/usr/share/octave/site/m/vlfeat/toolbox/misc/vl_homkermap.m is in octave-vlfeat 0.9.17+dfsg0-6+b1.
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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 | % VL_HOMKERMAP Homogeneous kernel map
% V = VL_HOMKERMAP(X, N) computes a 2*N+1 dimensional approximated
% kernel map for the Chi2 kernel. X is an array of data points. Each
% point is expanded into a vector of dimension 2*N+1 and saved to
% the output V. The expanded feature vectors are stacked along the
% first dimension, so that the output array V has the same
% dimensions of the input array X except for the first one, which is
% 2*N+1 times larger.
%
% The function accepts the following options:
%
% Kernel:: KCHI2
% One of KCHI2 (Chi2 kernel), KINTERS (intersection kernel), KJS
% (Jensen-Shannon kernel). The 'Kernel' option name can be omitted,
% i.e. VL_HOMKERMAP(..., 'kernel', 'kchi2') has the same effect of
% VL_HOMKERMAP(..., 'kchi2').
%
% Period:: [automatically tuned]
% Set the period of the kernel specturm. The approximation is
% based on periodicizing the kernel specturm. If not specified,
% the period is automatically set based on the heuristic described
% in [2].
%
% Window:: [RECTANGULAR]
% Set the window used to truncate the spectrum before The window
% can be either RECTANGULAR or UNIFORM window. See [2] and the API
% documentation for details.
%
% Gamma:: [1]
% Set the homogeneity degree of the kernel. The standard kernels
% are 1-homogeneous, but sometimes smaller values perform better
% in applications. See [2] for details.
%
% Example::
% The following code results in approximatively the same
% similarities matrices between points X and Y:
%
% x = rand(10,1) ;
% y = rand(10,100) ;
% psix = vl_homkermap(x, 3) ;
% psiy = vl_homkermap(y, 3) ;
% figure(1) ; clf ;
% ker = vl_alldist(x, y, 'kchi2') ;
% ker_ = psix' * psiy ;
% plot([ker ; ker_]') ;
%
% Note::
% The homogeneous kernels K(X,Y) are normally defined for
% non-negative data only. VL_HOMKERMAP defines them for both
% positive and negative data by using the definition
% SIGN(X)SIGN(Y)K(ABS(X),ABS(Y)) -- note that other extensions are
% possible as well (see [2]).
%
% REFERENCES::
% [1] A. Vedaldi and A. Zisserman
% `Efficient Additive Kernels via Explicit Feature Maps',
% Proc. CVPR, 2010.
%
% [2] A. Vedaldi and A. Zisserman
% `Efficient Additive Kernels via Explicit Feature Maps',
% PAMI, 2011 (submitted).
%
% See also: VL_HELP().
% Authors: Andrea Vedaldi
% Copyright (C) 2007-12 Andrea Vedaldi and Brian Fulkerson.
% All rights reserved.
%
% This file is part of the VLFeat library and is made available under
% the terms of the BSD license (see the COPYING file).
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