Lazhar Labiod

Co-clustering for Binary and Categorical Data with Maximum Modularity

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 use of the modularity in co-clustering and assessing the number of clusters contexts.

A Semi-NMF-PCA Unified Framework for Data Clustering

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.

Co-clustering under nonnegative matrix tri-factorization

The nonnegative matrix tri-factorization (NMTF) approach has recently been shown to be useful and effective to tackle the co-clustering. In this work, we embed this problem in the NMF framework and we derive from the double k-means objective function a new formulation of the criterion. To optimize it, we develop two algorithms based on two multiplicative update rules. In addition we show that the double k-means is equivalent to algebraic problem of NMF under some suitable constraints. Numerical experiments on simulated and real datasets demonstrate the interest of our approach.

Relational topological clustering

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 Kohonens model (conservation of topological order) and uses the Relational Analysis formalism by optimizing a cost function defined as a Condorcet criterion. We propose an hybrid algorithm, which deals linearly with large datasets, provides a natural clusters identification and allows a visualization of the clustering result on a two dimensional grid while preserving the a priori topological order of the data. The proposed approach called RTC was validated on several datasets and the experimental results showed very promising performances.

Simultaneous Semi-NMF and PCA for Clustering

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 partition of the set of objects. 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 learn low-dimensional representations that are better suited for clustering, outperforming not only Semi-NMF, but also other NMF variants.

A spectral algorithm for topographical Co-clustering

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 matrix and the definition of a new matrix taking into account the co-clustering problem. The proposed approach has been validated on multiple datasets and the experimental results have shown very promising performance.

Feature space transformation for transfer learning

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 used to detect the most relevant among them. New data representation is based on their projections on the weighted topological model. Each object in the dataset is described by a new representation consisting of the distances of this object to all components of the topological model (prototypes). For transfer learning, we propose a new method where the representation of data is done in the same way as in the first phase, but using a pruned topological model. This pruning is performed after labeling the units of the topological model using the labels available for transfer. The experiments are presented as a part of an International Challenge [1] where we have obtained promising results (5th rank).

Multi-manifold matrix decomposition for data co-clustering

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.

A Unified Framework for Data Visualization and Coclustering

We propose a new theoretical framework for data visualization. This framework is based on iterative procedure looking up an appropriate approximation of the data matrix  by using two stochastic similarity matrices from the set of rows and the set of columns. This process converges to a steady state where the approximated data  is composed of g similar rows and l similar columns. Reordering A according to the first left and right singular vectors involves an optimal data reorganization revealing homogeneous block clusters. Furthermore, we show that our approach is related to a Markov chain model, to the double k-means with g × l block clusters and to a spectral coclustering. Numerical experiments on simulated and real data sets show the interest of our approach.

A topographical nonnegative matrix factorization algorithm

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 Factorization) formalism using a neighborhood function which take into account the topological order of the data. TPNMF was validated on variant real datasets and the experimental results show a good quality of the topological ordering and homogenous clustering.