國立政治大學應用物理所

本次邀請《新加坡南洋理工大學/國立中山大學 顏聰文 博士》蒞臨演講，

活動相關訊息如下，請參考。

演講時間：110年3月3日(三)14:10~15:30

演講場地：志希樓2樓 理學院會議室

主  講  人：新加坡南洋理工大學/國立中山大學 顏聰文 博士

演講主題：Using topological data analysis (TDA) and persistent homology to analyze the stock markets in Singapore and Taiwan.

摘　　要：In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, data analysis, machine learning, computer vision, computational biology, brain functional networks, financial networks, haze detection, etc. In this talk, I will focus on stock markets and demonstrate how TDA can be useful in this regard. I first will explain signatures that can be detected using TDA, for three toy models of topological changes. I will then show how to go beyond network concepts like nodes (0-simplex) and links (1-simplex), and the standard minimal spanning tree (MST) or planar maximally filtered graph (PMFG) picture of the cross correlations in stock markets, to work with faces (2-simplex) or any k-dim simplex in TDA. By scanning through a full range of correlation thresholds in a procedure called filtration, we were able to examine robust topological features (i.e. less susceptible to random noise) in higher dimensions. To demonstrate the advantages of TDA, we collected time-series data from the Straits Times Index (STI), and Taiwan Capitalization Weighted Stock Index (TAIEX), and then computed barcodes, persistence diagrams, persistent entropy, the bottleneck distance, Betti numbers, and Euler characteristic. We found that during the periods of market crashes, the homology groups become less persistent as we vary the characteristic correlation. For both markets, we found consistent signatures associated with market crashes in the Betti numbers, Euler characteristics, and persistent entropy, in agreement with our theoretical expectations.

※本場次演講採自由入場，歡迎有興趣的師生共同參與。