MaxSkew: MaxSkew: skewness-based projection pursuit

Description

Finds Orthogonal Data Projections with Maximal Skewness

Usage

MaxSkew(data, iterations, components, plot)

Arguments

data

Data matrix where rows and columns represent units and variables.

iterations

It is a positive integer

components

Number of orthogonal projections maximizing skewness. It is a positive integer smaller than the number of variables.

plot

Dichotomous variable: TRUE/FALSE. If plot is set equal to TRUE (FALSE) the scatterplot appears (does not appear) in the output.

Value

projectionmatrix

Matrix of projected data. The i-th row represents the i-th unit, while the j-th column represents the j-th projection.

pairs(projectionmatrix[,2:i],labels=values,main="Projections")

It is the multiple scatterplot of the projections maximizing skewness.

.projectionBIV

Vector of projected data when the original data are bivariate.The user can obtain a scatterplot of the projection by writing plot(.projectionBIV)

References

de Lathauwer L., de Moor B.and Vandewalle J. (2000). Onthebestrank-1andrank-(R_1,R_2,...R_N) approximation of high-order tensors. SIAM Jour. Matrix Ana. Appl. 21, 1324-1342.

Loperfido, N. (2010). Canonical Transformations of Skew-Normal Variates. Test 19, 146-165.

Loperfido, N. (2013). Skewness and the Linear Discriminant Function. Statistics and Probability Letters 83, 93-99.

Malkovich, J.F. and Afifi, A.A. (1973). On Tests for Multivariate Normality. J. Amer. Statist. Ass. 68, 176-179