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nBasis->k
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variance->var

git-svn-id: svn+ssh://lumo.ucsd.edu/projects/p1/svnroot/pdollar/toolbox@3795 52fe0c90-79fe-0310-8a18-a0b98ad248f8
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pdollar committed Jan 11, 2007
1 parent 373da26 commit 203715d
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56 changes: 28 additions & 28 deletions classify/rbfComputeBasis.m
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Expand Up @@ -16,19 +16,19 @@
% ytest = rbfWeight * features(Xtest)
%
% The code below achieves all three steps:
% rbfBasis = rbfComputeBasis( Xtrain, nBasis, cluster, scale, show );
% rbfBasis = rbfComputeBasis( Xtrain, k, cluster, scale, show );
% rbfWeight = rbfComputeFeatures(Xtrain,rbfBasis) \ ytrain;
% ytest = rbfComputeFeatures(Xtest,rbfBasis) * rbfWeight;
%
% For an in depth discussion of rbf networks see:
% Christopher M. Bishop. "Neural Networks for Pattern Recognition"
%
% USAGE
% rbfBasis = rbfComputeBasis( X, nBasis, [cluster], [scale], [show] )
% rbfBasis = rbfComputeBasis( X, k, [cluster], [scale], [show] )
%
% INPUTS
% X - [N x d] N points of d dimensions each
% nBasis - number of basis functions to use
% k - number of basis functions to use
% [cluster] - [1]: Computes cluster centers for use as rbf functions.
% - 0: Evenly centered basis functions (for small d)
% [scale] - [5] Alter computed value of sigma by given factor
Expand All @@ -39,10 +39,10 @@
% OUTPUTS
% rfbBasis
% .d - feature vector size
% .nBasis - number of basis functions actually used
% .mu - [d x nBasis] rbf centers
% .variances- [1 x nBasis] rbf widths
% .variance - rbf average width
% .k - number of basis functions actually used
% .mu - [d x k] rbf centers
% .vars - [1 x k] rbf widths
% .var - rbf average width
%
% DATESTAMP
% 09-Jan-2007 1:00pm
Expand All @@ -53,8 +53,8 @@
% Written and maintained by Piotr Dollar pdollar-at-cs.ucsd.edu
% Please email me if you find bugs, or have suggestions or questions!

function rbfBasis = rbfComputeBasis( X, nBasis, cluster, scale, show )
if( nargin<2 || isempty(nBasis)); error('nBasis not specified'); end;
function rbfBasis = rbfComputeBasis( X, k, cluster, scale, show )
if( nargin<2 || isempty(k)); error('k not specified'); end;
if( nargin<3 || isempty(cluster)); cluster=1; end;
if( nargin<4 || isempty(scale)); scale=5; end;
if( nargin<5 || isempty(show)); show=0; end;
Expand All @@ -64,33 +64,33 @@
%%% CLUSTERS subsample, run kmeans
maxN=5000; if( N>maxN ); X=X(randperm2(N,maxN),:); N=maxN; end;
params = {'replicates', 5, 'display', 1};
[IDX,mu] = kmeans2( X, nBasis, params{:} );
mu = mu'; nBasis = size(mu,2);
[IDX,mu] = kmeans2( X, k, params{:} );
mu = mu'; k = size(mu,2);
else
%%% GRID generate locations evenly spaced on grid
if( d>4 ); error('d too high. curse of dimensionality..'); end;
nBasisPer = round( nBasis ^ (1/d) );
nBasis = nBasisPer ^ d;
nBasisPer = round( k ^ (1/d) );
k = nBasisPer ^ d;
minX = min(X,[],1 ); maxX = max(X,[],1 );
stepX = (maxX-minX)/(nBasisPer+1);
loc=cell(1,d); for i=1:d; loc{i}=(1:nBasisPer)*stepX(i)+minX(i); end;
grid=cell(1,d); if(d>1); [grid{:}]=ndgrid(loc{:}); else grid=loc; end;
mu=zeros(d,nBasis); for i=1:d; mu(i,:) = grid{i}(:); end;
mu=zeros(d,k); for i=1:d; mu(i,:) = grid{i}(:); end;
end;

%%% Set variance to be equal to average distance of neareast neighbor.
%%% Set var to be equal to average distance of neareast neighbor.
dist = dist_euclidean( mu', mu' );
dist = dist + realmax * eye( nBasis );
variances = min(dist)* scale;
variance = mean(variances);
variances = max( variances, variance/100 );
dist = dist + realmax * eye( k );
vars = min(dist)* scale;
var = mean(vars);
vars = max( vars, var/100 );

%%% store results
rbfBasis.d = d;
rbfBasis.nBasis = nBasis;
rbfBasis.mu = mu;
rbfBasis.variances = variances;
rbfBasis.variance = variance;
rbfBasis.d = d;
rbfBasis.k = k;
rbfBasis.mu = mu;
rbfBasis.vars = vars;
rbfBasis.var = var;

%%% optionally display
if( abs(show) )
Expand All @@ -103,8 +103,8 @@
figure(show); clf; hold on;
minX = min(X,[],1 ); maxX = max(X,[],1 );
xs = linspace( minX, maxX, 500 )';
for i=1:nBasis
ys = exp( -(xs-mu(i)).^2 / 2 / variance );
for i=1:k
ys = exp( -(xs-mu(i)).^2 / 2 / var );
plot( xs, ys );
end
elseif( d==2 ) % 2D data
Expand All @@ -114,9 +114,9 @@
xs2 = linspace(minX(2),maxX(2),25);
[xs1,xs2] = ndgrid( xs1, xs2 );
xs = [xs1(:) xs2(:)]; n = size(xs,1);
for i=1:nBasis
for i=1:k
mui = repmat(mu(:,i),[1 n])';
ys = exp( - sum( ((xs - mui)).^2, 2 ) / 2 / variance );
ys = exp( - sum( ((xs - mui)).^2, 2 ) / 2 / var );
surf( xs1, xs2, reshape(ys,size(xs1)) );
end;
elseif( d==3 ) % 3D data (show data+centers)
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20 changes: 10 additions & 10 deletions classify/rbfComputeFeatures.m
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Expand Up @@ -10,7 +10,7 @@
% rbfBasis - rbfBasis struct (see rbfComputeBasis)
%
% OUTPUT
% Xrbf - [N x nBasis] computed feature vectors
% Xrbf - [N x k] computed feature vectors
%
% DATESTAMP
% 09-Jan-2007 1:00pm
Expand All @@ -22,23 +22,23 @@
% Please email me if you find bugs, or have suggestions or questions!

function Xrbf = rbfComputeFeatures( X, rbfBasis )
N = size(X,1);
nBasis = rbfBasis.nBasis;
mu = rbfBasis.mu';
variance = rbfBasis.variance;
N = size(X,1);
k = rbfBasis.k;
mu = rbfBasis.mu';
var = rbfBasis.var;

%% for each point, compute values of all basis functions
%% mu=[nBasis x d]; onesVec=[nBasis x 1]; Xi=[1 x d];
Xrbf = zeros( N, nBasis );
onesVec = ones(nBasis,1);
%% mu=[k x d]; onesVec=[k x 1]; Xi=[1 x d];
Xrbf = zeros( N, k );
onesVec = ones(k,1);
for i=1:N
eucdist = sum( ((onesVec*X(i,:) - mu)).^2, 2 );
Xrbf(i,:) = eucdist' / 2 ./ variance;
Xrbf(i,:) = eucdist' / 2 ./ var;
end;
Xrbf = exp( -Xrbf );

%% normalize rbfs to sum to 1
if( 0 ); Xrbf = Xrbf ./ repmat( sum(Xrbf,2), [1 nBasis] ); end;
if( 0 ); Xrbf = Xrbf ./ repmat( sum(Xrbf,2), [1 k] ); end;

%% add constant vector of ones as last feature
if( 0 ); Xrbf = [Xrbf ones(N,1)]; end;
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8 changes: 4 additions & 4 deletions classify/rbfDemo.m
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Expand Up @@ -3,15 +3,15 @@
% See rbfComputeBasis for discussion of rbfs.
%
% USAGE
% rbfDemo( dataType, noiseSig, scale, nBasis, cluster, show )
% rbfDemo( dataType, noiseSig, scale, k, cluster, show )
%
% INPUTS
% dataType - 0: 1D sinusoid
% 1: 2D sinusoid
% 2: 2D stretched sinusoid
% noiseSig - std of idd gaussian noise
% scale - see rbfComputeBasis
% nBasis - see rbfComputeBasis
% k - see rbfComputeBasis
% cluster - see rbfComputeBasis
% show - figure to use for display (no display if == 0)
%
Expand All @@ -31,7 +31,7 @@
% Written and maintained by Piotr Dollar pdollar-at-cs.ucsd.edu
% Please email me if you find bugs, or have suggestions or questions!

function rbfDemo( dataType, noiseSig, scale, nBasis, cluster, show )
function rbfDemo( dataType, noiseSig, scale, k, cluster, show )

%%% generate train/test data
if( 1 )
Expand All @@ -40,7 +40,7 @@ function rbfDemo( dataType, noiseSig, scale, nBasis, cluster, show )
end;

%%% train/apply rbfs
rbfBasis = rbfComputeBasis( Xtrain, nBasis, cluster, scale, show )
rbfBasis = rbfComputeBasis( Xtrain, k, cluster, scale, show )
rbfWeight = rbfComputeFeatures(Xtrain,rbfBasis) \ ytrain;
yTrainRes = rbfComputeFeatures(Xtrain,rbfBasis) * rbfWeight;
yTestRes = rbfComputeFeatures(Xtest,rbfBasis) * rbfWeight;
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