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482
Survey of clustering algorithms
- IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
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Cited by 501 (4 self)
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Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
A systematic comparison and evaluation of biclustering methods for gene expression data
, 2006
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Graph mining: laws, generators, and algorithms
- ACM COMPUT SURV (CSUR
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in ..."
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Cited by 132 (7 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in real-world graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
Nonsmooth nonnegative matrix factorization (nsnmf
- IEEE transactions on
, 2006
"... Abstract—We propose a novel nonnegative matrix factorization model that aims at finding localized, part-based, representations of nonnegative multivariate data items. Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted “nonsmooth nonnegative matrix factoriz ..."
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Cited by 65 (4 self)
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Abstract—We propose a novel nonnegative matrix factorization model that aims at finding localized, part-based, representations of nonnegative multivariate data items. Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted “nonsmooth nonnegative matrix factorization ” (nsNMF), corresponds to the optimization of an unambiguous cost function designed to explicitly represent sparseness, in the form of nonsmoothness, which is controlled by a single parameter. In general, this method produces a set of basis and encoding vectors that are not only capable of representing the original data, but they also extract highly localized patterns, which generally lend themselves to improved interpretability. The properties of this new method are illustrated with several data sets. Comparisons to previously published methods show that the new nsNMF method has some advantages in keeping faithfulness to the data in the achieving a high degree of sparseness for both the estimated basis and the encoding vectors and in better interpretability of the factors. Index Terms—nonnegative matrix factorization, constrained optimization, datamining, mining methods and algorithms, pattern analysis, feature extraction or construction, sparse, structured, and very large systems. æ 1
Multi-way distributional clustering via pairwise interactions
- In ICML
, 2005
"... We present a novel unsupervised learning scheme that simultaneously clusters variables of several types (e.g., documents, words and authors) based on pairwise interactions between the types, as observed in co-occurrence data. In this scheme, multiple clustering systems are generated aiming at maximi ..."
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Cited by 60 (10 self)
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We present a novel unsupervised learning scheme that simultaneously clusters variables of several types (e.g., documents, words and authors) based on pairwise interactions between the types, as observed in co-occurrence data. In this scheme, multiple clustering systems are generated aiming at maximizing an objective function that measures multiple pairwise mutual information between cluster variables. To implement this idea, we propose an algorithm that interleaves top-down clustering of some variables and bottom-up clustering of the other variables, with a local optimization correction routine. Focusing on document clustering we present an extensive empirical study of two-way, three-way and four-way applications of our scheme using six real-world datasets including the 20 Newsgroups (20NG) and the Enron email collection. Our multi-way distributional clustering (MDC) algorithms consistently and significantly outperform previous state-of-the-art information theoretic clustering algorithms. 1.
Disco: Distributed co-clustering with map-reduce. ICDM
, 2008
"... Huge datasets are becoming prevalent; even as researchers, we now routinely have to work with datasets that are up to a few terabytes in size. Interesting real-world applications produce huge volumes of messy data. The mining process involves several steps, starting from pre-processing the raw data ..."
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Cited by 53 (1 self)
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Huge datasets are becoming prevalent; even as researchers, we now routinely have to work with datasets that are up to a few terabytes in size. Interesting real-world applications produce huge volumes of messy data. The mining process involves several steps, starting from pre-processing the raw data to estimating the final models. As data become more abundant, scalable and easyto-use tools for distributed processing are also emerging. Among those, Map-Reduce has been widely embraced by both academia and industry. In database terms, Map-Reduce is a simple yet powerful execution engine, which can be complemented with other data storage and management components, as necessary. In this paper we describe our experiences and findings in applying Map-Reduce, from raw data to final models, on an important mining task. In particular, we focus on co-clustering, which has been studied in many applications such as text mining, collaborative filtering, bio-informatics, graph mining. We propose the Distributed Co-clustering (DisCo) framework, which introduces practical approaches for distributed data pre-processing, and co-clustering. We develop DisCo using Hadoop, an open source Map-Reduce implementation. We show that DisCo can scale well and efficiently process and analyze extremely large datasets (up to several hundreds of gigabytes) on commodity hardware. 1
The discrete basis problem
, 2005
"... We consider the Discrete Basis Problem, which can be described as follows: given a collection of Boolean vectors find a collection of k Boolean basis vectors such that the original vectors can be represented using disjunctions of these basis vectors. We show that the decision version of this problem ..."
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Cited by 41 (13 self)
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We consider the Discrete Basis Problem, which can be described as follows: given a collection of Boolean vectors find a collection of k Boolean basis vectors such that the original vectors can be represented using disjunctions of these basis vectors. We show that the decision version of this problem is NP-complete and that the optimization version cannot be approximated within any finite ratio. We also study two variations of this problem, where the Boolean basis vectors must be mutually otrhogonal. We show that the other variation is closely related with the well-known Metric k-median Problem in Boolean space. To solve these problems, two algorithms will be presented. One is designed for the variations mentioned above, and it is solely based on solving the k-median problem, while another is a heuristic intended to solve the general Discrete Basis Problem. We will also study the results of extensive experiments made with these two algorithms with both synthetic and real-world data. The results are twofold: with the synthetic data, the algorithms did rather well, but with the real-world data the results were not as good.
Model-based overlapping clustering
- In KDD
, 2005
"... While the vast majority of clustering algorithms are partitional, many real world datasets have inherently overlapping clusters. Several approaches to finding overlapping clusters have come from work on analysis of biological datasets. In this paper, we interpret an overlapping clustering model prop ..."
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Cited by 40 (7 self)
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While the vast majority of clustering algorithms are partitional, many real world datasets have inherently overlapping clusters. Several approaches to finding overlapping clusters have come from work on analysis of biological datasets. In this paper, we interpret an overlapping clustering model proposed by Segal et al. [23] as a generalization of Gaussian mixture models, and we extend it to an overlapping clustering model based on mixtures of any regular exponential family distribution and the corresponding Bregman divergence. We provide the necessary algorithm modifications for this extension, and present results on synthetic data as well as subsets of 20-Newsgroups and EachMovie datasets.
MJ: TRICLUSTER: an effective algorithm for mining coherent clusters in 3Dmicroarray data
- In SIGMOD ’05: Proceedings of the 2005 ACM SIGMOD international
"... In this paper we introduce a novel algorithm called tri-Cluster, for mining coherent clusters in three-dimensional (3D) gene expression datasets. triCluster can mine arbi-trarily positioned and overlapping clusters, and depending on di®erent parameter values, it can mine di®erent types of clusters, ..."
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Cited by 38 (2 self)
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In this paper we introduce a novel algorithm called tri-Cluster, for mining coherent clusters in three-dimensional (3D) gene expression datasets. triCluster can mine arbi-trarily positioned and overlapping clusters, and depending on di®erent parameter values, it can mine di®erent types of clusters, including those with constant or similar values along each dimension, as well as scaling and shifting ex-pression patterns. triCluster relies on graph-based ap-proach to mine all valid clusters. For each time slice, i.e., a gene£sample matrix, it constructs the range multigraph, a compact representation of all similar value ranges between any two sample columns. It then searches for constrained maximal cliques in this multigraph to yield the set of bi-clusters for this time slice. Then triCluster constructs another graph using the biclusters (as vertices) from each time slice; mining cliques from this graph yields the ¯nal set of triclusters. Optionally, triCluster merges/deletes some clusters having large overlaps. We present a useful set of metrics to evaluate the clustering quality, and we show that triCluster can ¯nd signi¯cant triclusters in the real microarray datasets. 1.
