inchol {kernlab} | R Documentation |
inchol
computes the incomplete Cholesky decomposition
of the kernel matrix from a data matrix.
inchol(x, kernel="rbfdot", kpar=list(sigma=0.1), tol = 0.001, maxiter = dim(x)[1], blocksize = 50, verbose = 0)
x |
The data matrix indexed by row |
kernel |
the kernel function used in training and predicting.
This parameter can be set to any function, of class kernel ,
which computes the inner product in feature space 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 :
|
tol |
algorithm stops when remaining pivots bring less accuracy
then tol (default: 0.001) |
maxiter |
maximum number of iterations and colums in Z |
blocksize |
add this many columns to matrix per iteration |
verbose |
print info on algorithm convergence |
An incomplete cholesky decomposition calculates Z where K= ZZ' K being the kernel matrix. Since the rank of a kernel matrix is usually low, Z tends to be smaller then the complete kernel matrix. The decomposed matrix can be used to create memory efficient kernel-based algorithms without the need to compute and store a complete kernel matrix in memory.
An S4 object of class "inchol" which is an extension of the class "matrix". The object is the decomposed kernel matrix along with the slots :
pivots |
Indices on which pivots where done |
diagresidues |
Residuals left on the diagonal |
maxresiduals |
Residuals picked for pivoting |
slots can be accessed either by object@slot
or by accessor functions with the same name (e.g., pivots(object))
Alexandros Karatzoglou (based on Matlab code by
S.V.N. (Vishy) Vishwanathan and Alex Smola)
alexandros.karatzoglou@ci.tuwien.ac.at
code{csi}, code{inchol-class}, chol
data(iris) datamatrix <- as.matrix(iris[,-5]) # initialize kernel function rbf <- rbfdot(sigma=0.1) rbf Z <- inchol(datamatrix,kernel=rbf) dim(Z) pivots(Z) # calculate kernel matrix K <- crossprod(t(Z)) # difference between approximated and real kernel matrix (K - kernelMatrix(kernel=rbf, datamatrix))[6,]