基於核方法聚類過程之相似圖建構及核生成和標準化的研究

Abstract

聚類方法比如特徵值聚類，核k平均群聚類和對稱非負矩陣分解在資料探勘上扮演著重要的角色。這一篇論文聚焦在回答關於核聚類的方法的重要研究問題：相似矩陣的生成，稀疏化和標準化會如何影響聚類的結果？我們能不能辨別出一些能夠給出高質量聚類結果的上述組合。與此同時，在這一篇論文中我們提出了使用Laplacian圖來解釋為什麼使用K臨近圖稀疏化會使得效果更好。

Kernel-based clustering such as Spectral Clustering, Kernel K-Means, and Symmetry NMF plays an important role on data mining. This works aims at answering a critical research question regarding to kernel-based clustering: how the similarity matrix generations, sparsification, and the normalizations influence the clustering results? Can we identify a set of combinations among them to achieve high-quality clustering results. Furthermore, in this thesis we provide a interpretation of the graph sparsification, especially K-NN graph in terms of the graph Laplacian property to explain why it works.