# pdist2

## PURPOSE

Calculates the distance between sets of vectors.

## SYNOPSIS

function D = pdist2( X, Y, metric )

## DESCRIPTION

     Calculates the distance between sets of vectors.

     Let X be an m-by-p matrix representing m points in p-dimensional space
     and Y be an n-by-p matrix representing another set of points in the same
     space. This function computes the m-by-n distance matrix D where D(i,j)
     is the distance between X(i,:) and Y(j,:).  This function has been
     optimized where possible, with most of the distance computations
     requiring few or no loops.

     The metric can be one of the following:

     'euclidean' / 'sqeuclidean':
       Euclidean / SQUARED Euclidean distance.  Note that 'sqeuclidean'
       is significantly faster.

     'chisq'
       The chi-squared distance between two vectors is defined as:
        d(x,y) = sum( (xi-yi)^2 / (xi+yi) ) / 2;
       The chi-squared distance is useful when comparing histograms.

     'cosine'
       Distance is defined as the cosine of the angle between two vectors.

     'emd'
       Earth Mover's Distance (EMD) between positive vectors (histograms).
       Note for 1D, with all histograms having equal weight, there is a simple
       closed form for the calculation of the EMD.  The EMD between histograms
       x and y is given by the sum(abs(cdf(x)-cdf(y))), where cdf is the
       cumulative distribution function (computed simply by cumsum).

     'L1'
       The L1 distance between two vectors is defined as:  sum(abs(x-y));

     USAGE
      D = pdist2( X, Y, [metric] )

     INPUTS
      X        - [m x p] matrix of m p-dimensional vectors
      Y        - [n x p] matrix of n p-dimensional vectors
      metric   - ['sqeuclidean'], 'chisq', 'cosine', 'emd', 'euclidean', 'L1'

     OUTPUTS
      D        - [m x n] distance matrix

     EXAMPLE
      % simple example where points cluster well
      [X,IDX] = demoGenData(100,0,5,4,10,2,0);
      D = pdist2( X, X, 'sqeuclidean' );
      distMatrixShow( D, IDX );
      % comparison to pdist
      n=500; d=200; r=100; X=rand(n,d);
      tic, for i=1:r, D1 = pdist( X, 'euclidean' ); end, toc
      tic, for i=1:r, D2 = pdist2( X, X, 'euclidean' ); end, toc
      D1=squareform(D1); del=D1-D2; sum(abs(del(:)))

     See also pdist, distMatrixShow

     Piotr's Image&Video Toolbox      Version 2.52
     Copyright 2012 Piotr Dollar.  [pdollar-at-caltech.edu]
     Please email me if you find bugs, or have suggestions or questions!
     Licensed under the Simplified BSD License [see external/bsd.txt]