在這項研究中，我們提出使用階層式非負矩陣分解來探討主題間的關係，在階層式的結構中，越低的層數主題會越具體，而越高的層數中的主題則越抽象。藉由從較具體的主題，一層一層至抽象主題的這個過程，可以漸進式的了解主題間的關係。此外我們的模型可以觀察主題的演變，主題是會隨著時間演進、合併以及消失的。
在我們的實驗中，我們使用非負矩陣分解，去分解各階層間，主題以及術語組成的矩陣，探討每年中各階層間的主題演變，我們藉由樹和網路將主題間的關係視覺化，藉由網路的方式，可以去呈現出主題以及術語間的關係，而主題樹可以表現出各個階層間的主題與主題之間的關係。

In this thesis, we propose Hierarchical Non-negative Matrix Factorization(hNMF) to discover the hierarchical correlation among topics. The topics in lower layers are more concrete, whereas ones in higher layers are more abstract. Furthermore, our model could discover the evolution of topics, recognizing whether topics arise, merge or disappear. In our experiment, we applied nonnegative matrix factorization(NMF) on document-term matrix in each layer, detecting the evolution of topics in several years. We visualized the relationships by graphical model such as networks and trees. Topic networks present the communication between topics and terms, and topic trees reveal the hierarchical relationship among topics.

論文審定書 i
中文摘要 ii
英文摘要 iii
1. INTRODUCTION 1
2. BACKGROUND AND RELATED WORK 3
2.1 NON-NEGATIVE MATRIX FACTORIZATION (NMF) 3
2.2 HIERARCHICAL NON-NEGATIVE MATRIX FACTORIZATION(HNMF) 5
3. METHODOLOGY 5
3.1 HOW MANY KS? 6
3.2 HIERARCHICAL NON-NEGATIVE MATRIX FACTORIZATION 7
3.3 FIND THE EVOLUTION OF TOPIC 9
3.4 HNMF RELATIONSHIP BY NETWORK 11
4. EXPERIMENT 12
4.1 FIND TOPICS BY NMF WITH SAME K 12
4.2.1 TOPIC MODELING WITH HIERARCHICAL NON-NEGATIVE MATRIX FACTORIZATION 17
4.2.2 TOPIC TREE OF HIERARCHICAL NON-NEGATIVE MATRIX FACTORIZATION 27
4.3 DISPLAY TOPIC – HNMF RELATIONSHIP BY NETWORK 29
5. DISCUSSION 32
6. CONCLUSION 34
7. REFERENCE 34

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