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Kernel PCA

Source: R/kernel_pca.R
kPCA.Rd

`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.

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.

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.

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