RIKEN Center for Advanced Intelligence Project Functional Analytic Learning Unit

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

Japanese Page

Research Summary

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

Keywords

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).

Lab Members

Principal investigator

Minh Ha Quang: Unit Leader

Core members

Jean Carlo Guella: Postdoctoral Researcher

Contact Information

Nihonbashi 1-chome Mitsui Building, 15th floor,
1-4-1 Nihonbashi, Chuo-ku, Tokyo
103-0027, Japan
Tel：+81-(0)-6225-2482
Email: minh.haquang [at] riken.jp