Rank aggregation methods for the Web
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Algorithms for graph partitioning on the planted partition model
Random Structures & Algorithms
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Discovering local structure in gene expression data: the order-preserving submatrix problem
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Mixtures of distance-based models for ranking data
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SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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ACM Transactions on Knowledge Discovery from Data (TKDD)
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IEEE Transactions on Visualization and Computer Graphics
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IDA'07 Proceedings of the 7th international conference on Intelligent data analysis
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ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Survey of clustering algorithms
IEEE Transactions on Neural Networks
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We consider the problem of clustering a set of chains to k clusters. A chain is a totally ordered subset of a finite set of items. Chains are an intuitive way to express preferences over a set of alternatives, as well as a useful representation of ratings in situations where the item-specific scores are either difficult to obtain, too noisy due to measurement error, or simply not as relevant as the order that they induce over the items. First we adapt the classical k-means for chains by proposing a suitable distance function and a centroid structure. We also present two different approaches for mapping chains to a vector space. The first one is related to the planted partition model, while the second one has an intuitive geometrical interpretation. Finally we discuss a randomization test for assessing the significance of a clustering. To this end we present an MCMC algorithm for sampling random sets of chains that share certain properties with the original data. The methods are studied in a series of experiments using real and artificial data. Results indicate that the methods produce interesting clusterings, and for certain types of inputs improve upon previous work on clustering algorithms for orders.