`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()`).
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
)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.
Kernel matrix (class "matrix").
A logical value. If TRUE, the variables are zero-centered before the PCA. (Defaults: TRUE).
(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`.
(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.
(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.
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").
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.
Plot title.
Position of the legend.
Title of the legend. (Defaults: blank)
(optional) A vector of the same length than nrow(K). A name will be displayed next to each point.
(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.
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.
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
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