# kfa: Kernel Feature Analysis In kernlab: Kernel-Based Machine Learning Lab

 kfa R Documentation

## 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

```## S4 method for signature 'formula'
kfa(x, data = NULL, na.action = na.omit, ...)

## S4 method for signature 'matrix'
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 `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

### 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.

### 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.

### Author(s)

Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at

### 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

`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]))
```

kernlab documentation built on Feb. 16, 2023, 10:13 p.m.