mlsanityData to 14 Oct 2026

Learning in RKHM: a C^*-Algebraic Twist for Kernel Machines

arXiv 2210.11855 ↗First posted 21 Oct 2022stat.ML cs.LG math.OAcited by 7

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Abstract (arXiv)

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 to this rich literature by generalizing supervised learning in RKHS and vvRKHS to reproducing kernel Hilbert C^*-module (RKHM), and show how to construct effective positive-definite kernels by considering the perspective of C^*-algebra. Unlike the cases of RKHS and vvRKHS, we can use C^*-algebras to enlarge representation spaces. This enables us to construct RKHMs whose representation power goes beyond RKHSs, vvRKHSs, and existing methods such as convolutional neural networks. Our framework is suitable, for example, for effectively analyzing image data by allowing the interaction of Fourier components.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 14 of its 46 references that are in the map. First posted on arXiv 21 Oct 2022.

Builds on

14 of 46 references.

References · 14

  1. 2020A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospectscited by 397
  2. 2016A vector-contraction inequality for Rademacher complexitiescited by 142
  3. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 60
  4. 2014Convolutional Kernel Networkscited by 47
  5. 2016End-to-End Kernel Learning with Supervised Convolutional Kernel Networkscited by 28
  6. 2019Beyond Least-Squares: Fast Rates for Regularized Empirical Risk Minimization through Self-Concordancecited by 28
  7. 2019Globally Convergent Newton Methods for Ill-conditioned Generalized Self-concordant Lossescited by 17
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  9. 2014A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learningcited by 12
  10. 2022Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groupscited by 11
  11. 2021Reproducing kernel Hilbert C*-module and kernel mean embeddingscited by 10
  12. 2022C^*-algebra Net: A New Approach Generalizing Neural Network Parameters to C^*-algebracited by 9
2 more
  1. 2021Entangled Kernels -- Beyond Separabilitycited by 7
  2. 2013Stability of Multi-Task Kernel Regression Algorithmscited by 2

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Cited by year

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

7 papers.

  1. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  2. 2023Noncommutative C^*-algebra Net: Learning Neural Networks with Powerful Product Structure in C^*-algebracited by 4
  3. 2024C^*-Algebraic Machine Learning: Moving in a New Directioncited by 1
  4. 2024Spectral Truncation Kernels: Noncommutativity in C^*-algebraic Kernel Machinescited by 1
  5. 2025Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potentialcited by 1
  6. 2023Localisation of Regularised and Multiview Support Vector Machine Learningcited by 0
  7. 2024Quantum Circuit C^*-algebra Netcited by 0