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We propose a novel Multi-Manifold Matrix Decomposition for Co-clustering (M3DC) algorithm that considers the geometric structures of both the sample manifold and the feature manifold simultaneously. Specifically, multiple candidate manifolds are constructed separately to take local invariance into account. Then, we employ multi-manifold learning to approximate the optimal intrinsic manifold, which better reflects the local geometrical structure, by linearly combining these candidate manifolds. In M3DC, the candidate manifolds are obtained using various manifold-based dimensionality reduction methods. These methods are based on different rationales and use different metrics for data distances. Experimental results on several real data sets demonstrate the effectiveness of our proposed M3DC. HighlightsWe consider the geometric structures of both sample and feature manifolds.To reduces the complexity, we use two low-dimensional intermediate matrices.We employ multi-manifold learning to approximate the intrinsic manifold.The intrinsic manifold is constructed by linearly combining multiple manifolds.The candidate manifolds are constructed using six dimensionality reduction methods.

Spectral clustering is often carried out by combining spectral data embedding and $k$ -means clustering. However, the aims, dimensionality reduction and clustering, are usually not performed jointly. In this brief, we propose a novel approach to finding an optimal spectral embedding for identifying a partition of the set of objects; it iteratively alternates spectral embedding and clustering. In doing so, we show that our model can learn a low-dimensional representation more suited to clustering. Compared with classical spectral clustering methods, the proposed algorithm is not costly and outperforms not only these methods but also other nonnegative matrix factorization variants.

In this work, we propose a novel way to consider the clustering and the reduction of the dimension simultaneously. Indeed, our approach takes advantage of the mutual reinforcement between data reduction and clustering tasks. The use of a low-dimensional representation can be of help in providing simpler and more interpretable solutions. We show that by doing so, our model is able to better approximate the relaxed continuous dimension reduction solution by the true discrete clustering solution. Experiment results show that our method gives better results in terms of clustering than the state-of-the-art algorithms devoted to similar tasks for data sets with different proprieties.

International audience

International audience; In this paper, we present a novel feature selection approach based on an efficient selection of pair wise constraints. This aims at selecting the most coherent constraints extracted from labeled part of data. The relevance of features is then evaluated according to their efficient locality preserving and chosen constraint preserving ability. Finally, experimental results are provided for validating our proposal with respect to other known feature selection methods.

International audience; Nous présentons dans ce papier une nouvelle approche de co- classification automatique sur les tableaux de données continues. Cette approche est basée sur les cartes topologiques de Kohonen que nous appelons Bi-SOM (Bi-clustering based on one Self-Organizing Map). En outre de la question principale de la co-classification automatique liée au traitement simultané des lignes et des colonnes d'une matrice de données, nous proposons dans cette approche de répondre à plusieurs problématiques liées à cette tâche, à savoir: (1) la visualisation topologiques de bi-clusters avec une notion de voisinage, (2) l'optimisation de ces dits bi-clusters dans des macro-blocs et (3) la réduction de dimension par élimination itérative de blocs de "bruit". Enfin, nous présentons des résultats issus des expérimentations faites sur plusieurs bases de données réelles et d'autres synthétiques pour valider notre approche en comparaison avec d'autres méthodes de co-classification automatique.