EUSPACE

Convert PE space to Euclidean space

    B = A*EUSPACE
    B = A*EUSPACE(TYPE)
    V = W*EUSPACE(TYPE)

Input
A	Pseudo-Euclidean dataset
W	Pseudo-Euclidean mapping
TYPE	String defining conversion type, 'ass' (default), 'pos', 'neg' or  'dec' (for pe_datasets only).

Output
B	Euclidean dataset
V	Euclidean mapping

Description

The Pseudo-Euclidean (PE) space consist of two Euclidean subspaces, the  positive one and the negative one. A pseudo-Euclidean mapping as  constructed by PE_EM generates vectors for which the first p components  refer to the positive space and the next q components to the negative  space. The signature (p,q) can be retrieved by GETSIG.

This routine returns for TYPE = 'ass' the so-called associative space. B contains thereby the same set of vectors, but now with signature (p+q,0).  For TYPE = 'pos' just the positive part is returned, B = A(:,1:p). The  signature is now just (p,0). For TYPE = 'neg', the negative part is  returned, B = A(:,p+1:p+q) and the signature is set to (q,0) by which it  is interpreted as Euclidean. These conversions influence various mappings  and classifiers defined for the PE space.

TYPE = 'dec' determines the Euclidean correction found by adding a  sufficiently large positive constant to the off-diagonal elements of the  squared original dissmilarity matrix.

Reference(s)

[1] R.P.W. Duin, E. Pekalska, A. Harol, W.J. Lee, and H. Bunke, On Euclidean corrections for non-Euclidean dissimilarities, in: Proc. SSPR & SPR 2008, LNCS 5342, Springer, 2008, 551-561.

[2] R.P.W. Duin, E. Pekalska, Non-Euclidean Dissimilarities: Causes and Informativeness, in: SSPR & SPR 2010, LNCS 6218, Springer, 2010, 324-333.

See also

datasets, pe_em, getsig, pe_distm, pe_knnc, pe_parzenc, pe_nmc, pe_kernelm, pe_affine, pe_mtimes,