Clustering and Industry Comparison of Different Stocks Based on Topological Data Analysis Features

In today's complex financial environment, traditional analytical methods often rely on linear assumptions or backward-looking information, which often proves to be inadequate. This study proposes a stock grouping structure that combines topological data analysis (TDA) with machine learning techniques. By converting stock price series into persistent representations via Takens embedding, it is found that TDA-based grouping surpasses dynamic time warping (DTW) in terms of profile values and discriminability measures. The results show sector-specific arrangements as well as inter-sector connections, illustrating how TDA can identify linear market frameworks and persistent topological consistency, thus presenting an innovative methodology for financial series inspection.