Community detection is a fundamental problem in knowledge discovery and data mining. In this paper we propose a semi-binary matrix factorization (SBMF) model for community detection, which can be understood as a marriage between $K$ -means clustering and (semi-)nonnegative matrix factorization. This leads to an easy-to-interpret factorization that can naturally handle overlapping communities. Unlike $K$ -means, the proposed approach does not restrict each individual to belong to only a single community, nor does it restrict the sum of “soft membership” values to add up to one. We derive relatively easy-to-check uniqueness conditions suggesting that meaningful communities can be obtained via SBMF. Computing a (least-squares) optimal SBMF is a hard mixed integer nonconvex optimization problem. We bypass this challenge by converting the problem into a coupled matrix-tensor factorization form, which only involves continuous variables and can be tackled using tensor decomposition tools, and can also be used to initialize optimization based methods. We present experiments with real data to demonstrate the effectiveness of the proposed approach for community detection in coauthorship networks and in financial stock market data.

中文翻译：

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通过半二元矩阵分解进行重叠社区检测：可识别性和算法

社区检测是知识发现和数据挖掘中的一个基本问题。在本文中，我们提出了一种用于社区检测的半二元矩阵分解（SBMF）模型，可以理解为$K$ - 表示聚类和（半）非负矩阵分解。这导致易于解释的分解，可以自然地处理重叠社区。不像$K$ -意味着，所提出的方法不限制每个人只属于一个社区，也不限制“软成员”值的总和加起来为一个。我们得出了相对容易检查的唯一性条件，表明可以通过 SBMF 获得有意义的社区。计算（最小二乘）最优 SBMF 是一个硬混合整数非凸优化问题。我们通过将问题转换为耦合矩阵张量分解形式来绕过这一挑战，该形式仅涉及连续变量，可以使用张量分解工具解决，也可以用于初始化基于优化的方法。我们使用真实数据进行实验，以证明所提出的社区检测方法在合着网络和金融股票市场数据中的有效性。