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Seminars

Special Colloquium

Geometry-Adaptive Transforms: Learning the Underlying Analytic Structure for Matrix Denoising, Fast Algorithms, and Biomedical Data Understanding

2025/11/25 (Tue.) 10:00~11:00
  • Date : 2025/11/25 (Tue.) 10:00~11:00
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Pei-Chun Su (Yale University)
  • Abstract : Many high-dimensional datasets possess hidden analytic structure, such as local smoothness, hierarchical organization, and multiscale regularity, that classical algorithms cannot easily exploit. In this talk, I will present a unified framework of geometry-adaptive transforms that learns this underlying analytic structure directly from data and uses it to enable fast algorithms for matrix multiplication, optimal matrix denoising, and interpretable representations of complex scientific measurements.
    The framework builds on the Questionnaire algorithm and tree-Haar transforms to construct multiscale partitions and localized bases that adapt to the intrinsic geometry of the data. These data-driven transforms reveal hierarchical low-rank structure, enabling butterfly-style fast computation and matrix denoising via localized wavelet shrinkage, while maintaining variables that are fully grounded in observable measurements rather than latent coordinates. I will illustrate the power of this approach through applications in several scientific domains, including the recovery of fetal electrocardiograms (fECG) from maternal abdominal signals, the discovery of localized molecular markers in single-cell RNA data, and the extraction of structured activity patterns from neural recordings. Together, these examples show how geometry-adaptive transforms provide a principled bridge between harmonic analysis, numerical algorithms, and high-dimensional data understanding.
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