Cross product kernels for fuzzy set similarity

Author(s)

Guevara, Jorge ; Hirata, Roberto, Jr. ; Canu, Stephane ; IEEE

• Document type: Journal article
• Source: 2017 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ-IEEE); v. N/A, p. 6-pg., 2017-01-01.

Abstract

We present a new kernel on fuzzy sets: the Cross Product kernel on fuzzy sets. This kernel implements a similarity measure between fuzzy sets with a geometrical interpretation in Reproducing Kernel Hilbert Spaces. We prove that this kernel is a convolution kernel that 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 validated the kernel performance through experiments on supervised classification on noisy datasets. (AU)

• FAPESP's process: 15/01587-0 - Storage, modeling and analysis of dynamical systems for e-Science applications
• Grantee: João Eduardo Ferreira
• Support Opportunities: Research Grants - eScience and Data Science Program - Thematic Grants