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## Description

Principal component analysis of a kernel is a non-linear form related to the fundamentalComponent analysis.

## Use

` Method # S4 for formulaskpca (x, = data NULL, na.action, ...)  # S4 method for matrixkpca (x, kernel = Kpar "rbfdot", = list (sigma = 0,1),    = features 0, th means 1e-4, na.action = na.omit, ...)   # s4 method for kernelMatrixkpca (x, features is 0, th = 1e-4, ...)   # S4 method for listkpca (x, kernel is "stringdot", = kpar list (length = 4, lambda is 0.5),    equals 0, th = 1e-4, na.action means na.omit, ...)  `

## Arguments

x

the data matrix found for each row, or a formula containing Model or just a kernel matrix with the speed ` kernelMatrix ` or a list of charm vectors

data

optional frame data with reasons inSimulate this (if formula).

Kernel

kernel function used in learning predictions and. This parameter can be set with any kernel class function that computes the dot product with respect to two Vector arguments. kernlab offers the most common kernel featureswhich can be used very well by setting a kernel parameter to be as follows Channels:

• ` rbfdot ` The core of the radial basis follows the “Gaussian”

• ` polydot ` Kernel polynomial function

• ` vanilladot ` Linear Kernel Function

• ` tanhdot ` Tangent hyperbolic kernel function

• ` Laplacedot ` Laplace kernel function

• ` besseldot ` Bessel kernel function

• ` anovadot ` RBF Anova core function

• ` splinedot ` Spline kernel

A kernel parameter can sometimes refer to a single UDF. can be customized Kernel class by passing part of the function name as an argument.

kpar

hyperparameters report (kernel parameters). Here is a list of the types of parameters used The main function. Valid parameters for existing corn kernels:

• ` sigma ` reverse kernel for larger radial base Kernel function “rbfdot” as well as Laplace kernel “laplacedot”.

• ` Degree, scale, offset ` relative to the kernel of the “polydot” polynomial

• ` Scale, offset ` relative to the core of the hyperbolic tangent Successes with “tanhdot”

• ` Sigma, order, degree ` for the Bessel kernel “besseldot”.

• ` Sigma, degree `, which is for ANOVA core “anovadot”.

Hyperparameter users for specific kernels are easily accessible via kpar parameters also.

Characteristics

Number with feature components) (main for To revert to. (Default: 0 – all)

th

eigenvalue is below and this is also basic Things are ignored as valid (only when features = 0). (Default: 0.0001)

na.action

Function for specifying procedures to follow when < code> NA s is find. The default action is ` na.omit `, which will reject hits. with missing values ​​for each important variable. Alternative` na.fail ` leading to unintended ` NA ` casesto be found. If (Note: specified, this argument must have a name.)

## Value

the s4 object that contains the baseSome of the vectors, as well as the same eigenvalues.

pcv

matrix containing the main element of vectors (column sage)

eig

Associated eigenvalues ​​

rotates

Actual data is projected (rotated) onto required components

xmatrix

Source Data Matrix

all slots of objects can be called through accessor functions.

## Details

With kernel 1, functions can be efficiently computed Key Features in High Dimension Entity plots are linked to the input space through a series of nonlinear maps. Data can of course be sent to celebrate ` kpca ` in a ` matrix ` a or a. to be delivered` data.frame `, the ` kpca ` addon also provides input help asKernel matrix in class ` kernelMatrix ` or as a list of subscriber symbolsVectors requiring the use of a chained kernel.

## Sources

Schoelkopf B., A. Smola, K.-R. Müller: Nonlinear component as analysis of a problem with basic eigenvalues Nerve camJune 10, 1299-1319 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.1366

` kcca `, ` PC `

## Examples

` # DO NOT EXECUTE# another example of a new irisData (iris)Test <- sample (1: 150.20)kpc <- kpca (~., data = iris [-test, -5], kernel = "rbfdot",            kpar = list (sigma = 0.2), functions = 2)# print head vectorpcv (pda)# Track information projector component by componentgraph (rotation (kpc), col = as.integer (iris [-test, 5]),     xlab = "1st main component", ylab = "2nd main component")# Remaining scores are integratedemb <- forecasts (kpc, iris [test, -5])Points (emb, col = as.integer (iris [test, 5]))#`

is a matrix file that is indexed according to a formula or briefly describes a formula that Kernel model or class matrix ` kernelMatrix ` or case of character vectors

additional bike frame for transferring data with variables inoften a model (when using a formula).

A working kernel used in training and therefore in forecasting. This parameter can also be set for any function linkednoah with a kernel class that computes dept. product moved between two Vector arguments. kernlab offers many common kernel features sometimes it can be used with a kernel parameter, usually like this Channels:

• ` rbfdot ` Gaussian radial core kernel function

• ` polydot ` Kernel polynomial function

• ` vanilladot ` Linear Kernel Function

• ` tanhdot ` Tangent hyperbolic kernel function

• ` Laplacedot ` Laplace kernel function

• ` besseldot ` Bessel kernel function

• ` anovadot ` RBF Anova core function

• ` splinedot ` Spline kernel A kernel parameter can also be a user-defined parameter Program the kernel by passing the name of the function with one argument.

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• ` sigma ` inverse kernel for radial base width The position of the "rbfdot" kernel and the La kernelplaza "laplacedot".

• ` Degree, scale, offset ` for the "polydot" polynomial

• ` Scale, offset ` for the kernel of the hyperbolic tangent Tankdot function

• ` Sigma, order, degree ` for the Bessel kernel "besseldot".

• ` Sigma, degree ` of a person for ANOVA core "Anovadot".

Hyper settings users only for certain kernels can be used in. to be delivered The kpar parameter is just that good.

Number of functions (main components) up to To return to. (Default: nothing, everything)

the value of the part of the eigenvalue under the main Components are not taken into account (valid only if characteristics are equal to 0). (Default: 0.0001) Function if you want to specify the action to be carried over if ` NA ` is s find. The default action could be ` na.omit `, resulting in rejection due to cases with missing values ​​for each required variable. Alternativeequals ` na.fail `, which raises 1 on error ` NA `It remains to find. If (Note: given , this statement must be specified.)