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RIKEN Center for Advanced Intelligence Project Functional Analytic Learning Unit

Unit Leader: Minh Ha Quang (Ph.D.)

Research Summary

Minh  Ha Quang(Ph.D.)

The Functional Analytic Learning Unit focuses on theories and methods from functional analysis and related fields in machine learning, in particular methods based on reproducing kernel Hilbert spaces (RKHS), matrix and operator theory, Riemannian geometry, information geometry, and optimal transport. An important direction is the theoretical formulations and algorithms based on infinite-dimensional geometrical methods, especially in the RKHS setting. The targeted application domains include, but are not limited to, functional data analysis, computer vision, image and signal processing, brain imaging, and brain computer interfaces.

Research Subjects

  • Vector-valued Reproducing Kernel Hilbert Spaces
  • Geometrical methods in machine learning

Main Research Fields

  • Informatics

Related Research Fields

  • Mathematical & Physical Sciences
  • Intelligent Informatics
  • Mathematical Informatics
  • Mathematical Analysis


  • Reproducing kernel Hilbert spaces
  • Riemannian geometry
  • Information geometry
  • Optimal transport
  • Gaussian processes

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.

  • 1. Ha Quang Minh.:
    "Alpha-Beta Log-Determinant Divergences Between Positive Definite Trace Class Operators".
    Information Geometry(2) 101–176(2019)
  • 2. Ha Quang Minh.:
    "Infinite-dimensional Log-Determinant divergences between positive definite Hilbert–Schmidt operators".
    Positivity (24), pages 631–662(2020)
  • 3. Ha Quang Minh.:
    "Regularized Divergences Between Covariance Operators and Gaussian Measures on Hilbert Spaces".
    Journal of Theoretical Probability (2020)
  • 4. Ha Quang Minh.:
    "A unified formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt distances between positive definite operators".
    International Conference on Geometric Science of Information (GSI 2019), pages 475-483
  • 5. *Ha Quang Minh.:
    "Infinite-dimensional Log-Determinant divergences between positive definite trace class operators"
    Linear Algebra and Its Applications 528, pp. 331-383 (2017).
  • 6. *Ha Quang Minh, V. Murino.:
    "Covariances in Computer Vision and Machine Learning."
    Morgan & Claypool Synthesis Lectures on Computer Vision, November (2017).
  • 7. *Ha Quang Minh, L. Bazzani, V. Murino.:
    "A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning"
    Journal of Machine Learning Research 17(25), pp. 1-72 (2016).
  • 8. *Ha Quang Minh, M. San Biagio, L. Bazzani, V. Murino.:
    "Approximate Log-Hilbert-Schmidt distances between covariance operators for image classification"
    IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2016), Las Vegas, USA, June 2016.
  • 9. *Ha Quang Minh, M. San Biagio, and V. Murino.:
    "Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces."
    Advances in Neural Information Processing Systems(NIPS 2014), Montreal, Canada, December 2014.
  • 10. *Ha Quang Minh, L. Wiskott.:
    "Multivariate slow feature analysis and decorrelation filtering for blind source separation"
    IEEE Transactions on Image Processing, volume 22, issue 7, pp. 2737-2750 (2013).

Related Links

Lab Members

Principal investigator

Minh Ha Quang
Unit Leader

Core members

Thanh Tam Le
Visiting Scientist


Position Deadline
Seeking a Research Scientist or Postdoctoral Researcher (W22137) Open until filled

Contact Information

Nihonbashi 1-chome Mitsui Building, 15th floor,
1-4-1 Nihonbashi, Chuo-ku, Tokyo
103-0027, Japan
Email: minh.haquang [at] riken.jp