| （理論面の）対象 | Topological Data Analysis (TDA): A mathematical framework for analyzing the shape and structure of data using topology. It extracts topological features such as connected components, loops, and voids to uncover hidden patterns. |
| （理論面の）目標 | Develop and refine methods for extracting meaningful topological features from high-dimensional and complex data. |
| ここまでの成果/重要な発見 | I suggested the optimization problem that reflects topological properties from data, leading to high performance in the classification of time series data. |
| これからの目標/現在取り組んでいる目標 | I aim to develop a novel dimensionality reduction technique that effectively extracts the topological properties of data by combining Nonnegative Matrix Factorization (NMF) with topological regularization, and to apply this technique in medical and scientific data analysis. |
| 応用上の成果/目標 | A model for determining the presence of disease through geometric structural analysis. For example, lung diseases (honeycomb lung) and connectivity analysis in brain networks. |
| さらなる発展の可能性・方向性 | A research direction that enables intuitive understanding of machine learning results by analyzing the geometric structure of data. |
My research interest lies in Topological Data Analysis (TDA). The goal
of my research is to recover the original system from sampled data using
TDA and Machine Learning (ML). Specifically, this involves recovering a
dynamical system from time-series data, as well as addressing
optimization problems arising from it. Naturally, my research is related
to Hamiltonian dynamics, dimension reduction and related topological
optimization: nonconvex, nonsmooth optimization problems.
| キーワード | Topological time-series analysis, topological optimization |
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| 部門 | |
| リンク | Homepage |