kpca {kernlab} | R Documentation |
Kernel Principal Components Analysis
Description
Kernel Principal Components Analysis is a nonlinear form of principal component analysis.
Usage
## 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, ...)
Arguments
x |
the data matrix indexed by row or a formula describing the
model, or a kernel Matrix of class |
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:
The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument. |
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 :
Hyper-parameters for user defined kernels can be passed through the kpar parameter as well. |
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 |
... |
additional parameters |
Details
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.
Value
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.
Note
The predict function can be used to embed new data on the new space
Author(s)
Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at
References
Schoelkopf B., A. Smola, K.-R. Mueller :
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation 10, 1299-1319
doi:10.1162/089976698300017467.
See Also
kcca
, pca
Examples
# 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]))