smart (version 1.0.1)

TCA: Transelliptical Component Analysis

Description

A function to conduct Transelliptical Component Analysis

Usage

TCA(x, K, para, method = "kendall", algorithm = "tp", max.iter = 200, verbose = TRUE, eps.conv = 0.001)

Arguments

x

The n by d data matrix or d by d covariance matrix from the input

K

Number of components

para

A vector of length K, indicating the number of sparse loadings.

method

Method to be used to estimating the correlation matrix with 5 options: pearson, ns, npn, spearman and kendall. kendall as default.

algorithm

Algorithm to be used to obtain sparse loadings with 3 options: sp, spca and pmd. tp as default.

max.iter

Maximum number of iterations.

verbose

If verbose = FALSE, tracing information printing is disabled. The default value is TRUE.

eps.conv

Convergence criterion.

Value

cov.input

An indicator of the sample covariance.

loadings

The loadings of the sparse PCs.

pev

An indicator of the sample covariance.

PC

Projected PCs. existing if cov.input=TRUE.

method

The method used in estimating the correlation matrix.

algorithm

The algorithm used in obtaining the sparse loadings.

K

The number of components.

Details

PCA and Sparse PCA is sensitive to modeling assumption, outliers, missing values data dependency. We propose an alternative way using rank-based methods including ns, npn, spearman and kendall to approximate the correlation matrix. Details are refered to Han,F. and Liu,H. (2012). Three sparse PCA algorithms are used: truncated power (Yuan, X. and Zhang, T. (2011)), spca(Zou,H., Hastie, T., and Tibshirani, R. (2006)) and pmd (Witten, D., Tibshirani, R., and Hastie, T. (2009)).

References

1. Witten, D., Tibshirani, R., and Hastie, T., A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 2. Yuan, X. and Zhang, T. (2011). Truncated power method for sparse eigenvalue problems. Techinal Report, Rutgers, 2011. 3. Zou, H., Hastie, T. and Tibshirani, R. Sparse principal component analysis. JCGS, 2006.

Examples

x=matrix(rnorm(20000),100)
fit=TCA(x,K=6, para=c(10,10,10,5,5,5))
fit
plot(fit)