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Yuichi Ike Last modified date：2023.11.22

Associate Professor / Division of Industrial and Mathematical Statistics
Institute of Mathematics for Industry


Graduate School
Department of Mathematics
Graduate School of Mathematics
Undergraduate School
Department of Mathematics
School of Sciences


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Homepage
https://kyushu-u.elsevierpure.com/en/persons/yuichi-ike
　Reseacher Profiling Tool　Kyushu University Pure
https://sites.google.com/view/yuichi-ike
Phone
092-802-4406
Fax
092-802-4406
Academic Degree
Ph.D (mathematical science), The University of Tokyo, March 2018
Country of degree conferring institution (Overseas)
No
Field of Specialization
microlocal sheaf theory, topological data analysis
Total Priod of education and research career in the foreign country
00years03months
Outline Activities
I am mainly studying topological data analysis and microlocal sheaf theory. For topological data analysis, I am trying to develop effective methods for combining persistent homology and machine learning, such as filtration learning and optimization of persistent homology-based loss functions. For microlocal sheaf theory, I am interested in applying sheaf theory to symplectic geometry. I use an interleaving distance between sheaves to study the energy of Hamiltonian dynamical systems and use the completeness of the distances to study C0 symplectic geometry.

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Research
Research Interests
  • Topological data analysis and machine learning
    keyword : persistent homology, TDA-based loss functions, filtration learning
    2018.04～2028.03.
  • Microlocal sheaf theory and symplectic geometry
    keyword : microsupport, sheaf quanization
    2016.10～2025.04.
Academic Activities
Reports
 Show All Reports >>
1. Topological Data Analysis and Its Applications in Machine Learning.
Papers
 Show All Papers >>
1. Tomohiro Asano, Yuichi Ike, Sheaf quantization and intersection of rational Lagrangian immersions, Annales de l'Institut Fourier, 10.5802/aif.3554, 1-55, 2022.11.
2. Mathieu Carrière, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hariprasad Kannan, Optimizing persistent homology based functions, Proceedings of the 38th International Conference on Machine Learning (ICML2021), 2021.07, Solving optimization tasks based on functions and losses with a topological
flavor is a very active, growing field of research in data science and
Topological Data Analysis, with applications in non-convex optimization,
statistics and machine learning. However, the approaches proposed in the
literature are usually anchored to a specific application and/or topological
construction, and do not come with theoretical guarantees. To address this
issue, we study the differentiability of a general map associated with the most
common topological construction, that is, the persistence map. Building on real
analytic geometry arguments, we propose a general framework that allows us to
define and compute gradients for persistence-based functions in a very simple
way. We also provide a simple, explicit and sufficient condition for
convergence of stochastic subgradient methods for such functions. This result
encompasses all the constructions and applications of topological optimization
in the literature. Finally, we provide associated code, that is easy to handle
and to mix with other non-topological methods and constraints, as well as some
experiments showcasing the versatility of our approach..
3. Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs.
4. PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures.
5. Tomohiro Asano and Yuichi Ike, Persistence-like distance on Tamarkin's category and symplectic displacement energy, Journal of Symplectic Geometry, https://dx.doi.org/10.4310/JSG.2020.v18.n3.a1, 18, 3, 613-649, 2020.06.
Presentations
 Show All Presentations >>
1. Yuichi Ike, Convergence of stochastic subgradient descent for persistence-based loss functions, The 15th Mathematical Society of Japan-Seasonal Institute (MSJ-SI2022), Deepening and Evolution of Applied Singularity Theory, 2022.11, [URL].
2. Yuichi Ike, Completeness of interleaving distance on Tamarkin category and C^0-symplectic geometry, Séminaire symplectix, 2022.10, [URL].
3. Yuichi Ike, Interleaving distance for sheaves and symplectic geometry, Boston-Keio-Tsinghua Workshop 2022, 2022.06, [URL].
4. Yuichi Ike, Topological loss functions and topological representation learning, Workshop on Functional Inference and Machine Intelligence 2022, 2022.03, [URL].
5. Microlocal sheaf theory and energy estimates in symplectic geometry.
6. Persistence-like distance on a sheaf category and displacement energy in symplectic geometry.
7. Yuichi Ike, Stochastic subgradient descent for persistence-based functionals and automated vectorization method for persistence diagrams, Asia Pacific Seminar on Applied Topology and Geometry, 2020.12, [URL].
Membership in Academic Society
  • The Japan Society for Industrial and Applied Mathematics
Awards
  • Dean's Award for Master Thesis
  • Dean's Award for Doctoral Thesis
  • 第18回若手優秀講演賞 (2021年度)
Educational
Educational Activities
I am in charge of School of Engineering, Department of Mathematics, Graduate School of Mathematics, and Joint Graduate School of Mathematics for Innovation. Educational activities are conducted through lectures and seminars.
Social
Professional and Outreach Activities
I have developed some techniques for topological data analysis and counterfactual explanations that can be applied to real-world situations, through joint research with companies..


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