Non convex optimization techniques based on DC programming and DCA and evolution methods for clustering

Abstract : This thesis focus on four problems in data mining and machine learning: clustering data streams, clustering massive data sets, weighted hard and fuzzy clustering and finally the clustering without a prior knowledge of the clusters number. Our methods are based on deterministic optimization approaches, namely the DC (Difference of Convex functions) programming and DCA (Difference of Convex Algorithm) for solving some classes of clustering problems cited before. Our methods are also, based on elitist evolutionary approaches. We adapt the clustering algorithm DCA–MSSC to deal with data streams using two windows models: sub–windows and sliding windows. For the problem of clustering massive data sets, we propose to use the DCA algorithm with two phases. In the first phase, massive data is divided into several subsets, on which the algorithm DCA–MSSC performs clustering. In the second phase, we propose a DCA–Weight algorithm to perform a weighted clustering on the obtained centers in the first phase. For the weighted clustering, we also propose two approaches: weighted hard clustering and weighted fuzzy clustering. We test our approach on image segmentation application. The final issue addressed in this thesis is the clustering without a prior knowledge of the clusters number. We propose an elitist evolutionary approach, where we apply several evolutionary algorithms (EAs) at the same time, to find the optimal combination of initial clusters seed and in the same time the optimal clusters number. The various tests performed on several sets of large data are very promising and demonstrate the effectiveness of the proposed approaches.
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Minh Thuy Ta. Non convex optimization techniques based on DC programming and DCA and evolution methods for clustering. Other [cs.OH]. Université de Lorraine, 2014. English. ⟨NNT : 2014LORR0099⟩. ⟨tel-01750817⟩

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