Reproducing kernel Hilbert C*-module and kernel mean embeddings
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 -module (RKHM) and kernel mean embedding (KME) in RKHM. Since RKHM contains richer information than RKHS or vector-valued RKHS (vvRKHS), analysis with RKHM enables us to capture and extract structural properties in such as functional data. We show a branch of theories for RKHM to apply to data analysis, including the representer theorem, and the injectivity and universality of the proposed KME. We also show RKHM generalizes RKHS and vvRKHS. Then, we provide concrete procedures for employing RKHM and the proposed KME to data analysis.
Keywords
Cite
@article{arxiv.2101.11410,
title = {Reproducing kernel Hilbert C*-module and kernel mean embeddings},
author = {Yuka Hashimoto and Isao Ishikawa and Masahiro Ikeda and Fuyuta Komura and Takeshi Katsura and Yoshinobu Kawahara},
journal= {arXiv preprint arXiv:2101.11410},
year = {2021}
}
Comments
merged two unpablished papers arXiv:2003.00738 and 2007.14698 into this paper. arXiv admin note: text overlap with arXiv:2007.14698. Note regarding version 2: corrected typos and errors