图移位型算法的一个收敛定理
A Convergence Theorem for the Graph Shift-type Algorithms
摘要：
图移位（GS）算法是近年来在噪声数据中发现稠密子图的一种有效方法。然而，没有理论基础来证明GS算法的收敛性。在本文中，我们提出了一个通用的理论框架，包括三个关键GS组件：生成序列集的单纯形，单调和连续的目标函数和封闭映射。我们证明了GS算法与这样的组件可以被改造，以适应Zangwill的收敛定理，和GS程序产生的序列集总是终止于局部最大值，或在最坏的情况下，包含一个子序列收敛到局部最大值的相似性度量函数。该框架通过扩展到其他GS型算法和实验结果进行了验证。
英文摘要：
Graph Shift (GS) algorithms are recently focused as a promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the GS Algorithm. In this paper, we propose a generic theoretical framework consisting of three key GS components: simplex of generated sequence set, monotonic and continuous objective function and closed mapping. We prove that GS algorithms with such components can be transformed to fit the Zangwill's convergence theorem, and the sequence set generated by the GS procedures always terminates at a local maximum, or at worst, contains a subsequence which converges to a local maximum of the similarity measure function. The framework is verified by expanding it to other GS-type algorithms and experimental results.
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