R Graphical Manual

Browse All

Last data update: 2014.03.03

R: Kernel Local Fisher Discriminant Analysis for Supervised...

klfda

R Documentation

Kernel Local Fisher Discriminant Analysis for Supervised Dimensionality Reduction

Description

Performs kernel local fisher discriminant analysis on the given data, which is the non-linear version of LFDA (see details lfda).

Usage

klfda(k, y, r, metric = c("weighted", "orthonormalized", "plain"), knn = 6,
  reg = 0.001)

Arguments

`k`	n x n kernel matrix. Result of the `kmatrixGauss` function. n is the number of samples
`y`	n dimensional vector of class labels
`r`	dimensionality of reduced space (default: d)
`metric`	type of metric in the embedding space (default: 'weighted') 'weighted' — weighted eigenvectors 'orthonormalized' — orthonormalized 'plain' — raw eigenvectors
`knn`	parameter used in local scaling method (default: 6)
`reg`	regularization parameter (default: 0.001)

Value

list of the LFDA results:

`T`	d x r transformation matrix (Z = t(T) * X)
`Z`	r x n matrix of dimensionality reduced samples

Author(s)

Yuan Tang

References

Sugiyama, M (2007). - contain implementation 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

Examples

## Not run: 
## example without dimension reduction
k <- kmatrixGauss(x = trainData[,-1])
y <- trainData[,1]
r <- 26 # dimensionality of reduced space. Here no dimension reduction is performed
result <- klfda(k,y,r,metric="plain")
transformedMat <- result$Z # transformed training data
metric.train <- as.data.frame(cbind(trainData[,1],transformedMat))
colnames(metric.train)=colnames(trainData)

## example with dimension reduction
k <- kmatrixGauss(x = trainData[,-1])
y <- trainData[,1]
r <- 3 # dimensionality of reduced space
result <- klfda(k,y,r,metric="plain")
transformMat  <- result$T # transforming matrix - distance metric

# transformed training data with Style
transformedMat <- result$Z # transformed training data
metric.train <- as.data.frame(cbind(trainData[,1],transformedMat))
colnames(metric.train)[1] <- "Style"

# transformed testing data with Style (unfinished)
metric.test <- kmatrixGauss(x = testData[,-1])
metric.test <- as.matrix(testData[,-1]) %*% transformMat
metric.test <- as.data.frame(cbind(testData[,1],metric.test))
colnames(metric.test)[1] <- "Style"


## End(Not run)