|Yoshinobu Kawahara||Last modified date：2020.01.11|
Professor / Division for Intelligent Societal Implementation of Mathmatical Computation
Institute of Mathematics for Industry
Institute of Mathematics for Industry
Website of the laboratory (English) .
Website of Structure Learning Team, RIKEN AIP Center (English) .
Doctor of Engineering (The University of Tokyo)
Country of degree conferring institution (Overseas)
Field of Specialization
Machine learning (ML) is the research field that is relevant to data-driven studies in a variety of scientific fields and AI-related technologies. We conduct researches on a variety of topics related to (1) Development of new methodologies in statistical machine learning, and (2) Application of developed methods to scientific and industrial fields.
- Operator-theoretic Data Analysis of Nonlinear Dynamical Systems
keyword : time-series data, dynamical system, machine learning, transfer operator
- Machine Learning with Prior Information on Structures in Data
keyword : machine learning, structured learning, discrete structure
- Combinatorial Optimization for Machine Learning
keyword : machine learning, combinatorial optimization, submodular set-function
- Machine learning for time-series data
keyword : time-series prediction, change-point detection, learning dynamical systems
|1.||Keisuke Fujii, Naoya Takeishi, Benio Kibushi, Motoki Kouzaki, and Yoshinobu Kawahara, Data-driven spectral analysis for coordinative structures in periodic human locomotion, Scientific reports, 10.1038/s41598-019-53187-1, 9, 1, 2019.12.|
|2.||K. Fujii, and Y. Kawahara, Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables, Neural Networks, 10.1016/j.neunet.2019.04.020, 117, 94-103, 2019.09, [URL], Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data..|
|3.||I. Ishikawa, K. Fujii, M. Ikeda, Y. Hashimoto, and Y. Kawahara, Metric on nonlinear dynamical systems with Perron-Frobenius operators, Advances in Neural Information Processing Systems 31 (Proc. of NeurIPS'18), 2856-2866, 2018.12, [URL].|
|4.||K. Fujii, T. Kawasaki, Y. Inaba, and Y. Kawahara, Prediction and classification in equation-free collective motion dynamics, PLoS Computational Biology, 10.1371/journal.pcbi.1006545, 14, 11, e1006545, 2018.11, [URL].|
|5.||N. Takeishi, Y. Kawahara, and T. Yairi, Learning Koopman invariant subspaces for dynamic mode decomposition, Advances in Neural Information Processing Systems 30 (Proc. of NIPS'17), 1131-1141, 2017.12, [URL].|
|6.||H. Wang, Y. Kawahara, C. Weng, and J. Yuan, Representative Selection with Structured Sparsity, Pattern Recognition, 10.1016/j.patcog.2016.10.014, 63, 268-278, 2017.03, [URL].|
|7.||Y. Kawahara, Dynamic Mode Decomposition with Reproducing Kernels for Koopman Spectral Analysis, Advances in Neural Information Processing Systems 29 (Proc. of NIPS'16), 911-919, 2016.12, [URL].|
|8.||B. Xin, Y. Kawahara, Y. Wang, L. Hu, and W. Gao, Efficient generalized fused lasso and its applications, ACM Transactions on Intelligent Systems and Technology, 10.1145/2847421, 7, 4, 2016.05, [URL].|
|9.||Y. Kawahara, and M. Sugiyama, Sequential change-point detection based on direct density-ratio estimation, Statistical Analysis and Data Mining, 10.1002/sam.10124, 5, 2, 114-127, 2012.04, [URL].|
|10.||Y. Kawahara, K. Nagano, K. Tsuda, and J.A. Bilmes, Submodularity cuts and applications, Advances in Neural Information Processing Systems 22 (Proc. of NIPS'09), 916-924, 2009.12, [URL].|
Lectures in the Graduate School of Mathematics etc., and lectures and education in the Faculty of Mathematics
Professional and Outreach Activities
He currently serves as an Action Editor of Neural Networks (Elsevier), and has been a member of Program Committees / Senior Program Committees for several top-tier conferences in the related fields of computer science, including ICML, AAAI, IJCAI, AISTATS, and KDD..