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Rearrangement clustering: Pitfalls, remedies, and applications
 Journal of Machine Learning Research
, 2006
"... Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names ..."
Abstract

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Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names and reinvented several times, this clustering technique has been extensively used in many fields over the last three decades. In this paper, we point out two critical pitfalls that have been previously overlooked. The first pitfall is deleterious when rearrangement clustering is applied to objects that form natural clusters. The second concerns a similarity metric that is commonly used. We present an algorithm that overcomes these pitfalls. This algorithm is based on a variation of the Traveling Salesman Problem. It offers an extra benefit as it automatically determines cluster boundaries. Using this algorithm, we optimally solve four benchmark problems and a 2,467gene expression data clustering problem. As expected, our new algorithm identifies better clusters than those found by previous approaches in all five cases. Overall, our results demonstrate the benefits of rectifying the pitfalls and exemplify the usefulness of this clustering technique. Our code is available at our websites.
Algorithms and Experimental Study for the Traveling Salesman Problem of Second Order
"... Abstract. We introduce a new combinatorial optimization problem, which is a generalization of the Traveling Salesman Problem (TSP) and which we call Traveling Salesman Problem of Second Order (2TSP). It is motivated by an application in bioinformatics, especially the Permuted Variable Length Markov ..."
Abstract

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Abstract. We introduce a new combinatorial optimization problem, which is a generalization of the Traveling Salesman Problem (TSP) and which we call Traveling Salesman Problem of Second Order (2TSP). It is motivated by an application in bioinformatics, especially the Permuted Variable Length Markov model. We propose seven elementary heuristics and two exact algorithms for the 2TSP, some of which are generalizations of similar algorithms for the Asymmetric Traveling Salesman Problem (ATSP), some of which are new ideas. Finally we experimentally compare the algorithms for random instances and real instances from bioinformatics. Our experiments show that for the real instances most heuristics lead to optimum or almostoptimum solutions, and for the random instances the exact algorithms need less time than for the real instances.