隨著圖像式(Graph-structured)的資料近年來被廣泛的應用於各種不同的領域如生物網路，社群網路等等，如何有效率的分析這些資料就變得十分重要，因為往往可以從中發現有意義的資訊。圖像資料分析的方法有很多種，本研究主要探討網路比對(Network Alignment)這個主題，希望能在不同的網路中找尋相似的部份，更進一步完成不重複的跨網路配對。
一般而言，傳統演算法在處理網路比對問題時常會遭遇兩個挑戰，第一個是當網路規模大於萬個點時，計算時間會大幅的增加，導致實際應用的效果不佳，第二個則是傳統演算法的設計都是針對靜態的網路，也就是當網路進行更動時，就必須視為新的網路而重新計算，造成許多不必要的浪費。本研究參考了過去的兩個演算法(IsoRank演算法，NSD演算法)，利用張量積的性質加速網路比對的計算時間，並搭配平行運算的技巧進行實作，結果顯示速度都提升超過二十倍，尤其是當網路規模越大時，效果更加明顯。另外，本研究也利用了鄰接矩陣(adjacency matrix)的性質發展出了一套動態演算法，標記出在網路改變時不受影響的點，避免不需要的計算。實驗結果顯示當變動範圍不大時，動態演算法的效果相當顯著。最後，我們將網路比對做更實際的應用:新聞網路，透過網路比對的方式找出不同新聞平台中相似的新聞推薦給閱聽者，以避免陷入同一媒體所傳遞的意識形態之中。

With the extensively increasing use of graph-structured datasets, it has become significant to determine how to analyze large-scale structured data. These analyses, such as finding conserved subgraphs across networks, uncovering diversity of its structures by differentiating a graph and alignment have been widely investigated in recent decades.
In this study, we focus on the problem of network alignment (NA), which aims to find a mapping between nodes of two or more networks; more precisely, we revisit a global many-to-many multiple network alignment tool, IsoRankN, which incorporates the concept of the PageRank searching algorithm. IsoRankN is a state-of-the-art NA algorithm with good performance over protein-protein interaction networks. Briefly speaking, the aligner can be simply divided into two stages: computing pairwise topological similarity scores across networks and then finding alignment clusters. However, there are actually two challenges for current NA algorithms, including IsoRankN. First, it is quite time consuming at the stage of similarity scoring computation, especially when considering large-scale networks or multiple network alignment.
Therefore, the first goal of this study is trying to improve the efficiency of the IsoRankN algorithm using some matrix-multiplication speedup techniques, like Tensor product. The other challenge is that most of the existing NA algorithms consider static data only. However, most complex real-world systems evolve over time and should thus be modeled as dynamic networks. In order to avoid redundant computation load, we attempt to develop a dynamic version of IsoRankN in this study. The preliminary result shows that the power method can work in a more efficient way if dynamic operations occur locally. Next, we will present detailed experimental evaluation of two variations of IsoRankN. We will also compare it with the static one in some diverse network-structured data sets. We believe that this tool can be extended to more practical applications, e.g., social networking.

摘要 I
Abstract II
致謝 III
Contents IV
List of Figures and Tables V
1. Introduction and Motivation 1
2. Preliminary and Terminology 4
2.1 IsoRank inspired algorithm 4
2.2 Network similarity decomposition(NSD) inspired algorithm 6
2.2.1 Kronecker Product 6
2.2.2 Uncoupling Skill 8
2.2.3 Complexity Consideration 9
3. Dynamic Algorithm 10
3.1 Main Idea 10
3.2 D-IsoRank Algorithm 13
3.3 Complexity Consideration 13
4. Experimental Result 15
4.1 Environment and Biological dataset 15
4.2 Speed-up Techniques 15
4.3 Dynamical Update 18
5. Application 22
5.1 News Network Construction 23
5.2 Flow Chart 26
5.3 Evaluation Measures 26
5.4 Analyze Clustering Result 28
5.5 Dynamical Update on news network 30
6. Conclusion 32
Reference 33

Reference
1. Yuanyuan Tian Richard C. McEachin Carlos Santos David J. States Jignesh M. Patel (2007) SAGA: a subgraph matching tool for biological graphs Bioinformatics, Volume 23, Issue 2, 15 January 2007, Pages 232–239
2. Ernesto Estrada, Juan A. Rodriguez-Velazquez (2005) Subgraph Centrality in Complex Networks Physical Review E 71, 056103
3. Singh R., Xu J., Berger B. (2007) Pairwise Global Alignment of Protein Interaction Networks by Matching Neighborhood Topology. In: Speed T., Huang H. (eds) Research in Computational Molecular Biology. RECOMB 2007. Lecture Notes in Computer Science, vol 4453. Springer, Berlin, Heidelberg
4. G.H. Golub and C. Van Loan. (2006) Matrix computations. Johns Hopkins University
Press
5. Giorgos Kollias Shahin Mohammadi Ananth Grama (2012) Network Similarity Decomposition (NSD): A Fast and Scalable Approach to Network Alignment IEEE Transactions on Knowledge and Data Engineering (Volume: 24, Issue: 12, Dec. 2012)
6. Armadillo C++ linear algebra library: http://arma.sourceforge.net/license.html
7. Manning, Christopher D.; Raghavan, Prabhakar; Schütze, Hinrich (2008). "w-shingling". Introduction to Information Retrieval. Cambridge University Press. ISBN 978-1-139-47210-4.
8. Tan, Pang-Ning; Steinbach, Michael; Kumar, Vipin (2005), Introduction to Data Mining
9. R. Subhashini ; V. Jawahar Senthil Kumar (2010) Evaluating the Performance of Similarity Measures Used in Document Clustering and Information Retrieval. 2010 First International Conference on Integrated Intelligent Computing
10. 劉思葦 楊惟翔 高楚筠 (2015) 比對拓樸新聞網路_將跨平台隱含的相關新聞分群 清華大學工業工程與工程管理專題報告
11. The Cosine Similarity values for different documents, retrieved from http://blog.christianperone.com/2013/09/machine-learning-cosine-similarity-for vector-space-models-part-iii/