Huimin Xiao

Signed consensus problems on networks of agents with fixed and switching topologies

ABSTRACTThis paper deals with signed consensus problems for networks of agents in the presence of both fixed and switching topologies. By specifying signs for the agents, they are divided into two groups and are enabled to reach agreement on a consensus value which is the same in modulus for both groups but not in sign. Using nearest-neighbour interaction rules, we propose the distributed protocols and address their exponential convergence problem. It is shown that the quasi-strong connectivity of fixed networks or joint quasi-strong connectivity of switching networks can provide a necessary and sufficient guarantee for all agents to achieve signed consensus exponentially fast. In particular, the signed consensus results can include as special cases those of bipartite consensus in signed networks with fixed and switching topologies. Numerical simulations are also provided to illustrate the exponential convergence performance of the proposed signed consensus protocols.

Online Learning Algorithms for Double-Weighted Least Squares Twin Bounded Support Vector Machines

Twin support vector machine with two nonparallel classifying hyperplanes and its extensions have attracted much attention in machine learning and data mining. However, the prediction accuracy may be highly influenced when noise is involved. In particular, for the least squares case, the intractable computational burden may be incurred for large scale data. To address the above problems, we propose the double-weighted least squares twin bounded support vector machines and develop the online learning algorithms. By introducing the double-weighted mechanism, the linear and nonlinear double-weighted learning models are proposed to reduce the influence of noise. The online learning algorithms for solving the two models are developed, which can avoid computing the inverse of the large scale matrices. Furthermore, a new pruning mechanism which can avoid updating the kernel matrices in every iteration step for solving nonlinear model is also developed. Simulation results on three UCI data with noise demonstrate that the online learning algorithm for the linear double-weighted learning model can get least computation time as well considerable classification accuracy. Simulation results on UCI data and two-moons data with noise demonstrate that the nonlinear double-weighted learning model can be effectively solved by the online learning algorithm with the pruning mechanism.

On the cycles of Boolean networks

Using semi-tensor product, the Boolean network is converted into its algebraic form as a standard discrete-time linear system. From the rank and 1-eigenvector of structure matrix, we obtain the cycle structure of the Boolean network, such as the cycles and the number of the cycles with different length. In this paper, we just use the rank and 1-eigenvector of structure matrix to obtain the results, while in literature the different powers of structure matrix are used.

A converse Lyapunov theorem for the discrete switched system

In this paper, a converse Lyapunov theorem for discrete switched systems is presented, and a common Lyapunov function is constructed for a class of discrete switched systems whose subsystems are commutative.

Gene selection for cancer classification using improved group lasso

An improved group lasso is proposed for simultaneous cancer classification and gene selection. A new criterion is firstly proposed to evaluate the individual gene importance by using the conditional mutual information. Then the weights with biological explanation are constructed and the improved group lasso is presented. A blockwise descent algorithm for solving the proposed model is also developed. The experimental results on lung cancer and prostate cancer data sets demonstrate that the proposed method can effectively perform classification and gene selection.

Binary classification with noise via fuzzy weighted least squares twin support vector machine

A new weighted least squares twin support vector machine for binary classification with noise is proposed in this paper. By using the distances from the sample points to their class center, fuzzy weights are constructed. The fuzzy weighted least squares twin support vector machine is presented by following the fuzzy weighted mechanism, thus reducing the influence of the noise. The simulation results on three UCI data and two-moons data demonstrate the effectiveness of the proposed method.

Solution path algorithm for the fuzzy weighted doubly regularized support vector machine

A fuzzy weighted doubly regularized support vector machine for binary classification is proposed in this paper. Fuzzy weights are presented by using the distance information within each class. Then the fuzzy weighted doubly regularized support vector machine is proposed by combing the weighted hinge loss and the adaptive elastic net penalty. A reasonable correlation between two model parameters is also given and the solution path algorithm to compute the solution paths of the proposed support vector machine is developed. The simulation results on two data sets demonstrate the effectiveness of the proposed method.

Necessary and sufficient condition for observability of Boolean control networks

Using semi-tensor product of matrices, Boolean control network is expressed as a discrete-time linear system. Under this framework, a systematic method of controllability and observability of Boolean control networks (BCN) has been developed by professor Cheng in literature, and the controllability is a necessary condition for testing the observability of BCN. In this paper, using controllability of BCN avoiding states set, we give a new necessary and sufficient condition for testing the observability of BCN, which is a generalization of the known result obtained in literature.

Analysis of mix-valued logical control networks

Using semi-tensor product and the vector form of multi-valued logical variables, the mix-valued logical system is expressed as a linear discrete time system and the mix-valued logical control system is expressed as a bilinear discrete time system with respect to the state and control variables. In this paper, the topological property of mix-valued logical network and the reachability and controllability of mix-valued logical control systems are discussed. From the algebraic form of mix-valued logical network, we obtain the number of the logical system. The formula we obtained is based on the rank of structure matrix. Also, the necessary and sufficient conditions are obtained for testing the reachability and controllability.

Algebraic method to pseudo-Boolean function and its application in pseudo-Boolean optimization

In this paper, the optimization of pseudo-Boolean functions is considered. Boolean variables are expressed into their vector form. Using semi-tensor product, the pseudo-Boolean function is expressed as its normal form and algebraic form. Based on the normal form, we discuss the optimal approximation problem of pseudo-Boolean function.