/usr/share/octave/packages/nan-2.5.9/fss.m is in octave-nan 2.5.9-2.
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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 | function [idx,score] = fss(D,cl,N,MODE)
% FSS - feature subset selection and feature ranking
% the method is motivated by the max-relevance-min-redundancy (mRMR)
% approach [1]. However, the default method uses partial correlation,
% which has been developed from scratch. PCCM [3] describes
% a similar idea, but is more complicated.
% An alternative method based on FSDD is implemented, too.
%
% [idx,score] = fss(D,cl)
% [idx,score] = fss(D,cl,MODE)
% [idx,score] = fss(D,cl,MODE)
%
% D data - each column represents a feature
% cl classlabel
% Mode 'Pearson' [default] correlation
% 'rank' correlation
% 'FSDD' feature selection algorithm based on a distance discriminant [2]
% %%% 'MRMR','MID','MIQ' max-relevance, min redundancy [1] - not supported yet.
%
% score score of the feature
% idx ranking of the feature
% [tmp,idx]=sort(-score)
%
% see also: TRAIN_SC, XVAL, ROW_COL_DELETION
%
% REFERENCES:
% [1] Peng, H.C., Long, F., and Ding, C.,
% Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy,
% IEEE Transactions on Pattern Analysis and Machine Intelligence,
% Vol. 27, No. 8, pp.1226-1238, 2005.
% [2] Jianning Liang, Su Yang, Adam Winstanley,
% Invariant optimal feature selection: A distance discriminant and feature ranking based solution,
% Pattern Recognition, Volume 41, Issue 5, May 2008, Pages 1429-1439.
% ISSN 0031-3203, DOI: 10.1016/j.patcog.2007.10.018.
% [3] K. Raghuraj Rao and S. Lakshminarayanan
% Partial correlation based variable selection approach for multivariate data classification methods
% Chemometrics and Intelligent Laboratory Systems
% Volume 86, Issue 1, 15 March 2007, Pages 68-81
% http://dx.doi.org/10.1016/j.chemolab.2006.08.007
% $Id: fss.m 9104 2011-11-15 15:14:10Z carandraug $
% Copyright (C) 2009,2010 by Alois Schloegl <alois.schloegl@gmail.com>
% 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, see <http://www.gnu.org/licenses/>.
if nargin<3
MODE = [];
N = [];
elseif ischar(N)
MODE = N;
N = [];
elseif nargin<4,
MODE = [];
end
if isempty(N), N = size(D,2); end
score = repmat(NaN,1,size(D,2));
if 0, %strcmpi(MODE,'MRMR') || strcmpi(MODE,'MID') || strcmpi(MODE,'MIQ');
%% RMRM/MID/MIQ is not supported
%% TODO: FIXME
[tmp,t] = sort([cl,D]);
cl = t(:,1:size(cl,2));
D = t(:,1:size(D,2));
for k = 1:N,
V(k) = mi(cl, D(:,k));
for m = 1:N,
W(k,m) = mi(D(:,m), D(:,k));
end
MID(k) = V(k) - mean(W(k,:));
MIQ(k) = V(k) / mean(W(k,:));
end
if strcmpi(MODE,'MIQ')
[score,idx] = sort(MIQ,[],'descend');
else
[score,idx] = sort(MID,[],'descend');
end
elseif strcmpi(MODE,'FSDD');
[b,i,j]=unique(cl);
for k=1:length(b)
n(k,1) = sum(j==k);
m(k,:) = mean(D(j==k,:),1);
v(k,:) = var(D(j==k,:),1);
end
m0 = mean(m,1,n);
v0 = var(D,[],1);
s2 = mean(m.^2,1,n) - m0.^2;
score = (s2 - 2*mean(v,1,n)) ./ v0;
[t,idx] = sort(-score);
elseif isempty(MODE) || strcmpi(MODE,'rank') || strcmpi(MODE,'Pearson')
cl = cat2bin(cl);
if strcmpi(MODE,'rank'),
[tmp,D] = sort(D,1);
end
idx = repmat(NaN,1,N);
for k = 1:N,
f = isnan(score);
%%%%% compute partial correlation (X,Y|Z)
% r = partcorrcoef(cl, D(:,f), D(:,~f)); % obsolete, not very robust
%% this is a more robust version
X = cl; Y = D(:,f); Z = D(:,~f);
if (k>1)
X = X-Z*(Z\X);
Y = Y-Z*(Z\Y);
end
r = corrcoef(X,Y);
[s,ix] = max(sumsq(r,1));
f = find(f);
idx(k) = f(ix);
score(idx(k)) = s;
end
end
end
function I = mi(x,y)
ix = ~any(isnan([x,y]),2);
H = sparse(x(ix),y(ix));
pij = H./sum(ix);
Iij = pij.*log2(pij./(sum(pij,2)*sum(pij,1)));
Iij(isnan(Iij)) = 0;
I = sum(Iij(:));
end
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