www.pudn.com > ConstrainedEM.zip > RCA.m

%computes RCA of data  
 
%params: 
 
% TrainingSet - The data points as an N*D matrix, where N is the number of data points, 
% D the dimension of the data. Each data point is a row in the matrix. 
 
% chunkletAssignments - a vector of size N*1 describing the chunklets :                        
%               -1 in the i'th place says that point i doesn't belong to any chunklet 
%               integer j in place i says that point i belongs to chunklet j. 
%               The chunklets indexes should be 1:number_of chunklets 
 
% priorFlag - when this flag is set, the cov matrix is check for ill conditioning , and if  
%               it is found to be low rank, it is smothened by addition of eye(D). 
%             the default of this flag is 1. 
 
% returns : 
 
% B - the RCA suggested mahalanobis matrix. 
% A - the RCA suggested transformation of the data. 
% newData - the data after the RCA transformation (A). 
 
% the ouput argument fulfill : newData=A*data 
% for every two original data points x1,x2 with new images y1,y2: 
%  (x2-x1)'*B*(x2-x1) = Euclid norm of y2-y1 = (y2-y1)'*(y2-y1) 
 
function [ B, A, newData ] = RCA(TrainingSet,chunkletAssignments,priorFlag) 
 
if(~exist('priorFlag')) 
    priorFlag=1; 
end 
 
TrainingSet=TrainingSet';	% tomer conversion 
S= max(chunkletAssignments); 
ChunkletDataSet= []; 
ChunkletSizes= []; 
for i=1:S 
    inds= find(chunkletAssignments == i); 
    ChunkletSizes(i)= length(inds); 
    ChunkletDataSet= [ChunkletDataSet TrainingSet(:,inds)]; 
end 
 
[CenteredChunklets]=centerChunklets(ChunkletDataSet,ChunkletSizes); 
 
%compute the svd of the normalized chunklets 
Cov= CenteredChunklets*CenteredChunklets'; 
[dim N]= size(CenteredChunklets); 
 
%check for ill ranked RCA covmat in case of not enough chunklets: if 
%so smooth matrix: 
alpha= N/50; 
if(priorFlag)&(rank(Cov) < dim) 
    Cov= (Cov + alpha.*eye(dim))/(sum(ChunkletSizes)+alpha); 
else   
    Cov= Cov./N; 
end 
 
[U Sig V]= svd(Cov); 
 
% whiten the data set using RCA Transformation: 
 
A=(Sig^-0.5)*U'; 
newData = A*TrainingSet; 
 
% the mahalanovis matrix 
B=inv(Cov); 
 
 
%%%%%%%%%%% end of RCA function 
 
 
 
% This function computes the centroid of each chunklet and substracts it from all 
% chunklet members. 
% ChunkletSizes is a vector containing the size of each chunklet in the data set. 
% chunklets are assumed to be ordered. 
 
%HANADLES situations where the chunklet is of size 1. 
 
function [CenteredChunklets]= centerChunklets(DataSet, ... 
    ChunkletSizes) 
 
[rows cols]= size(DataSet); 
 
numOfChunklets= length(ChunkletSizes); 
i=1; 
 
for k=1:numOfChunklets 
     
    if(~ChunkletSizes(k)==0) 
        centroid= mean(DataSet(:,i:i+ChunkletSizes(k)-1)'); 
         
        DataSet(:,i:i+ChunkletSizes(k)-1)= DataSet(:,i:i+ChunkletSizes(k)-1)- ... 
            (centroid'*ones(1,ChunkletSizes(k))); 
    end 
     
    i= i+ChunkletSizes(k); 
end 
 
CenteredChunklets= DataSet;