Multivariate Analysis Toolbox for Matlab®

We have tried to break down a typical process of multivariate data analysis, in trying to identify key components. We then built a fully object-oriented toolbox, with an object fitting each of those key components.

Data objects. We have identified three entities, which are the building blocks of any multivariate data process. The sampleset object carries information about the different samples, also called observations, conditions, or experiments. grouping object carries information about labeling of the samples, i.e., their association with specific clusters. The measurements themselves are in a data matrix. The datamatrix object is the general framework of a datamatrix, from which more specialized data matrices are derived by object-oriented inheritence. These more specialized data matrices encompass most of the data organization forms one may encounter. The vsmatrix object describes a rectangular two-way matrix of variables-by-samples. For example, a result of a gene array experiment in the form of genes-by-conditions will be represented in our toolbox by a vsmatrix object. The ssmatrix object describes relationships between samples. For example, a distance matrix will be represented in our toolbox as a ssmatrix. The vvmatrix object describes relationships between variables. For example, a correlation matrix will be represented in our toolbox as a vvmatrix.

Graph theory. The graph object describes a general mathematical graph. This toolbox includes more specific graphs (such as digraphs and trees) that are derived from this general object.

Pairwise data objects. These objects describe specific forms of pairwise data, and are all derived from either ssmatrix or vvmatrix (see above). The covmatrix object describes a covariance or a correlation matrix. The distmatrix object describes a distance matrix. The dissimatrix and simatrix objects describe pairwise dissimilarity or similarity information, respectively.

Dimensionality reduction algorithms. Each object in this group stands for a particular dimensionality reduction technique. Currently available are pcatrans that makes principal component analysis (PCA), wpcatrans that makes weighted principal component analysis (wPCA), and fishtrans that identifies discriminant direction according to the Fisher linear discriminant analysis.

Statistics. This portion of the toolbox includes general statistical functions, mainly various hypothesis testing procedures, as well as the object ctable that describes a contingency table.

Navigate to:     General Description     List of Objects     List of Functions     Download

Core objects:

grouping

labeling of the data according to a classification scheme

sampleset

information about samples (observations, conditions, experiments)

variable

information about variables (features, coordinates)

Core data objects:

datamatrix

a two-way matrix object

ssmatrix

samples-by-samples two-way datamatrix (e.g., distance matrix)

vsmatrix

variable-by-samples two-way datamatrix (typical data matrix)

vvmatrix

variables-by-variables two-way datamatrix (e.g., correlation matrix)

dataset

repository of information regarding a certain dataset

graph

general undirected graph

digraph

general directed graph

tree

binary tree

bintree

binary tree

Pairwise data objects:

covmatrix

covariance matrix (inherits vvmatrix)

dissimatrix

dissimilarity matrix (inherits ssmatrix)

distmatrix

distance matrix (inherits ssmatrix)

simatrix

similarity matrix (inherits ssmatrix)

Dimensionality reduction algorithms:

lintrans

general dimensionality reduction by linear transformation

fishtrans

Fisher linear discriminant analysis

pcatrans

principal component analysis (PCA)

wpcatrans

weighted principal component analysis (wPCA)

Statistics:

ctable

contingency table

Combinatorics:

multinom

computes the multinomial coefficient.

Data manipulations:

lineup

ranks a vector in increasing order.

majority

finds the most frequent entry.

subs_incomp_data

substitue given data in an incompleted data array

subsample

picks up at random a subsample of a vector.

substitute

substitutes values in a list with a different set of values.

Graph Theory:

chowliu

applies the Chow-Liu algorithm.

code2dag

finds the DAG associated with a DAG-code.

code2rank

finds the rank of a DAG-code.

dispdagcode

displays a DAG code to the screen.

enumdagcodes

enumerates all DAG codes for a fixed number of nodes.

enummarkovclasses

enumerates all DAG codes for a fixed number of nodes.

nodags

computes the number of DAGs with fixed number of nodes.

rank2code

finds the DAG-code whose rank is {r}.

thd2wgt

computes, given THD, a default weight matrix.

wgt2thd

computes, given weights, a default THD matrix.

Grouping:

group

turns a list into assignment vector and naming cell array.

Hypothesis testing:

testbinom

computes the p-value of testing a binomial parameter.

testchi2hist

uses the chi2 test to compare a histograms to a standard.

testchi2hists

uses the chi2 test to compare two histograms.

testchi2independence

computes the p-value of independence hypothesis.

testfisherexact

computes the p-value of Fisher's exact test (© A. Trujillo-Ortiz et al.).

testfisheromnibus

computes p-value for the Fisher Omnibus test.

testkshist

uses KS test to compare a histograms to a standard.

testkshists

uses KS test to compare two histograms.

testmultinom

computes the p-value of testing multinomial parameters.

Information Theory:

centropy

computes the conditional entropy between two variables.

emutualentropy

estimates pairwise mutual entropy

entropy

computes the entropy of a distribution.

kdiv

computes the K-divergence between distributions p and q.

kl

computes the relative entropy.

ldiv

computes the L-divergence between distributions p and q.

Linear transformations:

fa_engin

performs factor analysis on the data.

factorscores

estimate the scores after factor analysis.

fish_engin

performs Fisher transformation of a grouped dataset.

pca_engin

performs PCA analysis on the data.

Pairwise Relationships:

distmat

calculates distance matrix.

Regression analysis:

regress1d

linearly regress one variable on another.

Statistics:

allstats

computes all common statistics (© D.C. Hanselman).

fdr

calculates

kendall

computes the Kendall rank correlation matrix.

pearson

computes the Pearson (linear) correlation matrix.

spearman

computes the Spearman rank correlation matrix.

Visualization:

scatter2d_engin

the engine used for 2D scatter plots.

scatter3d_engin

the engine used for 3D scatter plots.

The toolbox is freely available from this site. The latest release is MVA_13Sep2010.
Prerequisite: the toolbox General Utilities.

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