Bipartite graph partitioning and data clustering

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.Comment: Proceedings of ACM CIKM 2001, the Tenth International Conference on Information and Knowledge Management, 200

Approximate Computation and Implicit Regularization for Very Large-scale Data Analysis

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by statisticians, scientific computers, machine learners, and other who work on what may be broadly termed statistical data analysis. In this article, I will address fundamental aspects of this algorithmic-statistical disconnect, with an eye to bridging the gap between these two very different approaches. A concept that lies at the heart of this disconnect is that of statistical regularization, a notion that has to do with how robust is the output of an algorithm to the noise properties of the input data. Although it is nearly completely absent from computer science, which historically has taken the input data as given and modeled algorithms discretely, regularization in one form or another is central to nearly every application domain that applies algorithms to noisy data. By using several case studies, I will illustrate, both theoretically and empirically, the nonobvious fact that approximate computation, in and of itself, can implicitly lead to statistical regularization. This and other recent work suggests that, by exploiting in a more principled way the statistical properties implicit in worst-case algorithms, one can in many cases satisfy the bicriteria of having algorithms that are scalable to very large-scale databases and that also have good inferential or predictive properties.Comment: To appear in the Proceedings of the 2012 ACM Symposium on Principles of Database Systems (PODS 2012

Visual-hint Boundary to Segment Algorithm for Image Segmentation

Image segmentation has been a very active research topic in image analysis area. Currently, most of the image segmentation algorithms are designed based on the idea that images are partitioned into a set of regions preserving homogeneous intra-regions and inhomogeneous inter-regions. However, human visual intuition does not always follow this pattern. A new image segmentation method named Visual-Hint Boundary to Segment (VHBS) is introduced, which is more consistent with human perceptions. VHBS abides by two visual hint rules based on human perceptions: (i) the global scale boundaries tend to be the real boundaries of the objects; (ii) two adjacent regions with quite different colors or textures tend to result in the real boundaries between them. It has been demonstrated by experiments that, compared with traditional image segmentation method, VHBS has better performance and also preserves higher computational efficiency.Comment: 45 page