12 citations · 24 across the 14 of their papers we have counts for
14 papers
Koopman spectral analysis of skew-product dynamics on Hilbert -modules
Dimitrios Giannakis, Yuka Hashimoto, Masahiro Ikeda +2
We introduce a linear operator on a Hilbert -module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it ad…
Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator
Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri
Reproducing kernel Hilbert -module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of -algebra, and the Perron-Frobenius operator is a line…
Koopman-based generalization bound: New aspect for full-rank weights
Yuka Hashimoto, Sho Sonoda, Isao Ishikawa +2
We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight…
Noncommutative -algebra Net: Learning Neural Networks with Powerful Product Structure in -algebra
Ryuichiro Hataya, Yuka Hashimoto
We propose a new generalization of neural network parameter spaces with noncommutative -algebra, which possesses a rich noncommutative structure of products. We show that this…
Learning in RKHM: a -Algebraic Twist for Kernel Machines
Yuka Hashimoto, Masahiro Ikeda, Hachem Kadri
Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist t…
Operator-theoretic Analysis of Mutual Interactions in Synchronized Dynamics
Yuka Hashimoto, Masahiro Ikeda, Hiroya Nakao +1
Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we…
-algebra Net: A New Approach Generalizing Neural Network Parameters to -algebra
Yuka Hashimoto, Zhao Wang, Tomoko Matsui
We propose a new framework that generalizes the parameters of neural network models to -algebra-valued ones. -algebra is a generalization of the space of complex numbers.…
Normal integral bases and Gaussian periods in the simplest cubic fields
Yu Hashimoto, Miho Aoki
We give all normal integral bases for the simplest cubic field generated by the roots of Shanks' cubic polynomial when these bases exist, that is, is tamely r…
Reproducing kernel Hilbert C*-module and kernel mean embeddings
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda +3
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 th…
Shifting chain maps in quandle homology and cocycle invariants
Yu Hashimoto, Kokoro Tanaka
Quandle homology theory has been developed and cocycles have been used to define invariants of oriented classical or surface links. We introduce a shifting chain map on each qu…
Kernel Mean Embeddings of Von Neumann-Algebra-Valued Measures
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda +2
Kernel mean embedding (KME) is a powerful tool to analyze probability measures for data, where the measures are conventionally embedded into a reproducing kernel Hilbert space (RKH…
Analysis via Orthonormal Systems in Reproducing Kernel Hilbert -Modules and Applications
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda +3
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 th…
Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noise
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda +2
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods…
Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators
Isao Ishikawa, Keisuke Fujii, Masahiro Ikeda +2
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonline…