class_gmm TrainClassGmm train_class_gmm TrainClassGmm TrainClassGmm are reproducible, the seed
value of the random number generator is passed in
RandSeed RandSeed RandSeed RandSeed RandSeed randSeed .
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.
This operator returns a handle. Note that the state of an instance of this handle type may be changed by specific operators even though the handle is used as an input parameter by those operators.
Number of dimensions of the feature space.
Default value: 3
Suggested values: 1, 2, 3, 4, 5, 8, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100
Restriction: NumDim >= 1
Number of classes of the GMM.
Default value: 5
Suggested values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Restriction: NumClasses >= 1
Number of centers per class.
Default value: 1
Suggested values: 1, 2, 3, 4, 5, 8, 10, 15, 20, 30
Restriction: NumClasses >= 1
Type of the covariance matrices.
Default value:
'spherical'
"spherical"
"spherical"
"spherical"
"spherical"
"spherical"
List of values: 'diag' "diag" "diag" "diag" "diag" "diag" , 'full' "full" "full" "full" "full" "full" , 'spherical' "spherical" "spherical" "spherical" "spherical" "spherical"
Type of preprocessing used to transform the
feature vectors.
Default value:
'normalization'
"normalization"
"normalization"
"normalization"
"normalization"
"normalization"
List of values: 'canonical_variates' "canonical_variates" "canonical_variates" "canonical_variates" "canonical_variates" "canonical_variates" , 'none' "none" "none" "none" "none" "none" , 'normalization' "normalization" "normalization" "normalization" "normalization" "normalization" , 'principal_components' "principal_components" "principal_components" "principal_components" "principal_components" "principal_components"
Preprocessing parameter: Number of transformed
features (ignored for Preprocessing Preprocessing Preprocessing Preprocessing Preprocessing preprocessing
= 'none' "none" "none" "none" "none" "none" and Preprocessing Preprocessing Preprocessing Preprocessing Preprocessing preprocessing
= 'normalization' "normalization" "normalization" "normalization" "normalization" "normalization" ).
Default value: 10
Suggested values: 1, 2, 3, 4, 5, 8, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100
Restriction: NumComponents >= 1
Seed value of the random number generator that
is used to initialize the GMM with random
values.
Default value: 42
* Classification with Gaussian Mixture Models
create_class_gmm (NumDim , NumClasses, [1,5], 'full', 'none',\
NumComponents, 42, GMMHandle)
* Add the training data
for J := 0 to NumData-1 by 1
* Features := [...]
* ClassID := [...]
add_sample_class_gmm (GMMHandle, Features, ClassID, Randomize)
endfor
* Train the GMM
train_class_gmm (GMMHandle, 100, 0.001, 'training', 0.0001, Centers, Iter)
* Classify unknown data in 'Features'
classify_class_gmm (GMMHandle, Features, 1, ID, Prob, Density, KSigmaProb)
clear_class_gmm (GMMHandle)
If the parameters are valid, the operator create_class_gmm create_class_gmm CreateClassGmm create_class_gmm CreateClassGmm CreateClassGmm
returns the value 2 (H_MSG_TRUE). If necessary an exception is
raised.
add_sample_class_gmm add_sample_class_gmm AddSampleClassGmm add_sample_class_gmm AddSampleClassGmm AddSampleClassGmm ,
add_samples_image_class_gmm add_samples_image_class_gmm AddSamplesImageClassGmm add_samples_image_class_gmm AddSamplesImageClassGmm AddSamplesImageClassGmm
create_class_mlp create_class_mlp CreateClassMlp create_class_mlp CreateClassMlp CreateClassMlp ,
create_class_svm create_class_svm CreateClassSvm create_class_svm CreateClassSvm CreateClassSvm
clear_class_gmm clear_class_gmm ClearClassGmm clear_class_gmm ClearClassGmm ClearClassGmm ,
train_class_gmm train_class_gmm TrainClassGmm train_class_gmm TrainClassGmm TrainClassGmm ,
classify_class_gmm classify_class_gmm ClassifyClassGmm classify_class_gmm ClassifyClassGmm ClassifyClassGmm ,
evaluate_class_gmm evaluate_class_gmm EvaluateClassGmm evaluate_class_gmm EvaluateClassGmm EvaluateClassGmm ,
classify_image_class_gmm classify_image_class_gmm ClassifyImageClassGmm classify_image_class_gmm ClassifyImageClassGmm ClassifyImageClassGmm
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.
Foundation