高維度資料的結構分析：計算拓樸與其在影片摘要的應用

Topological data analysis (TDA) is one of the sub-fields of mathematics, offering a rich source of valuable information to study problems involving data described in high dimensional space. TDA has the advantage of capturing novel invariant structural features of high dimensional data. However, applied TDA is challenging, because it requires advanced mathematical background not easily accessible to most computer science practitioners. In this research project, we have developed computational TDA tools, which are especially suitable for vision and image processing. Moreover, we have demonstrated how TDA can be used for automatically summarizing videos. Our experimental results show the potential of TDA based approaches to facilitate tasks involving the understanding and analysis of structural information inherited in videos. We also find that TDA has the potential to complement and enhance the deep-learning techniques. We have been continuing the researches on integrating TDA into deep models.