Reproducing kernel Hilbert C*-module and kernel mean embeddings
Authors: Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda, Fuyuta Komura, Takeshi Katsura, Yoshinobu Kawahara
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Then, we apply the developed theories to generalize kernel PCA (Sch olkopf and Smola, 2001), analyze time-series data with the theory of dynamical system, and analyze interaction effects for infinite dimensional data. The remainder of this paper is organized as follows. ... In Sections 5, we propose a KME in RKHMs, and show the connection between the injectivity of the KME and the universality of RKHM. Then, in Section 6, we discuss applications of the developed results to kernel PCA, time-series data analysis, and the analysis of interaction effects in finite or infinite dimensional data. ... Numerical examples ... Experiments with synthetic data ... Experiments with real-world data |
| Researcher Affiliation | Collaboration | Yuka Hashimoto EMAIL NTT Network Service Systems Laboratories, NTT Corporation ... Isao Ishikawa EMAIL Center for Data Science, Ehime University ... Masahiro Ikeda EMAIL Center for Advanced Intelligence Project, RIKEN ... Fuyuta Komura EMAIL Faculty of Science and Technology, Keio University |
| Pseudocode | No | The paper describes methods like 'Gradient descent on Hilbert C -modules' (Section 6.1.2) using mathematical formulas and prose, but does not include any clearly labeled pseudocode blocks or algorithms with structured steps. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing source code for the described methodology, nor does it include links to code repositories. |
| Open Datasets | Yes | Experiments with real-world data To show the proposed PCA with RKHMs extracts the continuous dependencies of samples on the principal axes as we insisted in Section 3, we conducted experiments with climate data in Japan1. The data is composed of the maximum and minimum daily temperatures at 47 prefectures in Japan in 2020. ... 1. available at https://www.data.jma.go.jp/gmd/risk/obsdl/ ... Numerical examples To show the proposed analysis with RKHMs captures continuous changes of values of kernels along functional data as we insisted in Section 3, we conducted experiments with river flow data of the Thames River in London2. The data is composed of daily flow at 10 stations. ... 2. available at https://nrfa.ceh.ac.uk/data/search |
| Dataset Splits | No | The paper mentions generating synthetic data and using real-world data from publicly available sources but does not specify any training, testing, or validation splits for these datasets. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not specify any particular software or library versions used for implementation or experiments. |
| Experiment Setup | Yes | Experiments with synthetic data ... The parameters were set as λ = 0.1 and ηt = 0.01. ... Numerical examples ... The parameter λ in the objective function of the PCA was set as 0.5. |