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.