Semisupervised Feature Selection via Generalized Uncorrelated Constraint and Manifold Embedding

Unsupervised Feature Selection via Graph Regularized Nonnegative CP Decomposition

Unsupervised feature selection has attracted remarkable attention recently. With the development of data acquisition technology, multi-dimensional tensor data has been appeared in enormous real-world applications. However, most existing unsupervised feature selection methods are non-tensor-based which results the vectorization of tensor data as a preprocessing step. This seemingly ordinary operation has led to an unnecessary loss of the multi-dimensional structural information and eventually restricted the quality of the selected features. To overcome the limitation, in this paper, we propose a novel unsupervised feature selection model: Nonnegative tensor CP (CANDECOMP/PARAFAC) decomposition based unsupervised feature selection, CPUFS for short. In specific, we devise new tensor-oriented linear classifier and feature selection matrix for CPUFS. In addition, CPUFS simultaneously conducts graph regularized nonnegative CP decomposition and newly-designed tensor-oriented pseudo label regression and feature selection to fully preserve the multi-dimensional data structure. To solve the CPUFS model, we propose an efficient iterative optimization algorithm with theoretically guaranteed convergence, whose computational complexity scales linearly in the number of features. A variation of the CPUFS model by incorporating nonnegativity into the linear classifier, namely CPUFSnn, is also proposed and studied. Experimental results on ten real-world benchmark datasets demonstrate the effectiveness of both CPUFS and CPUFSnn over the state-of-the-arts.

Implicit consensus clustering from multiple graphs

Dealing with relational learning generally relies on tools modeling relational data. An undirected graph can represent these data with vertices depicting entities and edges describing the relationships between the entities. These relationships can be well represented by multiple undirected graphs over the same set of vertices with edges arising from different graphs catching heterogeneous relations. The vertices of those networks are often structured in unknown clusters with varying properties of connectivity. These multiple graphs can be structured as a three-way tensor, where each slice of tensor depicts a graph which is represented by a count data matrix. To extract relevant clusters, we propose an appropriate model-based co-clustering capable of dealing with multiple graphs. The proposed model can be seen as a suitable tensor extension of mixture models of graphs, while the obtained co-clustering can be treated as a consensus clustering of nodes from multiple graphs. Applications on real datasets and comparisons with multi-view clustering and tensor decomposition methods show the interest of our contribution.