Centers & Labs

RIKEN Center for Advanced Intelligence Project

Functional Analytic Learning Unit

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

The Functional Analytic Learning Unit focuses on functional analytic and geometrical methods in machine learning, in particular methods based on Riemannian geometry, matrix and operator theory, and vector-valued Reproducing Kernel Hilbert Spaces (RKHS). An important direction is the theoretical formulations and algorithms based on the geometry of positive definite operators, especially RKHS covariance operators. 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.

Main Research Field

Computer Science

Related Research Fields


Research Subjects

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

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.
  1. *Ha Quang Minh.:
    "Infinite-dimensional Log-Determinant divergences between positive definite trace class operators"
    Linear Algebra and Its Applications 528, pp. 331-383 (2017).
  2. *Ha Quang Minh, V. Murino.:
    "Covariances in Computer Vision and Machine Learning."
    Morgan & Claypool Synthesis Lectures on Computer Vision, November (2017).
  3. *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).
  4. *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.
  5. *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.
  6. *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).
  7. *V.Sindhwani, H.Q. Minh, A.C. Lozano.:
    "Scalable Matrix-valued Kernel Learning for Highdimensional Nonlinear Multivariate Regression and Granger Causality"
    Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI 2013), July 2013, Bellevue, Washington, USA, Microsoft Best Paper Award, IBM Pat Goldberg Memorial Best Paper Award.
  8. *Minh Ha Quang, S. H. Kang, and T. Le.:
    "Image and Video Colorization Using Vector-Valued Reproducing Kernel Hilbert Spaces"
    Journal of Mathematical Imaging and Vision, volume 37, number 1, pp. 49-65 (2010).
  9. *Ha Quang Minh.:
    "Some Properties of Gaussian Reproducing Kernel Hilbert Spaces and Their Implications for Function Approximation and Learning Theory"
    Constructive Approximation, volume 32, number 2, pp. 307-338 (2010).
  10. *Ha Quang Minh, P. Niyogi, and Y. Yao.:
    "Mercer's Theorem, Feature Maps, and Smoothing"
    Proceedings of the 19th Conference on Learning Theory (COLT 2006), Springer Lecture Notes in Computer Science volume 4005, pp. 154-168 (2006).

Contact information

Nihonbashi 1-chome Mitsui Building, 15th floor,
1-4-1 Nihonbashi, Chuo-ku, Tokyo
103-0027, Japan

Email: minh.haquang [at]

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