kPCA: Kernel PCA

In kerntools: Kernel Functions and Tools for Machine Learning Applications

Kernel PCA

Description

'kPCA()' computes the kernel PCA from a kernel matrix and, if desired, produces a plot. The contribution of the original variables to the Principal Components (PCs), sometimes referred as "loadings", is NOT returned (to do so, go to 'kPCA_imp()').

Usage

kPCA(
  K,
  center = TRUE,
  Ktest = NULL,
  plot = NULL,
  y = NULL,
  colors = "black",
  na_col = "grey70",
  title = "Kernel PCA",
  pos_leg = "right",
  name_leg = "",
  labels = NULL,
  ellipse = NULL
)

Arguments

K	Kernel matrix (class "matrix").
center	A logical value. If TRUE, the variables are zero-centered before the PCA. (Defaults: TRUE).
Ktest	(optional) An additional kernel matrix corresponding to test samples, with dimension Ntest x Ntraining. These new samples are projected (using the color defined by 'na_col') over the kernel PCA computed from K. Remember than the data that generated 'Ktest' should be centered beforehand, using the same values used for centering 'K'.
plot	(optional) A 'ggplot2' is displayed. The input should be a vector of integers with length 2, corresponding to the two Principal Components to be displayed in the plot.
y	(optional) A factor, or a numeric vector, with length equal to 'nrow(K)' (number of samples). This parameter allows to paint the points with different colors.
colors	A single color, or a vector of colors. If 'y' is numeric, a gradient of colors between the first and the second entry will be used to paint the points. (Defaults: "black").
na_col	Color of the entries that have a NA in the parameter 'y', or the entries corresponding to 'Ktest' (when 'Ktest' is not NULL). Otherwise, this parameter is ignored.
title	Plot title.
pos_leg	Position of the legend.
name_leg	Title of the legend. (Defaults: blank)
labels	(optional) A vector of the same length than nrow(K). A name will be displayed next to each point.
ellipse	(optional) A float between 0 and 1. An ellipse will be drawn for each group of points defined by 'y'. Here 'y' should be of class "factor." This parameter will indicate the spread of the ellipse.

Details

As the ordinary PCA, kernel PCA can be used to summarize, visualize and/or create new features of a dataset. Data can be projected in a linear or nonlinear way, depending on the kernel used. When the kernel is 'Linear()', kernel PCA is equivalent to ordinary PCA.

Value

A list with two objects:

* The PCA projection (class "matrix"). Please note that if K was computed from a NxD table with N > D, only the first N-D PCs may be useful.

* (optional) A 'ggplot2' plot of the selected PCs.

Examples

dat <- matrix(rnorm(150),ncol=50,nrow=30)
K <- Linear(dat)

## Projection's coordinates only:
pca <- kPCA(K)

## Coordinates + plot of the two first principal components (PC1 and PC2):
pca <- kPCA(K,plot=1:2, colors = "coral2")
pca$plot

kerntools documentation built on April 3, 2025, 7:52 p.m.