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| ## ruiling@ 07/08/2012 | |
| ## input: | |
| ## x: sample data matrix, d×n | |
| ## d is the dimension of original sample | |
| ## n is the number of samples | |
| ## y: class label vector, n×1 | |
| ## r: reduced dimension | |
| ## metric：type of metric in the embedding space | |
| ## 'weighted' ------ weighted eigenvectors | |
| ## 'orthonormalized' ------ orthonormalized | |
| ## 'plain' ------ raw eigenvectors | |
| ## knn: parameter used in local scaling method(default:7) | |
| ## | |
| ## ouput: | |
| ## T: d×r transformation matrix (Z=T^(-1)*x) | |
| ## Z: r×n matrix of dimensionality reduce samples | |
| ## | |
| ##------------------------------------------------------ | |
| ## test data | |
| ##------------------------------------------------------ | |
| # x=matrix(c(1:20),4,5) | |
| # x=x[1:2,] | |
| # y=c(1,2,2,1,2) | |
| # r=2 | |
| # metric='weighted' | |
| # k=1 | |
| # setwd("C:/Users/ruiling/Desktop/mylfda") | |
| ##------------------------------------------------------------- | |
| ## connect to Matlab Server and call Matlab function | |
| ## step1 load R.matlab | |
| ## step2 Start Matlab | |
| ## step3 Create a Matlab clent object used to communicate with Matlab | |
| ## step4 connect to the Matlab server | |
| ##--------------------------------------------------------------- | |
| # library(R.matlab) | |
| # Matlab$startServer() | |
| # matlab <- Matlab(host="localhost",port=9999) | |
| # Isopen<-open(matlab) | |
| ##------------------------------------------------------------ | |
| ## repeat a matrix like the MATLAB grammar | |
| ##------------------------------------------------------------ | |
| repmat<-function(A,N,M){ | |
| kronecker(matrix(1,N,M),A) | |
| } | |
| lfda<-function(x,y,r,metric=c('weighted', 'orthonormalized', 'plain'),knn=7){ | |
| ## metric='weighted' | |
| n=ncol(x) | |
| d=nrow(x) | |
| if(is.null(r)) r=d | |
| metric=match.arg(metric) | |
| tSb=mat.or.vec(d,d) | |
| tSw=mat.or.vec(d,d) | |
| for(c in unique(y)){ | |
| xc=x[,y==c] # d×nc | |
| nc=dim(xc)[2] | |
| ##------- Define classwise affinity matrix A -------- | |
| A=mat.or.vec(nc,nc) | |
| xc2=t(as.matrix(colSums(xc^2))) | |
| distance2=repmat(xc2,nc,1)+repmat(t(xc2),1,nc)-2 * t(xc) %*% xc | |
| sorted=apply(distance2,2,sort) | |
| index=apply(distance2,2,order) | |
| KNNdist2=t(as.matrix(sorted[knn+1, ])) | |
| sigma=sqrt(KNNdist2) | |
| localscale=t(sigma) %*% sigma | |
| flag=(localscale != 0) | |
| A[flag]=exp(-distance2[flag]/localscale[flag]) | |
| ##------ Within-class & between-class scatter matrix ----- | |
| xc1=as.matrix(rowSums(xc)) | |
| G=xc %*% (repmat(as.matrix(colSums(A)),1,d)*t(xc))-xc %*% A %*% t(xc) | |
| tSb=tSb+G/n+xc%*%t(xc)*(1-nc/n)+xc1%*%t(xc1)/n | |
| tSw=tSw+G/nc | |
| } | |
| x1=as.matrix(rowSums(x)) | |
| tSb=tSb-x1%*%t(x1)/n-tSw | |
| tSb=(tSb+t(tSb))/2 | |
| tSw=(tSw+t(tSw))/2 | |
| setVariable(matlab,tSb=tSb,tSw=tSw,r=r) | |
| if(r==d){ | |
| evaluate(matlab,"[eigvec,eigval]=eig(tSb,tSw);") | |
| eigVec=getVariable(matlab,"eigvec")$eigvec | |
| eigVal_matrix=getVariable(matlab,"eigval")$eigval | |
| }else{ | |
| evaluate(matlab,"[eigvec,eigval]=eigs(tSb,tSw,r,'la');") | |
| eigVec=getVariable(matlab,"eigvec")$eigvec | |
| eigVal_matrix=getVariable(matlab,"eigval")$eigval | |
| } | |
| eigval=diag(eigVal_matrix) | |
| sort_eigval=apply(t(eigval),1,sort) | |
| sort_eigval_index=apply(t(eigval),1,order) | |
| T0 = eigVec[,sort_eigval_index[1:r]] | |
| T0=as.matrix(T0) | |
| T=switch(metric, | |
| weighted=T0*repmat(t(sqrt(eigval)),d,1), | |
| orthonormalized = qr.Q(qr(T0)), | |
| plain=T0 | |
| ) | |
| Z=t(T)%*%x | |
| return(list("T" = T, "Z" = Z)) | |
| } | |
| ##close(matlab) | |
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