Mental Arithmetic Task Recognition Using Effective Connectivity and Hierarchical Feature Selection from EEG Signals

Introduction: Mental arithmetic analysis based on Electroencephalogram (EEG) signal for monitoring the state of the user’s brain functioning can be helpful for understanding some psychological disorders such as attention deficit hyperactivity disorder, autism spectrum disorder, or dyscalculia where the difficulty in learning or understanding the arithmetic exists. Most mental arithmetic recognition systems rely on features of a single channel of EEG; however, the relationships among EEG channels in the form of effective brain connectivity analysis can contain valuable information. The aim of this paper is to identify a set of discriminative effective brain connectivity features from EEG signal and develop a hierarchical feature selection structure for classification of mental arithmetic and baseline tasks effectively. Methods: We estimated effective connectivity using Directed Transfer Function (DTF), direct Directed Transfer Function (dDTF) and Generalized Partial Directed Coherence (GPDC) methods. These measures determine the causal relation between different brain areas. To select most significant effective connectivity features, a hierarchical feature subset selection method is used. First Kruskal–Wallis test was performed and consequently, five feature selection algorithms namely Support Vector Machine ( SVM ) method based on Recursive Feature Elimination, Fisher score, mutual information, minimum Redundancy Maximum Relevance and concave minimization and SVM are used to select the best discriminative features. Finally, SVM method was used for classification. Results: Results show that the best EEG classification performance in 29 participants and 60 trials is obtained using GPDC and feature selection via concave minimization method in Beta2 (15−22Hz) frequency band with 89% accuracy. Conclusion: This new hierarchical automated system could be useful for discrimination of mental arithmetic and baseline tasks from EEG signal effectively.

A Branch-and-bound algorithm for concave minimization problem with upper bounded variables

This paper presents a branch-and-bound algorithm for solving the concave minimization problems with upper bounded variables. The algorithm uses simplex to construct the branching and the bounding procedure. The linear convex envelope (the objective function of the subproblem) is uniquely determined on the candidate simplex which contains the subset of the local minimal points. The optimal solution of the subproblem is a local optimum of the original concave problem and used in reducing the list of active subproblems. The branching process splits the candidate simplex into two subsimplices by fixing the selected branching variable at value 0 or upper bound. Then the subsimplices are one less dimensional than the candidate. It means that the size of the subproblems gradually decreases. Further research needs to be focused on the efficient determination method of the simplex. The algorithm of this paper can be applied to solving the concave minimization problems under knapsack type constraints.

Energy-Efficient User Association Strategy for Hyperdense Heterogeneous Networking in the Fifth Generation Systems

Redesigning user association strategies to improve energy efficiency (EE) has been viewed as one of the promising shifting paradigms for the fifth generation (5G) cellular networks. In this paper, we investigate how to optimize users’ association to enhance EE for hyper dense heterogeneous networking in the 5G cellular networks, where the low-power node (LPN) much outnumbers the high-power node (HPN). To characterize that densely deployed LPNs would undertake a majority of high-rate services, while HPNs mainly support coverage; the EE metric is defined as average weighted EE of access nodes with the unit of bit per joule. Then, the EE optimization objective function is formulated and proved to be nonconvex. Two mathematical transformation techniques are presented to solve the nonconvex problem. In the first case, the original problem is reformulated as an equivalent problem involving the maximization of a biconcave function. In the second case, it is equivalent to a concave minimization problem. We focus on the solution of the biconcave framework, and, by exploiting the biconcave structure, a novel iterative algorithm based on dual theory is proposed, where a partially optimal solution can be achieved. Simulation results have verified the effectiveness of the proposed algorithm.