Cross product kernels for fuzzy set similarity

Jorge Guevara (1) , Roberto Hirata (2) , Stéphane Canu (3)

1 IBM Research - Brazil
2 Instituto de Geociências [São Paulo]
3 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

We present a new kernel on fuzzy sets: the cross product kernel on fuzzy sets which can be used to estimate similarity measures between fuzzy sets with a geometrical interpretation in terms of inner products. We show that this kernel is a particular case of the convolution kernel and it generalizes the widely-know kernel on sets towards the space of fuzzy sets. Moreover, we show that the cross product kernel on fuzzy sets performs an embedding of probability measures into a reproduction kernel Hilbert space. Finally, we experimentally show the applicability of this kernel on a supervised classification task on noisy datasets.

Domaines: Apprentissage [cs.LG]

Jorge Guevara, Roberto Hirata, Stéphane Canu. Cross product kernels for fuzzy set similarity. 2017. ⟨hal-01438607v2⟩