|Last modified date：2023.11.22
Associate Professor / Division of Industrial and Mathematical Statistics / Institute of Mathematics for Industry
|Last modified date：2023.11.22
|Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, Yuichi Ike, Claude Viterbo, The γ-support as a micro-support, Comptes Rendus Mathématique , 2023.12.
|Kohei Ueda, Yuichi Ike, and Kenji Yamanishi , Change Detection with Probabilistic Models on Persistence Diagrams, 2022 IEEE International Conference on Data Mining (ICDM), 10.1109/ICDM54844.2022.00153, 2022.12.
|Ryo Yuki, Yuichi Ike, and Kenji Yamanishi, Dimensionality Selection of Hyperbolic Graph Embeddings using Decomposed Normalized Maximum Likelihood Code-Length, 2022 IEEE International Conference on Data Mining (ICDM), 10.1109/ICDM54844.2022.00077, 2022.12.
|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.
|Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki, Algebraic stability theorem for derived categories of zigzag persistence modules, Journal of Topology and Analysis, 2022.08, We study distances on zigzag persistence modules from the viewpoint of
derived categories. It is known that the derived categories of ordinary and
arbitrary zigzag persistence modules are equivalent. Through this derived
equivalence, we define distances on the derived category of arbitrary zigzag
persistence modules and prove an algebraic stability theorem. We also compare
our distance with the distance for purely zigzag persistence modules introduced
by Botnan--Lesnick and the sheaf-theoretic convolution distance due to
|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..
|Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs.
|ATOL: Measure Vectorisation for Automatic Topologically-Oriented Learning
Robust topological information commonly comes in the form of a set of
persistence diagrams, finite measures that are in nature uneasy to affix to
generic machine learning frameworks. We introduce a learnt, unsupervised
measure vectorisation method and use it for reflecting underlying changes in
topological behaviour in machine learning contexts. Relying on optimal measure
quantisation results the method is tailored to efficiently discriminate
important plane regions where meaningful differences arise. We showcase the
strength and robustness of our approach on a number of applications, from
emulous and modern graph collections where the method reaches state-of-the-art
performance to a geometric synthetic dynamical orbits problem. The proposed
methodology comes with only high level tuning parameters such as the total
measure encoding budget, and we provide a completely open access software..
|Viewpoint Planning of Projector Placement for Spatial Augmented Reality using Star-Kernel Decomposition.
|PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures.
|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.
|Kentaro Kanamori, Takuya Takagi, Ken Kobayashi, Yuichi Ike, Kento Uemura, Hiroki Arimura, Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization, Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI2021), 2021.02, Post-hoc explanation methods for machine learning models have been widely
used to support decision-making. One of the popular methods is Counterfactual
Explanation (CE), which provides a user with a perturbation vector of features
that alters the prediction result. Given a perturbation vector, a user can
interpret it as an "action" for obtaining one's desired decision result. In
practice, however, showing only a perturbation vector is often insufficient for
users to execute the action. The reason is that if there is an asymmetric
interaction among features, such as causality, the total cost of the action is
expected to depend on the order of changing features. Therefore, practical CE
methods are required to provide an appropriate order of changing features in
addition to a perturbation vector. For this purpose, we propose a new framework
called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective
function that evaluates a pair of an action and an order based on feature
interaction. To extract an optimal pair, we propose a mixed-integer linear
optimization approach with our objective function. Numerical experiments on
real datasets demonstrated the effectiveness of our OrdCE in comparison with
unordered CE methods..
|Yuichi Ike, Compact exact Lagrangian intersections in cotangent bundles via sheaf quantization, Publications of the Research Institute for Mathematical Sciences, 55, 4, 737-778, 2019.10.
|Categorical localization for the coherent-constructible correspondence.
|Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets.
|Yuichi Ike, Microlocal Lefschetz classes of graph trace kernels, 10.4171/PRIMS/175, 52, 1, 83-101, 2016.01.