On the relationship of kernels in machine learning and fuzzy similarity relations

Autoren Bernhard Moser
TitelOn the relationship of kernels in machine learning and fuzzy similarity relations
TypTechnischer Bericht
NummerSCCH-TR-0508
OrtHagenberg, Austria
InstitutionSCCH
AbteilungKVS
Jahr2005
SCCH ID#508
Abstract

In this paper, we present a view of kernels from a fuzzy set theoretical perspective. Indeed, it turns out that kernels which are positive definite functions have to fulfill a consistency property given by the so-called T-transitivity of a fuzzy T-equivalence relation with respect to the triangular norm T. As a result, we introduce a triangular norm TCos which is characterized as being the greatest one for which all kernels are TCos-equivalences. Finally, a way of constructing kernels by means of fuzzy sets is outlined.