VLFeat - Documentation - Matlab API - MISC

V = VL_HOMKERMAP(X, N, L) computes a finite dimensional approximated kernel map for the Chi2 kernel. N is the approximation order and L is the sampling step (see [1] for details). X is an array of data points. Each point is expanded into a vector of dimension 2*N+1 and saved to V. Vectors are stacked along the first dimension of X, so that V has the same dimensions of X except for the first, which is multiplied by 2*N+1.

The function accepts the following options:

KChi2

Compute the map for the Chi2 kernel.

KL1

Compute the map for the L1 (intersection) kernel.

KJS

Compute the map for the JS (Jensen-Shannon) kernel.

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, .4) ;
  psiy = vl_homkermap(y, 3, .4) ;
  figure(1) ; clf ;
  ker = vl_alldist(x, y, 'kchi2') ;
  ker_ = psix' * psiy ;
  plot([ker ; ker_]') ;

REFERENCES [1] A. Vedaldi and A. Zisserman

    `Efficient Additive Kernels via Explicit Feature Maps',
    Proc. CVPR, 2010.

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