kernlab (version 0.9-24)

kfa: Kernel Feature Analysis

Description

The Kernel Feature Analysis algorithm is an algorithm for extracting structure from possibly high-dimensional data sets. Similar to kpca a new basis for the data is found. The data can then be projected on the new basis.

Usage

"kfa"(x, data = NULL, na.action = na.omit, ...)
"kfa"(x, kernel = "rbfdot", kpar = list(sigma = 0.1), features = 0, subset = 59, normalize = TRUE, na.action = na.omit)

Arguments

x

The data matrix indexed by row or a formula describing 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 an 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:

• rbfdot Radial Basis kernel function "Gaussian"
• polydot Polynomial kernel function
• vanilladot Linear kernel function
• tanhdot Hyperbolic tangent kernel function
• laplacedot Laplacian kernel function
• besseldot Bessel kernel function
• anovadot ANOVA RBF kernel function
• splinedot Spline kernel

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 :

• sigma inverse kernel width for the Radial Basis kernel function "rbfdot" and the Laplacian kernel "laplacedot".
• degree, scale, offset for the Polynomial kernel "polydot"
• scale, offset for the Hyperbolic tangent kernel function "tanhdot"
• sigma, order, degree for the Bessel kernel "besseldot".
• sigma, degree for the ANOVA kernel "anovadot".

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)

subset

the number of features sampled (used) from the data set

normalize

normalize the feature selected (default: TRUE)

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

Value

kfa returns an object of class kfa containing the features selected by the algorithm.

xmatrix

contains the features selected

alpha

contains the sparse alpha vector

The predict function can be used to embed new data points into to the selected feature base.

Details

Kernel Feature analysis is similar to Kernel PCA, but instead of extracting eigenvectors of the training dataset in feature space, it approximates the eigenvectors by selecting training patterns which are good basis vectors for the training set. It works by choosing a fixed size subset of the data set and scaling it to unit length (under the kernel). It then chooses the features that maximize the value of the inner product (kernel function) with the rest of the patterns.

References

Alex J. Smola, Olvi L. Mangasarian and Bernhard Schoelkopf Sparse Kernel Feature Analysis Data Mining Institute Technical Report 99-04, October 1999 ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/99-04.ps

See Also

kpca, kfa-class

Examples

data(promotergene)
f <- kfa(~.,data=promotergene,features=2,kernel="rbfdot",
         kpar=list(sigma=0.01))
plot(predict(f,promotergene),col=as.numeric(promotergene[,1]))