Analysis via orthonormal systems in reproducing kernel hilbert c-modules and applications

Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda, Fuyuta Komura, Takeshi Katsura, Yoshinobu Kawahara

Research output: Contribution to journalArticlepeer-review

Abstract

Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with reproducing kernel Hilbert C-module (RKHM), which is another generalization of RKHS than vector-valued RKHS (vv-RKHS). Analysis with RKHMs enables us to deal with structures among variables more explicitly than vv-RKHS. We show the theoretical validity for the construction of orthonormal systems in Hilbert C-modules, and derive concrete procedures for orthonormalization in RKHMs with those theoretical properties in numerical computations. Moreover, we apply those to generalize with RKHM kernel principal component analysis and the analysis of dynamical systems with Perron-Frobenius operators. The empirical performance of our methods is also investigated by using synthetic and real-world data.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 Mar 2

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'Analysis via orthonormal systems in reproducing kernel hilbert c<sup>∗</sup>-modules and applications'. Together they form a unique fingerprint.

Cite this