KERNELM

Trainable kernel mapping, dissimilarity representation

    [W,J] = KERNELM(A,KERNEL,SELECT,P1,P2 , ...)
     W = A*KERNELM([],KERNEL,SELECT,P1,P2 , ...)
     W = A*KERNELM(KERNEL,SELECT,P1,P2 , ...)
     K = B*W

Input
A,B	Datasets
KERNEL	Untrained kernel / dissimilarity representation,  a mapping computing proximities between objects.  default: Euclidean dissimilarities: PROXM('d',1)
SELECT	Name of object selection procedure, see below
P1,P2,	... Additional parameters for SELECT

Output
W	Mapping
J	Vector with indices of selected objects for representation
K	Kernel matrix, dissimilarity representation,  size [SIZE(B,1) LENGTH(J)]

Description

Computes the kernel mapping W for the representation objects in A. The  computation of the kernel matrix, which is a proximity matrix (similarities  or dissimilarities) should be defined in KERNEL by an untrained mapping  like PROXM for predefined proximities or USERKERNEL for user specified  proximities.  A*KERNEL should 'train' the kernel, i.e. specify A as representation set.  B*(A*KERNEL) should compute the kernel matrix: a dataset.

The only advantage of this routine over kernel mappings defined by PROXM or USERKERNEL is that it includes some options for object selection  (prototype selection) of the initial representation set.

Initially, the kernel mapping has a size [SIZE(A,2) SIZE(A,1)]. For  increased efficiency or accuracy the representation set may be reduced  by a routine given by the string SELECT to select to objects J, using  possibly additional parameters P1, P2, etcetera.

The following choices for SELECT are supported

'random'	random selection of P1 objects, maximum P2
'gendat'	[X,Y,J] = GENDAT(A,P1)
'kcentres'	[LAB,J] = KCENTRES(DISTM(A),P1,P2)
'modeseek'	[LAB,J] = MODESEEK(DISTM(A),P1)
'edicon'	J = EDICON(DISTM(A),P1,P2,P3)
'featsel'	J = +FEATSELM(A*KERNELM(A,TYPE,P),P1,P2,P3)

Reference(s)

1. E.Pekalska, R.P.W.Duin, P.Paclik, Prototype selection for dissimilarity- based classification, Pattern Recognition, vol. 39, no. 2, 2006, 189-208.
2. E.Pekalska and R.P.W.Duin, The Dissimilarity Representation for Pattern Recognition, Foundations and Applications, World Scientific, 2005, 1-607.

Example(s)

 a = gendatb;
 w = (scalem*kernelm([],'random',5)*fisherc); 
 scatterd(a)
 plotc(a*w)
 plotc(a*w,'r')
 plotc(a*w,'b')

See also

datasets, mappings, proxm, userkernel, kernelc,