KLFDA: Kernel Local Fisher Discriminant Analysis (KLFDA)

In DA: Discriminant Analysis for Evolutionary Inference

Description

Kernel Local Fisher Discriminant Analysis (KLFDA). This function implements the Kernel Local Fisher Discriminant Analysis with an unified Kernel function. Different from KLFDA function, which adopts the Multinomial Kernel as an example, this function empolys the kernel function that allows you to choose various types of kernels. See the kernel function from "kernelMatriax" (kernlab).

Usage

KLFDA(x, y, kernel = kernlab::polydot(degree = 1, scale = 1, offset = 1), 
r = 20, tol, prior, CV = FALSE, usekernel = TRUE, 
fL = 0.5, metric = c("weighted", "orthonormalized", "plain"), 
knn = 6, reg = 0.001, ...)

Arguments

x	The input training data
y	The training labels
kernel	The kernel function used to calculate kernel matrix. Choose the corresponding kernel you want, see details.
r	The number of reduced features you want to keep.
tol	The tolerance used to reject the uni-variance. This is important when the variance between classes is small, and setting the large tolerance will avoid the data distortion.
prior	The weight of each class, or the proportion of each class.
CV	Whether to do cross validation.
usekernel	whether to use kernel classifier, if TRUE, pass to Naive Bayes classifier.
fL	If usekernel is TRUE, pass to the kernel function.
metric	type of metric in the embedding space (default: 'weighted') 'weighted' - weighted eigenvectors 'orthonormalized' - orthonormalized 'plain' - raw eigenvectors
knn	The number of nearest neighbours
reg	The regularization parameter
...	additional arguments for the classifier

Details

This function empolys three different classifiers, the basic linear classifier, the Mabayes (Bayes rule and the Mahalanobis distance), and Niave Bayes classifier. The argeument "kernel" in the klfda function is the kernel function used to calculate the kernel matrix. If usekernel is TRUE, the corresponding kernel parameters will pass the the Naive Bayes kernel classifier. The kernel 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 initialized by using the following functions:

rbfdot Radial Basis kernel function

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 the Spline kernel

(see example.)

kernelFast is mainly used in situations where columns of the kernel matrix are computed per invocation. In these cases, evaluating the norm of each row-entry over and over again would cause significant computational overhead.

Value

The results give the classified classes and the posterior possibility of each class using different classifier.

class	The class labels from linear classifier
posterior	The posterior possibility of each class from linear classifier
bayes_judgement	Discrimintion results using the Mabayes classifier
bayes_assigment	Discrimintion results using the Naive bayes classifier
Z	The reduced features

Author(s)

[e-mail]

References

Sugiyama, M (2007).Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis. Journal of Machine Learning Research, vol.8, 1027-1061.

Sugiyama, M (2006). Local Fisher discriminant analysis for supervised dimensionality reduction. In W. W. Cohen and A. Moore (Eds.), Proceedings of 23rd International Conference on Machine Learning (ICML2006), 905-912.

Original Matlab Implementation: http://www.ms.k.u-tokyo.ac.jp/software.html#LFDA

Tang, Y., & Li, W. (2019). lfda: Local Fisher Discriminant Analysis inR. Journal of Open Source Software, 4(39), 1572.

Moore, A. W. (2004). Naive Bayes Classifiers. In School of Computer Science. Carnegie Mellon University.

Pierre Enel (2020). Kernel Fisher Discriminant Analysis (https://www.github.com/p-enel/MatlabKFDA), GitHub. Retrieved March 30, 2020.

Karatzoglou, A., Smola, A., Hornik, K., & Zeileis, A. (2004). kernlab-an S4 package for kernel methods in R. Journal of statistical software, 11(9), 1-20.

See Also

predict.KLFDA, KLFDAM

Examples

require(kernlab)
btest=KLFDA(as.matrix(iris[,1:4]),as.matrix(as.data.frame(iris[,5])),
kernel=kernlab::rbfdot(sigma = 0.1),
r=3,prior=NULL,tol=1e-90,
reg=0.01,metric =  'plain')
pred=predict.KLFDA(btest,testData=as.matrix(iris[1:10,1:4]),prior=NULL)

DA documentation built on July 12, 2021, 9:07 a.m.