Wpca {WCluster}

Weighted PCA

Description

This function performs PCA on the given data matrix, with row and column weights.

Usage

Wpca(x, wrow = rep(1, nrow(x)), wcol = rep(1, ncol(x)), corr = FALSE)

Arguments

x

A data matrix (data frame, data table, matrix, etc) containing only entries of class numeric.

wrow

Row Weights: vector of length nrow(x) of weights for each observation in the dataset. Must be of class numeric or integer or table. If NULL, the default value is a vector of 1 with length nrow(x), i.e., weights equal 1 for all observations.

wcol

Column Weights: Vector of length ncol(x) of weights for each variable in the dataset. Must be of class numeric or integer or table. If NULL, the default value is a vector of 1 with length ncol(x), i.e., weights equal 1 for all columns.

corr

A logical value indicating whether to use correlation matrix. This is recommended when the column weights are not equal. The default value is FALSE.

Details

PCA with row and column weights is conducted by eigen method.

Value

A list containing the following components:

sdev

the standard deviations of the weighted principal components (i.e., the square roots of the eigenvalues of the weighted covariance/correlation matrix).

rotation

The matrix of the loading vectors for each of the weighted prinicipal components.

x

The weighted prinicipal components.

center, scale

the weighted centering and scaling used.

wrow, wcol

row weights and column weights used.

Author(s)

Javier Cabrera, Yajie Duan, Ge Cheng

References

Amaratunga, D., & Cabrera, J. (2009). Exploration and analysis of DNA microarray and protein array data. John Wiley & Sons (Vol. 605).

Cherasia, K. E., Cabrera, J., Fernholz, L. T., & Fernholz, R. (2022). Data Nuggets in Supervised Learning. In Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler (pp. 429-449). Cham: Springer International Publishing.

Beavers, T., Cheng, G., Duan, Y., Cabrera, J., Lubomirski, M., Amaratunga, D., Teigler, J. (2023). Data Nuggets: A Method for Reducing Big Data While Preserving Data Structure (Submitted for Publication)

Examples

    require(cluster)

    # The Ruspini data set from the package "cluster""
    x = as.matrix(ruspini)

    # assign random weights to observations
    w = sample(1:20,nrow(x),replace = TRUE)

    #PCA with observational weights
    res = Wpca(x, wrow = w)

    #weighted prinicipal components
    pc = res$x
    pc

    #loading vectors
    loadings = res$rotation
    loadings