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On the complexity of minimum sumofsquares clustering. Cahiers du GERAD
"... Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. A BranchandCut SDPBased Algorithm for ..."
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. A BranchandCut SDPBased Algorithm for
On approximate balanced biclustering
 The Eleventh International Computing and Combinatorics Conference (COCOON
, 2005
"... In this paper, we consider the socalled balanced biclustering problem for n entities in a suitable space where the number of entities in each cluster is bounded. A special case of the balanced biclustering, where the number of entities in each cluster is fixed, is discussed. We present several al ..."
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In this paper, we consider the socalled balanced biclustering problem for n entities in a suitable space where the number of entities in each cluster is bounded. A special case of the balanced biclustering, where the number of entities in each cluster is fixed, is discussed. We present several algorithms, including deterministic and heuristic to attack these problems. In particular, a novel and efficient heuristic, in which we first reformulate the constrained biclustering problem into a quadratic programming(QP) problem and then try to solve it by optimization technique, is proposed. We prove that our approximation algorithm can provide a 2approximate solution to the original problem. Promising numerical results are reported.
TITLE: Approximation Methods to Clustering Analysis
"... ii Clustering involves partitioning a given data set into several groups based on some similarity/dissimilarity measurements. Cluster analysis has been widely used in information retrieval, text and web mining, pattern recognition, image segmentation and software reverse engineering. Kmeans is the ..."
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ii Clustering involves partitioning a given data set into several groups based on some similarity/dissimilarity measurements. Cluster analysis has been widely used in information retrieval, text and web mining, pattern recognition, image segmentation and software reverse engineering. Kmeans is the most intuitive and popular clustering algorithm and the working horse for clustering. However, the classical Kmeans suffers from several flaws. First, the algorithm is very sensitive to the initialization method and can be easily trapped at a local minimum regarding to the measurement (the sum of squared errors) used in the model. On the other hand, it has been proved that finding a global minimal sum of the squared errors is NPhard even when k = 2. In the present model for Kmeans clustering, all the variables are required to be discrete and the objective is nonlinear and nonconvex. In the first part of the thesis, we consider the issue of how to derive an
CONTINUOUS OPTIMIZATION APPROACHES FOR CLUSTERING VIA MINIMUM SUM OF SQUARES
"... Abstract: In this paper, we survey the usage of semidefinite programming (SDP), and nonsmooth optimization approaches for solving the minimum sum of squares problem which is of fundamental importance in clustering. We point out that the main clustering idea of support vector clustering (SVC) metho ..."
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Abstract: In this paper, we survey the usage of semidefinite programming (SDP), and nonsmooth optimization approaches for solving the minimum sum of squares problem which is of fundamental importance in clustering. We point out that the main clustering idea of support vector clustering (SVC) method could be interpreted as a minimum sum of squares problem and explain the derivation of semidefinite programming and a nonsmooth optimization formulation for the minimum sum of squares problem. We compare the numerical results produced by the semidefinite formulation of minimum sum of squares with the results obtained from approaching it via nonsmooth optimization on two datasets.