This paper considers the proportional fair (PF) based subcarrier allocation problem in a multihop orthogonal frequency division multiple access (OFDMA) broadcast system with decode-and-forward (DF) relays. The problem is formulated as a mixed binary integer programming problem with the objective to achieve proportional fairness among users and exploit the diversity provided by the independent frequency selective fading among hops. Since it is prohibitive to find the optimal solution, two efficient heuristic schemes are proposed. Simulation results indicate that with the same fairness performance, the proposed schemes achieve considerable capacity gain over the conventional PF scheduling method.

Clustering is known to be an effective means of reducing energy dissipation and prolonging network lifetime in wireless sensor networks (WSNs). Recently, game theory has been used to search for optimal solutions to clustering problems. The residual energy of each node is vital to balance a WSN, but was not used in the previous game-theory-based studies when calculating the final probability of being a cluster head. Furthermore, the node payoffs have also not been expressed in terms of energy consumption. To address these issues, the final probability of being a cluster head is determined by both the equilibrium probability in a game and a node residual energy-dependent exponential function. In the process of computing the equilibrium probability, new payoff definitions related to energy consumption are adopted. In order to further reduce the energy consumption, an assistant method is proposed, in which the candidate nodes with the most residual energy in the close point pairs completely covered by other neighboring sensors are firstly selected and then transmit same sensing data to the corresponding cluster heads. In this paper, we propose an efficient energy-aware clustering protocol based on game theory for WSNs. Although only game-based method can perform well in this paper, the protocol of the cooperation with both two methods exceeds previous by a big margin in terms of network lifetime in a series of experiments.

Neighborhood preserving embedding is a widely used manifold reduced dimensionality technique. But NPE has to encounter two problems. One problem is that it suffers from the small-sample-size (SSS) problem. Another is that the performance of NPE is seriously sensitive to the neighborhood size k. To overcome the two problems, an exponential neighborhood preserving embedding (ENPE) is proposed in this paper. The main idea of ENPE is that the matrix exponential is introduced to NPE, then the SSS problem is avoided and low sensitivity to the neighborhood size k is gotten. The experiments are conducted on ORL, Georgia Tech and AR face database. The results show that, ENPE shows advantageous performance over other unsupervised methods, such as PCA, LPP, ELPP and NPE. Another is that ENPE is much less sensitive to the neighborhood parameter k contrasted with the unsupervised manifold learning methods LPP, ELPP and NPE.

As an effective method, exponential discriminant analysis (EDA) has been proposed and widely used to solve the so-called small-sample-size (SSS) problem. In this paper, a simple and effective generalization of EDA is presented and named as GEDA. In GEDA, a general exponential function, where the base of exponential function is larger than the Euler number, is used. Due to the property of general exponential function, the distance between samples belonging to different classes is larger than that of EDA, and then the discrimination property is largely emphasized. The experiment results on the Extended Yale and CMU-PIE face databases show that, GEDA gets more advantageous recognition performance compared to EDA.