mlsanityData to 14 Oct 2026

Reproducing kernel Hilbert C*-module and kernel mean embeddings

arXiv 2101.11410 ↗First posted 27 Jan 2021stat.ML cs.LG math.OAcited by 10

Not on the map. Why?

Abstract (arXiv)

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) 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.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 11 of its 63 references that are in the map. First posted on arXiv 27 Jan 2021.

Builds on

11 of 63 references.

References · 11

  1. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  2. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
  3. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 158
  4. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 60
  5. 2017Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spacescited by 48
  6. 2014A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learningcited by 12
  7. 2018Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observablescited by 12
  8. 2018Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operatorscited by 7
  9. 2019Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noisecited by 7
  10. 2019Kernel Mean Matching for Content Addressability of GANscited by 5
  11. 2017The Matrix Hilbert Space and Its Application to Matrix Learningcited by 2

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Cited by year

Citing papers per year: 2022: 2; 2023: 3; 2024: 4; 2025: 1.

10 papers.

  1. 2022C^*-algebra Net: A New Approach Generalizing Neural Network Parameters to C^*-algebracited by 9
  2. 2024Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spacescited by 9
  3. 2022Learning in RKHM: a C^*-Algebraic Twist for Kernel Machinescited by 7
  4. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  5. 2023Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebracited by 4
  6. 2024C^*-Algebraic Machine Learning: Moving in a New Directioncited by 1
  7. 2024Spectral Truncation Kernels: Noncommutativity in C^*-algebraic Kernel Machinescited by 1
  8. 2025Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potentialcited by 1
  9. 2023Localisation of Regularised and Multiview Support Vector Machine Learningcited by 0
  10. 2024Quantum Circuit C^*-algebra Netcited by 0