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GMM.rar （19个子文件）

GMM

manual.pdf 222KB

GMM.H 910B

GMM.C 3KB

GMM

clust_io.h 2KB

subcluster.h 2KB

clust_util.c 5KB

clust_util.h 2KB

classify_util.c 5KB

eigen.c 5KB

alloc_util.h 449B

clust_io.c 6KB

SplitClasses.c 3KB

invert.c 3KB

alloc_util.c 3KB

clust_defs.h 4KB

classify_util.h 2KB

clust_invert.c 5KB

classify.c 3KB

subcluster.c 20KB

CLUSTER: An Unsupervised Algorithm

for Modeling Gaussian Mixtures

Charles A. Bouman

School of Electrical Engineering

Purdue University

West Lafayette IN 47906

bouman@ecn.purdue.edu

(765) 494-0340

http://www.ece.purdue.edu/~bouman

Version 2 - April 1997

Version 3 - September 1998

Version 3.2 - December 1999; May 2000 - manpage update

Version 3.3 - September 2000 - manpage update

Version 3.4 - October 2001 - manpage update

Version 3.6.4 - July 2005 - manpage update

Developed by:

Charles A. Bouman; School of ECE, Purdue University

Michael Shapiro; NCSA

Gregory W. Cook; School of ECE, Purdue University

C. Brian Atkins; School of ECE, Purdue University

Hui Cheng; School of ECE, Purdue University

Jennifer G. Dy; School of ECE, Purdue University

Sean Borman; Department of Electrical Engineering, University of Notre Dame

Permission to use, copy, modify, and distribute this software and its documentation for any purpose,

without fee, and without written agreement is hereby granted, provided that the above copyright notice and

the following two paragraphs appear in all copies of this software.

In no event shall Purdue University be liable to any party for direct, indirect, special, incidental, or

consequential damages arising out of the use of this software and its documentation, even if Purdue University

has been advised of the possibility of such damage.

Purdue University speciﬁcally disclaims any warranties, including, but not limited to, the implied war-

ranties of merchantability and ﬁtness for a particular purpose. The software provided hereunder is on an “as

is” basis, and Purdue Univeristy has no obligation to provide maintenance, support, updates, enhancements,

or modiﬁcations.

Contents

1 Introduction 3

2 Demo 4

2.1 example1 - GMM Parameter Estimation . . . . . . . . . . . . . . . . . . . . 4

2.2 example2 - ML Classiﬁcation using GMM Models . . . . . . . . . . . . . . . 4

2.3 example3 - Unsupervised Clustering . . . . . . . . . . . . . . . . . . . . . . . 5

3 Clustering 5

4 Program Manual Pages 10

5 Example Parameter File 12

A Appendix: Parameter Estimation for Gaussian Mixture Models 14

1 Introduction

The Cluster software package is used to automatically estimate the parameters of a Gaus-

sian mixture model from sample data. This process is essentially similar to conventional

clustering except that it allows cluster parameters to be accurately estimated even when the

clusters overlap substantially. The resulting mixture model is useful for a variety of applica-

tions including texture and multispectral image segmentation (see the SMAP segmentation

package.)

The “clust” program applies the expectation-maximization (EM) algorithm together with

an agglomerative clustering strategy to estimate the number of clusters which best ﬁt the

data. The estimation is based on the Rissenen order identiﬁcation criteria known as mini-

mum discription length (MDL). This is equivalent to maximum-likelihood (ML) estimation

when the number of clusters is ﬁxed, but in addition it allows the number of clusters to be

accurately estimated.

The package also includes two addition programs which make “clust” more useful. The

program “classify” can be used to perform maximum likelihood classiﬁcation from the pa-

rameter ﬁles generated by “clust”, and the program “SplitClasses” can be used along with

“clust” and “classify” to perform unsupervised classiﬁcation.

The software package is written in ANSI-C and is set up to compile on a wide variety of

unix platforms. The main ﬁle directory contains the following subdirectories.

documentation - This subdirectory contains this manual and other documentation.

example1 - Example showing how to run “clust” program. This subdirectory contains

a shell script that runs a simple example showing how the ”clust” program can be used

to estimate the parameters of a Gaussian mixture model from training data.

example2 - Example showing how to use the “cluster” and “classify” programs to-

gether to classify vectors. This subdirectory contains a shell script that ﬁrst runs the

“cluster” to estimate two Gaussian mixture models (GMM). It then runs the “classify”

program to perform maximum likelihood classiﬁcation of vectors from the two GMM

distributions.

example3 - Example showing how to use the “clust”, “classify”, and “SplitClasses” to

perform unsupervised classiﬁcation of data vectors. First “clust” forms a GMM. Next

”SplitClasses” separates each component of the GMM into a separate class. Finally,

“classify” is used to classify the original training vectors.

Makeﬁle - This makeﬁle constructs the compiled binaries. These makeﬁles have been

tested for the gcc compiler under linux, but it should also work with little or no

modiﬁcation on other platforms supporting ANSI-C code.

src - This subdirectory contains the ANSI-C source code and header ﬁles required for

the “clust” program and library.

2 Demo

The Cluster software package contains a number of simple demos which illustrate its use.

To run these examples, simply execute the shell script “exampleN/Demo” where “N” cor-

responds to the demo number. If you are using MS Windows, then you can just read the

contents of the demo ﬁles, and type in the commands manually. In some cases, the demo

ﬁles contain matlab commands that are commented out. People with Matlab can use the

included Matlab commands, and associated Matlab scripts, to perform additional functions;

but everything in the package runs without Matlab.

2.1 example1 - GMM Parameter Estimation

This example shows how to use the program “clust” to cluster data vectors by estimating the

parameters of a Gaussian mixture model. The program extracts mixture model parameters

for the sample vectors contained in the ﬁle “data”. The demo runs four examples, and the

GMM parameters resulting from these examples are stored in the four output ﬁles listed

below:

params - This ﬁle is the default method which estimates the number of clusters using

the MDL method and uses full covariance matrix for each cluster.

params full5 - This method generates a user speciﬁed number of clusters (i.e. 5) and

a full covariance matrix for each cluster.

params diag - This method estimates the number of clusters using the MDL method

and uses a diagonal covariance matrix for each cluster. This option is useful when the

amount of training data is limited.

params diag5 - This method generates a user speciﬁed number of clusters (i.e. 5)

and uses a diagonal covariance matrix for each cluster. This option is useful when the

amount of training data is limited.

All parameter ﬁles are ASCII and human readable. The speciﬁc formate of the output ﬁles

is discussed in section 5.

The demo can also generate new sample data using matlab. To do this, simply run the

m-ﬁle “mk data.m”.

2.2 example2 - ML Classiﬁcation using GMM Models

This example shows how the “classify” program can be used to classify test vectors into

classes where each class is model with a GMM distribution. To do this, we ﬁrst run “clust”

to estimate the GMM parameters for two diﬀerent training sets, e.g. one GMM model for

each class. The parameters for each of the two GMM’s are stored in a single parameters

ﬁle. By viewing the “params” ﬁle in a text editor, you can see that the parameters for each

class are stored in a structure starting with the words “class” and ending with the words

“endclass”.

Once the GMM parameters are estimated for each class, they are passed to the “classify”

program. The “classify” program performs ML classiﬁcation of test vectors using these two

GMM classes. The “classify” program is easy to modify by any experienced C programmer,

so you can incorportate the classiﬁer into your own programs.

2.3 example3 - Unsupervised Clustering

This example shows how the Cluster package can be used to perform unsupervised clustering

of data vectors. First, a GMM model is extracted from the data vectors using the “clust”

algorithm. This produces a parameter ﬁle with a single class. However, this class typically

contains a number of multivariate Gaussian components. Each of these components is des-

ignated in the parameter ﬁle by “subclass” and “endsubclass”. The “SplitClasses” program

reads in the parameter ﬁle, separates each subclass into its own individual class, and stores

the resulting parameter ﬁle. Once this is done, the “classify” program can be used to classify

the vectors into each subcluster. This results in unsupervised clustering of the data vectors.

3 Clustering

The clust program is designed to process M distinct data sets in a single pass. The program

will extract a mixture model for each data set and store the M mixture models in a signal

parameter ﬁle. This is usefull for applications such as segmentation when each mixture

model represents one of M distinct classes that must be modeled.

In order to run the clust algorithm a data ﬁle must be created for each of the M data sets.

Each data ﬁle contains a series of vectors in ASCII ﬂoating point format and on separate

lines. Each vector should be a sample from the multivariate distribution of interest. The

clust program will use these data vectors to estimate a Gaussian mixture model that best ﬁts

the sample data in the corresponding ﬁle. The Gaussian mixture model is formed by adding

together multivariate Gaussian distributions each with diﬀerent mean and covariance. Each

of these component component distributions is a cluster (or subclass) of the distribution.

After a Gaussian mixture model has been extracted for each data set, the clust program

will then generate a params ﬁle which contains all the parameters of all M Gaussian mixture

distributions. Section 5 contains information on the contents of the parameter ﬁle.

The speciﬁcs of the algorithm are described in Appendix A; however, Fig. 1 illustrates

the basic operations performed in the clust program. The algorithm is started by initializing

with a set of cluster parameters and a user selected number of clusters. The cluster means

are generated by selecting the appropriate number of samples from the training data, and the

cluster covariances are set to all be equal to the covariance of the complete data set. After

this initialization, the algorithm enters a loop in which clusters are combined (or eliminated

when empty) until only one cluster remains.

Figs. 2 and 4 and Table 1 show the results of a simple experiment using the Cluster

algorithm. (This experiment is included as an example with the package. You may run this

example by executing the “example/Demo” ﬁle.) Figs. 2 shows a scatter plot of 500 samples

from a two dimensional random vector. The random vector is chosen to have a distribution

formed by the mixture of three bi-variate Gaussian distributions. Each component of the

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