VLFeat - Documentation - Matlab API - MISC

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:

KChi2

Compute the map for the Chi2 kernel.

KINTERS

Compute the map for the intersection kernel.

KL1

Same as KINTERS, but deprecated as the name is not fully accurate.

KJS

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

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).

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