kha {kernlab} | R Documentation |
Kernel Hebbian Algorithm is a nonlinear iterative algorithm for principal component analysis.
## S4 method for signature 'formula': kha(x, data = NULL, na.action, ...) ## S4 method for signature 'matrix': kha(x, kernel = "rbfdot", kpar = list(sigma = 0.1), features = 5, eta = 0.005, th = 1e-4, maxiter = 10000, verbose = FALSE, na.action = na.omit, ...)
x |
The data matrix indexed by row or a formula descibing the model. Note, that an intercept is always included, whether given in the formula or not. |
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 the inner product in feature space between two
vector arguments (see kernels ).
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 :
|
features |
Number of features (principal components) to return. (default: 5) |
eta |
The hebbian learning rate (default : 0.005) |
th |
the smallest value of the convergence step (default : 0.0001) |
maxiter |
the maximum number of iterations. |
verbose |
print convergence every 100 iterations. (default : FALSE) |
na.action |
A function to specify the action to be taken if NA s 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 |
The original form of KPCA can only be used on small data sets since it requieres the estimation of the eigenvectors of a full kernel matrix. The Kernel Hebbian Algorithm iteratively estimates the Kernel Principal Components with only linear order memory complexity. (see ref. for more details)
An S4 object containing the principal component vectors along with the corresponding normalization values.
pcv |
a matrix containing the principal component vectors (column wise) |
eig |
The normalization values |
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
Kwang In Kim, M.O. Franz and B. Schölkopf
Kernel Hebbian Algorithm for Iterative Kernel Principal Component Analysis
Max-Planck-Institut für biologische Kybernetik, Tübingen (109)
http://www.kyb.tuebingen.mpg.de/publications/pdfs/pdf2302.pdf
# another example using the iris data(iris) test <- sample(1:150,20) kpc <- kha(~.,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(predict(kpc,iris[,-5]),col=as.integer(iris[,5]),xlab="1st Principal Component",ylab="2nd Principal Component")