/usr/share/octave/packages/nan-2.8.1/train_lda_sparse.m is in octave-nan 2.8.1-1ubuntu2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 | function [CC] = train_lda_sparse(X,G,par,tol)
% Linear Discriminant Analysis for the Small Sample Size Problem as described in
% Algorithm 1 of J. Duintjer Tebbens, P. Schlesinger: 'Improving
% Implementation of Linear Discriminant Analysis for the High Dimension/Small Sample Size
% Problem', Computational Statistics and Data Analysis, vol. 52, no. 1, pp. 423-437, 2007.
% Input:
% X ...... (sparse) training data matrix
% G ...... group coding matrix of the training data
% test ...... (sparse) test data matrix
% Gtest ...... group coding matrix of the test data
% par ...... if par = 0 then classification exploits sparsity too
% tol ...... tolerance to distinguish zero eigenvalues
% Output:
% err ...... Wrong classification rate (in %)
% trafo ...... LDA transformation vectors
%
% Reference(s):
% J. Duintjer Tebbens, P. Schlesinger: 'Improving
% Implementation of Linear Discriminant Analysis for the High Dimension/Small Sample Size
% Problem', Computational Statistics and Data Analysis, vol. 52, no. 1,
% pp. 423-437, 2007.
%
% Copyright (C) by J. Duintjer Tebbens, Institute of Computer Science of the Academy of Sciences of the Czech Republic,
% Pod Vodarenskou vezi 2, 182 07 Praha 8 Liben, 18.July.2006.
% This work was supported by the Program Information Society under project
% 1ET400300415.
%
%
% Modified for the use with Matlab6.5 by A. Schloegl, 22.Aug.2006
%
% $Id$
% This function is part of the NaN-toolbox
% http://pub.ist.ac.at/~schloegl/matlab/NaN/
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License
% as published by the Free Software Foundation; either version 3
% of the License, or (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Step (1)
%p = length(X(1,:));n = length(X(:,1));g = length(G(1,:));
G = sparse(G);
[n,p]=size(X);
g = size(G,2);
for j=1:g
nj(j) = norm(G(:,j))^2;
end
Dtild = spdiags(nj'.^(-1),0,g,g);
Xtild = X*X';
Xtild1 = Xtild*ones(n,1);
help = ones(n,1)*Xtild1'/n - (ones(1,n)*Xtild'*ones(n,1))/(n^2);
matrix = Xtild - Xtild1*ones(1,n)/n - help;
% eliminate non-symmetry of matrix due to rounding error:
matrix = (matrix+matrix')/2;
[V0,S] = eig(matrix);
% [s,I] = sort(diag(S),'descend');
[s,I] = sort(-diag(S)); s = -s;
cc = sum(s<tol);
count = n-cc;
V1 = V0(:,I(1:count));
D1inv = diag(s(1:count).^(-1.0));
Dhalfinv = diag(s(1:count).^(-0.5));
Dhalf = diag(s(1:count).^(0.5));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Step (2)
help2 = V1*D1inv;
M1 = Dtild*G'*Xtild;
B1 = (G*(M1*(speye(n)-1/n))-help)*help2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Step (3)
opts.issym = 1;opts.isreal = 1;opts.disp = 0;
%if 0,
try,
[V0,S,flag] = eigs(B1'*B1,g-1,'lm',opts);
EV = Dhalfinv*V0;
[s,I] = sort(-diag(S)); s = -s;
%else
catch
% needed as long as eigs is not supported by Octave
[V0,S] = eig(B1'*B1);
flag = 0;
[s,I] = sort(-diag(S)); s = -s(I(1:g-1));
EV = Dhalfinv * V0(:,I(1:g-1));
I = 1:g-1;
end;
%EV = Dhalfinv*V0;
%[s,I] = sort((diag(S)),'descend');
%[s,I] = sort(-diag(S)); s = -s;
if flag ~= 0,
'eigs did not converge';
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Step (4)
for j=1:g-1,
C(:,j) = EV(:,I(j))/norm(EV(:,I(j)));
end
cc = 0;
for j=1:g-1,
if (1-s(j))<tol
cc = cc+1;
V2(:,j) = EV(:,I(j));
else
break
end
end
if cc > 0
[Q,R] = qr(V2,0);
matrix = B1*Dhalf*Q;
[V0,S] = eig(matrix'*matrix);
%[s,I] = sort(diag(S),'descend');
[s,I] = sort(-diag(S)); s = -s;
for j=1:cc
C(:,j) = Q*V0(:,I(j));
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Step (5)
C1 = help2*Dhalf*C;
trafo(:,1:g-1) = X'*C1 - (X'*ones(n,1))*(ones(1,n)*C1/n);
for j=1:g-1
trafo(:,j) = trafo(:,j)/norm(trafo(:,j));
end
CC.trafo = trafo;
if par == 0
% X2 = full(test*X');
% [pred] = classifs(C1,M1,X2);
CC.C1 = C1;
CC.M1 = M1;
CC.X = X;
else
% M = Dtild*G'*X;
% [pred] = classifs(trafo,M,test);
CC.C1 = trafo;
CC.M1 = Dtild*G'*X;
end
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