在本論文中，我們討論了在有號網路 (signed network) 的社群偵測。在有號網路中，鏈結符號為正代表有好關係，鏈結符號若為負則表示敵對關係。Haray’s Theorem 告訴我們一個結構平衡 (structurally balanced) 的兩群網路中，每個迴圈的負號的鏈結個數會是偶數。我們使用錯誤更正碼中漢明距離的概念來更正錯誤的鏈結，藉由最小化漢明距離，我們提出了三種方法：1. 多數決演算法 2. 機率決演算法 3. 符號反轉演算法。另外在分群方法中，初始化的問題一直備受討論，對於這個問題，我們在機率決演算法中也推導出了特徵向量的初始化方式。我們也找到了對於最小化漢明距離的充分必要條件，藉此我們提出了符號反轉演算法。最後，我們延伸我們的演算法到多群的網路偵測上。在和SDP演算法、LR-SVP演算法以及Kset-plus演算法比較過後，實驗結果顯示我們提出的演算法均有不錯的表現。

In this thesis, we consider the community detection problem in signed networks. In signed networks, there are two types of edges: positive edges (friends) and negative edges (enemies). Harary's theorem states that a structurally balanced signed network is clusterable and it can be separated into several communities. We link the community detection problem in a signed network with two communities to the decoding problem for a parity-check code. Each cycle in a signed network can be viewed as a parity-check constraint. Based on minimizing the Hamming distance, we propose three algorithms: (i) the majority vote decoding algorithm, (ii) the probabilistic decoding algorithm, and (iii) the sign flipping algorithm. We also derive an eigenvector initialization as the initial condition. Moreover, a necessary and sufficient condition for the minimum Hamming distance leads to the sign flipping decoder algorithm. Further, we extend our algorithm to more than two communities. We compare the performance of our algorithm with the SDP algorithm, the LR-SVP algorithm, and the Kset$^+$ algorithm. Our experimental results show that our algorithms have a good performance than the others.

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