| kpca {kernlab} | R Documentation |
Kernel Principal Components Analysis is a nonlinear form of principal component analysis.
## S4 method for signature 'formula':
kpca(x, data = NULL, na.action, ...)
## S4 method for signature 'matrix':
kpca(x, kernel = "rbfdot", kpar = list(sigma = 0.1), features = 0,
th = 1e-4, na.action = na.omit, ...)
## S4 method for signature 'kernelMatrix':
kpca(x, features = 0, th = 1e-4, ...)
## S4 method for signature 'list':
kpca(x, kernel = "stringdot", kpar = list(length = 4, lambda = 0.5), features = 0, th = 1e-4, na.action = na.omit, ...)
x |
the data matrix indexed by row or a formula descibing the
model, or a kernel Matrix of class kernelMatrix, or a list of character vectors |
data |
an optional data frame containing the variables in the model (when using a formula). |
kernel |
the kernel function used in training and predicting.
This parameter can be set to any function, of class kernel, which computes a dot product between two
vector arguments. kernlab provides the most popular kernel functions
which can be used by setting the kernel parameter to the following
strings:
|
kpar |
the list of hyper-parameters (kernel parameters).
This is a list which contains the parameters to be used with the
kernel function. Valid parameters for existing kernels are :
|
features |
Number of features (principal components) to return. (default: 0 , all) |
th |
the value of the eigenvalue under which principal components are ignored (only valid when features = 0). (default : 0.0001) |
na.action |
A function to specify the action to be taken if NAs are
found. The default action is na.omit, which leads to rejection of cases
with missing values on any required variable. An alternative
is na.fail, which causes an error if NA cases
are found. (NOTE: If given, this argument must be named.) |
... |
additional parameters |
Using kernel functions one can efficiently compute
principal components in high-dimensional
feature spaces, related to input space by some non-linear map.
The data can be passed to the kpca function in a matrix or a
data.frame, in addition kpca also supports input in the form of a
kernel matrix of class kernelMatrix or as a list of character
vectors where a string kernel has to be used.
An S4 object containing the principal component vectors along with the corresponding eigenvalues.
pcv |
a matrix containing the principal component vectors (column wise) |
eig |
The corresponding eigenvalues |
rotated |
The original data projected (rotated) on the principal components |
xmatrix |
The original data matrix |
all the slots of the object can be accessed by accessor functions.
The predict function can be used to embed new data on the new space
Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at
Schoelkopf B., A. Smola, K.-R. Mueller :
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation 10, 1299-1319
http://mlg.anu.edu.au/~smola/papers/SchSmoMul98.pdf
kcca, pca
# another example using the iris data(iris) test <- sample(1:150,20) kpc <- kpca(~.,data=iris[-test,-5],kernel="rbfdot",kpar=list(sigma=0.2),features=2) #print the principal component vectors pcv(kpc) #plot the data projection on the components plot(rotated(kpc),col=as.integer(iris[-test,5]),xlab="1st Principal Component",ylab="2nd Principal Component") #embed remaining points emb <- predict(kpc,iris[test,-5]) points(emb,col=as.integer(iris[test,5]))