kisomap_test.m

实现核ISOMAP算法,解决测试点问题和ROBUST问题

function [TestY, TestD] = kisomap_test(TestX, TrainX, U, BK0, D, K, BMLam);
% [TestY, TestD] = kisomap_test(TestX, TrainX, U, BK0, D, K); 
%
% INPUT
%   TestX: Test Data 
%   TrainX: Train Data which was used for Training...
%   U: EigenVector of Kernel Matrix
%   BK0: Gram matrix of Training Data in Feature space.
%   D: Euclidean Distance
%   K: the number of neighborhood
%
% OUTPUT
%   TestY: Projected Data
%   TestD: Euclidean Distance between Training Data and Test Data
%
%   This code uses some functions of Tenenbaum's Isomap code
% 
%   For the details, See
%   H. Choi, S. Choi, "Kernel Isomap," Electronics Letters, vol. 40, no. 25, pp. 1612-1613, 2004 
%   
% 2004.06.04 
% by [e-mail], http://home.postech.ac.kr/~hychoi/
%   Heeyoul Choi
%   Dept. of Computer Science
%   POSTECH, Korea

TrainN = size(TrainX, 2);
TestN = size(TestX, 2);

% Neighborhood...
TestD = zeros(TestN, TrainN);
for idx = 1:TestN
    ND = L2_distance(TestX(:,idx), TrainX, 1);
    [tmp, ind] = sort(ND); 
    
    ND(1,ind(1, (2+K):end)) = 0; 
    ND = [D ND'; ND 0];
    ND = sparse(ND); 
    ND = max(ND,ND');         
    
    TD = dijkstra(ND, TrainN+1); % Shortest Path....
    TestD(idx,:) = TD(1, 1:TrainN);
end
TestD = TestD + BMLam;

% Kernel Trick...
diagB = diag(BK0)';
K0 = -.5*(TestD.^2 - repmat(diagB, TestN, 1) - repmat(sum(TestD.^2, 2)/TrainN, 1, TrainN) ...
    + sum(diagB)/TrainN);

%% Centering is meaningless
% K0 = K0 - ones(TestN, TrainN)/TrainN * BK0 - K0 * ones(TrainN, TrainN)/TrainN ...
%    + ones(TestN, TrainN)/TrainN * BK0 * ones(TrainN, TrainN)/TrainN;
TestY = (K0*U)';