| （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 primary research interest lies in the intersection of Topological Data Analysis (TDA) and Machine Learning (ML). I focus on optimization problems in TDA, specifically by incorporating topological regularization into dimension reduction techniques like Nonnegative Matrix Factorization (Top-NMF). My goal is to extract semantically interpretable fundamental units from data by quantifying structural features—such as connectivity and holes—using persistent homology. Currently, I am applying this theoretical framework to medical imaging analysis for ultra-early disease diagnosis.
| キーワード | Topological Data Analysis (TDA), Optimization problems in TDA |
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| リンク | Homepage |