Spectral clustering is often carried out by combining spectral data embedding and -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.

Several studies have demonstrated the importance of co-clustering which aims to cluster simultaneously the sets of objects and features. The co-clustering is often more effective than one-side clustering, especially when considering sparse high dimensional data. In this paper, we propose a novel way to consider the co-clustering and the reduction of the dimension simultaneously. Our approach takes advantage of the mutual reinforcement between Principal Component Analysis (PCA) which provides a low-dimensional representation of data and Semi-Nonnegative Matrix Factorization (SemiNMF) that learns this low-dimensional representation and lends itself to a co-clustering interpretation. In other words, the proposed framework aims to find an optimal subspace of multi-dimensional variables for effectively identifying a partition of the set of objects. We show that by doing so, our model is able to learn low-dimensional representations that are better suited for co-clustering, outperforming not only spectral methods, but also co-clustering graph-regularized-based methods.

Spectral clustering methods use the Laplacian eigenvalues and eigenvectors to obtain a low-dimensional embedding that can be trivially clustered. For that purpose, spectral clustering is often based on a tandem approach where the two steps: affinity matrix eigendecomposition and k-means clustering, are performed separately. The potential flaw of such common practice is that the obtained relaxed continuous spectral solution can severely deviate from the true discrete clustering solution. Given the high computational cost of such spectral clustering methods, this paper provides the so-called PSDEC framework. PSDEC performs simultaneously the eigendecomposition of the affinity matrix and clustering tasks, and uses the Power method to speed up the unified process convergence. In PSDEC, the selected top eigenvectors of the Laplacian matrix can be of help in detecting a cluster structure of objects and providing simpler and more interpretable solutions. We show that by doing so, our method can learn low-dimensional representations that are better suited to clustering, outperforming not only spectral clustering algorithms but also some NMF variants.

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.

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.