DisTools Contents DisTools User Guide
euspace

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)

 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.

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