Identifying Smallest Unique Subgraphs in a Heterogeneous Social Network

本研究旨在尋找一個網路中的對於任一單元周邊發現有價值的網路結構。對於價值我們給予一個新的定義─簡單但獨特。而為了有效尋找這種結構我們將它化為一個子圖找尋問題。接著我們先檢驗這個問題所需要的複雜度不適合實際應用。再提出一個貪婪的作法在可行的時間內盡可能尋找最好的結構。最後我們將它應用在一個實際的社群網路上以驗證這個方法的實用性和有效性。This paper proposes to study a novel problem, discovering a Smallest Unique Subgraph (SUS) for any node of interest specified by user in a heterogeneous social network. The rationale of the SUS problem lies in how a person is different from any others in a social network, and how to represent the identity of a person using her surrounding relational structure in a social network. To deal with the proposed SUS problem, we develop an Ego-Graph Heuristic (EGH) method to efficiently solve the SUS problem in an approximated manner. EGH intelligently examine whether one graph is not isomorphic to the other, instead of using the conventional subgraph isomorphism test. We also prove SUS is a NP-complete problem through doing a reduction from Minimum Vertex Cover (MVC) in a homogeneous tree structure. Experimental results conducted on a real-world movie heterogeneous social network data show both the promising efficiency and compactness of our method.摘要 ………………………………………………………………………… i Abstract ………………………………………………………………………. i 目錄 ……………………………………………………………………………… ii List of Feagures ………………………………………………………………….. iii List of Tables ……………………………………………………………………. vi Chapter 1. Introduction…………………………………………………… 1 Chapter 2. Problem Statement and Analysis …………………………… 4 Chapter 3. Ego-Graph Heuristics Approach …………………………… 5 3-1. Algorithm Overview …………………………………………… 5 3-2. Extract k-layer Subgraph as Candidates …………………………. 6 3-3. Egocentric Information Table……………………………………… 6 3-4. Uniqueness Validation and Discovery……………………………… 9 3-5. Finding Unique Subgraphs………………………………………… 12 Chapter 4. Smallest Unique Subtree ……………………………………… 14 4-1. Problem Statement…………………………………………………… 15 4-2. Proof Sketch for the Reduction from MVC to SUS-T……………… 18 4-3. Problem Mapping ………………………………………………… 19 Chapter 5. Experiments ………………………………………………… 20 5-1. Dataset……………………………………………………………… 20 5-2. Evaluation Settings………………………………………………… 20 5-3. Experiment Results………………………………………………… 21 Chapter 6. Related Work ……………………………………………… 23 Chapter 7. Conclusion…………………………………………………… 23 參考文獻…………………………………………………………………….…… 25 附錄………………………………………………………………………………. 2