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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(More)
To tackle the co-clustering problem for binary and categorical data, we propose a generalized modularity measure and a spectral approximation of the modularity matrix. A spectral algorithm maximizing the modularity measure is then presented. Experimental results are performed on a variety of simulated and real-world data sets confirming the interest of the(More)
This paper proposes a spectral algorithm for cross-topographic clustering. It leads to a simultaneous clustering on the rows and columns of data matrix, as well as the projection of the clusters on a two-dimensional grid while preserving the topological order of the initial data. The proposed algorithm is based on a spectral decomposition of this data(More)
This paper introduces a new topological clustering formalism, dedicated to categorical data arising in the form of a binary matrix or a sum of binary matrices. The proposed approach is based on the principle of the Kohonen's model (conservation of topological order) and uses the Relational Analysis formalism by optimizing a cost function defined as a(More)
Cluster analysis is often carried out in combination with dimension reduction. The Semi-Non-negative Matrix Factorization (Semi-NMF) that learns a low-dimensional representation of a data set lends itself to a clustering interpretation. In this work we propose a novel approach to finding an optimal subspace of multi-dimensional variables for identifying a(More)
In this paper we propose a spectral based clustering algorithm to maximize an extended Modularity measure for categorical data; first, we establish the connection with the Relational Analysis criterion. Second, the maximization of the extended modularity is shown as a trace maxi-mization problem. A spectral based algorithm is then presented to search for(More)
In this paper, we propose a study on the use of weighted topological learning and matrix factorization methods to transform the representation space of a sparse dataset in order to increase the quality of learning, and adapt it to the case of transfer learning. The matrix factorization allows us to find latent variables, weighted topological learning is(More)
We explore in this paper a novel topological organization algorithm for data clustering and visualization named TPNMF. It leads to a clustering of the data, as well as the projection of the clusters on a two-dimensional grid while preserving the topological order of the initial data. The proposed algorithm is based on a NMF (Nonnegative Matrix(More)
This paper addresses the problem of cluster characterization by selecting a subset of the most relevant features for each cluster from a categorical dataset in an autonomous way. The proposed autonomous model is based on the Relational Topological Clustering (RTC) associated with a statistical test which allows to detect the most important variables in an(More)