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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…
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…
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…