Finite mixture modeling and model-based clustering of matrices based on matrix Gaussian mixture and matrix transformation mixture models.

Description

The utility of this package is the clustering of random matrices. Finite mixture modeling and model-based clustering based on matrix Gaussian mixtures and matrix transformation mixtures are employed.

Details

Function 'MatTrans.init' runs the initialization for the EM algorithm.

Function 'MatTrans.EM' runs the EM algorithm for matrix-variate mixtures to cluster matrices.

Author(s)

Xuwen Zhu and Volodymyr Melnykov.

Maintainer: Xuwen Zhu <xuwen.zhu@louisville.edu>

IMDb data

Description

Data collected from IMDb.com on the ratings of 105 popular comedy movies.

Usage

data(IMDb)

Format

A list of 2 objects: Y and name, where Y represents the data array of ratings and name represents the comedy movie names. Y is the of dimensionality 2 x 4 x 105 with ratings on 105 movies from female and male by age groups 0-18, 18-29, 30-44, 45+.

Details

The data are publicly available on www.IMDb.com.

Examples

data(IMDb)

EM algorithm for matrix clustering

Description

Runs the EM algorithm for matrix clustering

Usage

MatTrans.EM(Y, initial = NULL, la = NULL, nu = NULL, 
model = NULL, trans = "None", la.type = 0, 
row.skew = TRUE, col.skew = TRUE, tol = 1e-05, 
short.iter = NULL, long.iter = 1000, all.models = TRUE, 
size.control = 0, silent = TRUE)

Arguments

Details

Runs the EM algorithm for modeling and clustering matrices for a provided dataset. Both matrix Gaussian mixture, matrix Power mixture and matrix Manly transformation mixture can be employed. The user should use the MatTrans.init() function to get initial parameters and input them as 'initial'. In the case when transformation parameters are not provided but 'trans' is specified to be 'Power' or 'Manly', 'la' and 'nu' take value of 0.5. 'model' can be specified as 'X-XXX-XX'. The first digit 'X' stands for the mean structure. It is either 'G': general mean or 'A': additive mean. The second 'XXX' specifies the variance-covariance Sigma. There are 14 options including EII, VII, EEI, VEI, EVI, VVI, EEE, EVE, VEE, VVE, EEV, VEV, EVV and VVV with detailed explanation as follows: "EII" spherical, equal volume "VII" spherical, unequal volume "EEI" diagonal, equal volume and shape "VEI" diagonal, varying volume, equal shape "EVI" diagonal, equal volume, varying shape "VVI" diagonal, varying volume and shape "EEE" ellipsoidal, equal volume, shape, and orientation "EVE" ellipsoidal, equal volume and orientation (*) "VEE" ellipsoidal, equal shape and orientation (*) "VVE" ellipsoidal, equal orientation (*) "EEV" ellipsoidal, equal volume and equal shape "VEV" ellipsoidal, equal shape "EVV" ellipsoidal, equal volume (*) "VVV" ellipsoidal, varying volume, shape, and orientation The last 2-digit 'XX' specifies the variance-covariance Psi. There are 8 options including II, EI, VI, EE, VE, EV, VV, AR. The user can specify the 'model' to be for example 'X-VVV-EV', then both 'G' and 'A' mean structures will be fitted while Sigma and Psi are fixed at 'VVV' and 'EV', respectively. Similarly, 'model' can be specified as 'G-XXX-EV' or 'G-VVV-XX' for selection of Sigma and Psi structures.

Value

No return value, called for side effects

Initialization for the EM algorithm for matrix clustering

Description

Runs the initialization for the EM algorithm for matrix clustering

Usage

MatTrans.init(Y, K, n.start = 10, scale = 1)

Arguments

Details

Random starts are used to obtain different starting values. The number of clusters, the skewness parameters, and number of random starts need to be specified. In the case when transformation parameters are not provided, the function runs the EM algorithm without any transformations, i.e., it is equivalent to the EM algorithm for a matrix Gaussian mixture. Notation: n - sample size, p x T - dimensionality of the random matrices, K - number of mixture components.

Value

Examples

set.seed(123)
data(crime)
Y <- crime$Y[c(2,7),,] / 1000
p <- dim(Y)[1]
T <- dim(Y)[2]
n <- dim(Y)[3]
K <- 2
init <- MatTrans.init(Y, K = K, n.start = 2)

Mean coordinate plot

Description

Mean coordinate plot provided for the best fitted model returned by MatTrans.EM model.

Usage

MatTrans.plot(X, model = NULL, xlab = "", 
ylab = "", rownames = NULL, colnames = NULL, 
lwd.obs = 0.8, lwd.mean = 2, line.cols = NULL, ...)

Arguments

Details

Provides the mean profile plot for the fitted data by MatTrans.EM model.

Value

No return value, called for side effects

Salary data

Description

Data collected from the Chronicle of Higher Education web site reporting the average faculty salaries from 696 universities presented in the form of a 2 by 3 by 13 -dimensional tensor.

Usage

data(Salary)

Format

A list of 2 objects: Y, uni_info. Y represents the salary data array from 696 universities. uni_info has the university names, state and category. Y is of dimensionality 2 by 3 by 13 categorized by the following factors: gender (Male, Female), professor rank (Assistant, Associate, Full), and academic year (2003-2004,2015-2016).

Details

The data have been made publicly available by the Chronicle of Higher Education web site.

Examples

data(Salary)

Crime data

Description

Data collected by FBI's Uniform Crime on the violent and property crimes of 236 cities.

Usage

data(crime)

Format

A list of 3 objects: Y, department and state. Y represents the crime rate data array from 236 cities. Department is the police department names and state represents the states where each city is located at. Y is of dimensionality 10 x 13 x 236 with 236 crime rates on the following 10 variables from year 2000 through 2012.

Population

Population of each city;

Violent Crime rate

Total number of violent crimes;

Murder and non-negligent manslaughter rate

Number of murders;

Forcible rape rate

Number of rape crimes;

Robbery rate

Number of robberies;

Aggravated assault rate

Number of assaults;

Property crime rate

Total number of property crimes;

Burglary rate

Number of burglary crimes;

Larceny-theft rate

Number of theft crimes;

Motor vehicle theft rate

Number of vehicle theft crimes;

Details

The data have been made publicly available by FBI's Uniform Crime Reports.

Examples

data(crime)

Functions for Printing or Summarizing Objects

Description

EM classes for printing and summarizing objects.

Usage

## S3 method for class 'EM'
print(x, ...)
## S3 method for class 'EM'
summary(object, ...)

Arguments

Details

Some useful functions for printing and summarizing results.

Value

No return value, called for side effects

See Also

MatTrans.EM.