A Linearly Involved Generalized Moreau Enhancement of ℓ2,1-Norm with Application to Weighted Group Sparse Classification

This paper proposes a new group-sparsity-inducing regularizer to approximate ℓ2,0 pseudo-norm. The regularizer is nonconvex, which can be seen as a linearly involved generalized Moreau enhancement of ℓ2,1-norm. Moreover, the overall convexity of the corresponding group-sparsity-regularized least squares problem can be achieved. The model can handle general group configurations such as weighted group sparse problems, and can be solved through a proximal splitting algorithm. Among the applications, considering that the bias of convex regularizer may lead to incorrect classification results especially for unbalanced training sets, we apply the proposed model to the (weighted) group sparse classification problem. The proposed classifier can use the label, similarity and locality information of samples. It also suppresses the bias of convex regularizer-based classifiers. Experimental results demonstrate that the proposed classifier improves the performance of convex ℓ2,1 regularizer-based methods, especially when the training data set is unbalanced. This paper enhances the potential applicability and effectiveness of using nonconvex regularizers in the frame of convex optimization.

A multi-objective sparse evolutionary framework for large-scale weapon target assignment based on a reward strategy

The asset-based weapon target assignment (ABWTA) problem is one of the important branches of the weapon target assignment (WTA) problem. Due to the current large-scale battlefield environment, the ABWTA problem is a multi-objective optimization problem (MOP) with strong constraints, large-scale and sparse properties. The novel model of the ABWTA problem with the operation error parameter is established. An evolutionary algorithm for large-scale sparse problems (SparseEA) is introduced as the main framework for solving large-scale sparse ABWTA problem. The proposed framework (SparseEA-ABWTA) mainly addresses the issue that problem-specific initialization method and genetic operators with a reward strategy can generate solutions efficiently considering the sparsity of variables and an improved non-dominated solution selection method is presented to handle the constraints. Under the premise of constructing large-scale cases by the specific case generator, two numerical experiments on four outstanding multi-objective evolutionary algorithms (MOEAs) show Runtime of SparseEA-ABWTA is faster nearly 50% than others under the same convergence and the gap between MOEAs improved by the mechanism of SparseEA-ABWTA and SparseEA-ABWTA is reduced to nearly 20% in the convergence and distribution.

Towards an Intelligent OLAP System Facing Sparse Problems

Exploring intelligent data stored in data warehouses may efficiently assist the knowledge-seeker in his decision process. Such traced information related to performed analysis by decision-makers on data warehouses are stored in OLAP log files. These files contain useful knowledge about the analysts' preferences. Sometimes, some formulated queries provide no results. Such a dilemma is known as the sparsity problem. In this paper, to overcome this limitation in user-centric data warehouses, the authors focus on a specific class of preferences, namely the conflicting preferences. Indeed, a conflicting preference describes a low frequency preference stored in OLAP log files, so that it is considered as tailored to given analysts. Such preferences are characterized by their rarity. To deal with this issue, the authors introduce a new approach to discover these preferences through mining of rare association rules using a new introduced method for generating the N highest confidence rare association rules. The derived rare preferences will be used to reformulate the launched query avoiding an empty result. The carried out experiments on their built online recruitment data warehouse point out the efficiency of their approach.