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612
Consensus clustering  A resamplingbased method for class discovery and visualization of gene expression microarray data
 MACHINE LEARNING 52 (2003) 91–118 FUNCTIONAL GENOMICS SPECIAL ISSUE
, 2003
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ModelBased Clustering and Data Transformations for Gene Expression Data
, 2001
"... Motivation: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particula ..."
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Cited by 149 (8 self)
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Motivation: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, modelbased clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications.
Learning systems of concepts with an infinite relational model
 In Proceedings of the 21st National Conference on Artificial Intelligence
, 2006
"... Relationships between concepts account for a large proportion of semantic knowledge. We present a nonparametric Bayesian model that discovers systems of related concepts. Given data involving several sets of entities, our model discovers the kinds of entities in each set and the relations between ki ..."
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Cited by 147 (19 self)
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Relationships between concepts account for a large proportion of semantic knowledge. We present a nonparametric Bayesian model that discovers systems of related concepts. Given data involving several sets of entities, our model discovers the kinds of entities in each set and the relations between kinds that are possible or likely. We apply our approach to four problems: clustering objects and features, learning ontologies, discovering kinship systems, and discovering structure in political data. Philosophers, psychologists and computer scientists have proposed that semantic knowledge is best understood as a system of relations. Two questions immediately arise: how can these systems be represented, and how are these representations acquired? Researchers who start with the
Integrating topics and syntax
 In Advances in Neural Information Processing Systems 17
, 2005
"... Statistical approaches to language learning typically focus on either shortrange syntactic dependencies or longrange semantic dependencies between words. We present a generative model that uses both kinds of dependencies, and can be used to simultaneously find syntactic classes and semantic topics ..."
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Cited by 135 (15 self)
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Statistical approaches to language learning typically focus on either shortrange syntactic dependencies or longrange semantic dependencies between words. We present a generative model that uses both kinds of dependencies, and can be used to simultaneously find syntactic classes and semantic topics despite having no representation of syntax or semantics beyond statistical dependency. This model is competitive on tasks like partofspeech tagging and document classification with models that exclusively use short and longrange dependencies respectively. 1
Computing communities in large networks using random walks
 J. of Graph Alg. and App. bf
, 2004
"... Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advan ..."
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Cited by 113 (2 self)
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Dense subgraphs of sparse graphs (communities), which appear in most realworld complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2 log n) and space O(n 2) in most realworld cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.
Learning spectral clustering
, 2003
"... Spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clusters having low similarity. In this paper, we derive a new cost fu ..."
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Cited by 99 (5 self)
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Spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clusters having low similarity. In this paper, we derive a new cost function for spectral clustering based on a measure of error between a given partition and a solution of the spectral relaxation of a minimum normalized cut problem. Minimizing this cost function with respect to the partition leads to a new spectral clustering algorithm. Minimizing with respect to the similarity matrix leads to an algorithm for learning the similarity matrix. We develop a tractable approximation of our cost function that is based on the power method of computing eigenvectors. 1
Learning the k in kmeans
 In Proc. 17th NIPS
, 2003
"... When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The Gmeans algorithm is based on a statistical test for the hypothesis t ..."
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Cited by 93 (5 self)
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When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The Gmeans algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. Gmeans runs kmeans with increasing k in a hierarchical fashion until the test accepts the hypothesis that the data assigned to each kmeans center are Gaussian. Two key advantages are that the hypothesis test does not limit the covariance of the data and does not compute a full covariance matrix. Additionally, Gmeans only requires one intuitive parameter, the standard statistical significance level α. We present results from experiments showing that the algorithm works well, and better than a recent method based on the BIC penalty for model complexity. In these experiments, we show that the BIC is ineffective as a scoring function, since it does
Toward Objective Evaluation of Image Segmentation Algorithms
, 2007
"... Unsupervised image segmentation is an important component in many image understanding algorithms and practical vision systems. However, evaluation of segmentation algorithms thus far has been largely subjective, leaving a system designer to judge the effectiveness of a technique based only on intui ..."
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Cited by 80 (2 self)
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Unsupervised image segmentation is an important component in many image understanding algorithms and practical vision systems. However, evaluation of segmentation algorithms thus far has been largely subjective, leaving a system designer to judge the effectiveness of a technique based only on intuition and results in the form of a few example segmented images. This is largely due to image segmentation being an illdefined problem—there is no unique groundtruth segmentation of an image against which the output of an algorithm may be compared. This paper demonstrates how a recently proposed measure of similarity, the Normalized Probabilistic Rand (NPR) index, can be used to perform a quantitative comparison between image segmentation algorithms using a handlabeled set of groundtruth segmentations. We show that the measure allows principled comparisons between segmentations created by different algorithms, as well as segmentations on different images. We outline a procedure for algorithm evaluation through an example evaluation of some familiar algorithms—the meanshiftbased algorithm, an efficient graphbased segmentation algorithm, a hybrid algorithm that combines the strengths of both methods, and expectation maximization. Results are presented on the 300 images in the publicly available Berkeley Segmentation Data Set.
Spectral learning
 In IJCAI
, 2003
"... We present a simple, easily implemented spectral learning algorithm which applies equally whether we have no supervisory information, pairwise link constraints, or labeled examples. In the unsupervised case, it performs consistently with other spectral clustering algorithms. In the supervised case, ..."
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Cited by 77 (5 self)
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We present a simple, easily implemented spectral learning algorithm which applies equally whether we have no supervisory information, pairwise link constraints, or labeled examples. In the unsupervised case, it performs consistently with other spectral clustering algorithms. In the supervised case, our approach achieves high accuracy on the categorization of thousands of documents given only a few dozen labeled training documents for the 20 Newsgroups data set. Furthermore, its classification accuracy increases with the addition of unlabeled documents, demonstrating effective use of unlabeled data. By using normalized affinity matrices which are both symmetric and stochastic, we also obtain both a probabilistic interpretation of our method and certain guarantees of performance. 1
Comparing clusterings: an axiomatic view
 In ICML ’05: Proceedings of the 22nd international conference on Machine learning
, 2005
"... This paper views clusterings as elements of a lattice. Distances between clusterings are analyzed in their relationship to the lattice. From this vantage point, we first give an axiomatic characterization of some criteria for comparing clusterings, including the variation of information and the unad ..."
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Cited by 73 (3 self)
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This paper views clusterings as elements of a lattice. Distances between clusterings are analyzed in their relationship to the lattice. From this vantage point, we first give an axiomatic characterization of some criteria for comparing clusterings, including the variation of information and the unadjusted Rand index. Then we study other distances between partitions w.r.t these axioms and prove an impossibility result: there is no “sensible” criterion for comparing clusterings that is simultaneously (1) aligned with the lattice of partitions, (2) convexely additive, and (3) bounded. 1.