二分图划分与数据聚类
Bipartite graph partitioning and data clustering
摘要：
从数据采掘应用中产生的许多数据类型可以被建模为二分图，示例包括文本语料库中的术语和文档、购物篮分析中的客户和购买项目以及电影推荐系统中的评论者和电影。在本文中，我们提出了一种新的数据聚类方法的基础上划分的基础二分图。通过最小化二分图的不匹配顶点对之间的边权重的归一化和来构造分区。我们表明，通过计算相关的二分图的边权重矩阵的部分奇异值分解（SVD），可以得到一个近似的解决方案的最小化问题。我们指出我们的聚类算法的连接，对应分析中使用的多元分析。我们还简要讨论了将数据对象分配到多个集群的问题。在实验结果中，我们将我们的聚类算法应用于文档聚类问题，以说明其有效性和效率。
英文摘要：
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. We point out the connection of our clustering algorithm to correspondence analysis used in multivariate analysis. We also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, we apply our clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.
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