16046090
Nonlinear blind source separation using higher order statistics and a genetic algorithm
This paper presents a novel method for blindly separating unobservable independent source signals from their nonlinear mixtures. The demixing system is modeled using a parameterized neural network whose parameters can be determined under the criterion of independence of its outputs. Two cost functions based on higher order statistics are established to measure the statistical dependence of the outputs of the demixing system. The proposed method utilizes a genetic algorithm (GA) to minimize the highly nonlinear and nonconvex cost functions. The GA-based global optimization technique is able to obtain superior separation solutions to the nonlinear blind separation problem from any random initial values. Compared to conventional gradient-based approaches, the GA-based approach for blind source separation is characterized by high accuracy, robustness, and convergence rate. In particular, it is very suitable for the case of limited available data. Simulation results are discussed to demonstrate that the proposed GA-based approach is capable of separating independent sources from their nonlinear mixtures generated by a parametric separation model.
8287323
A recurrent neural network for solving linear projection equations
Linear projection equations arise in many optimization problems and have important applications in science and engineering. In this paper, we present a recurrent neural network for solving linear projection equations in real time. The proposed neural network has two layers and is amenable to parallel implementation with simple hardware. In the theoretical aspect, we prove that the proposed neural network can converge globally to the solution set of the problem when the matrix involved in the problem is positive semidefinite and can converge exponentially to a unique solution when the matrix is positive definite. In addition, we analyze the stability of the related dynamic system in detail. As an application, we show that the proposed neural network can be used directly to solve linear and convex quadratic programming problems and linear complementary problems with positive semidefinite matrices. The validity and transient behavior of the neural network are demonstrated by using three numerical examples.
18821545
Multiperiodicity and Exponential Attractivity Evoked by Periodic External Inputs in Delayed Cellular Neural Networks
We show that an n-neuron cellular neural network with time-varying delay can have 2n periodic orbits located in saturation regions and these periodic orbits are locally exponentially attractive. In addition, we give some conditions for ascertaining periodic orbits to be locally or globally exponentially attractive and allow them to locate in any designated region. As a special case of exponential periodicity, exponential stability of delayed cellular neural networks is also characterized. These conditions improve and extend the existing results in the literature. To illustrate and compare the results, simulation results are discussed in three numerical examples.
18182406
Recurrent neural networks for minimum infinity-norm kinematic control of redundant manipulators
This paper presents two neural network approaches to minimum infinity-norm solution of the velocity inverse kinematics problem for redundant robots. Three recurrent neural networks are applied for determining a joint velocity vector with its maximum absolute value component being minimal among all possible joint velocity vectors corresponding to the desired end-effector velocity. In each proposed neural network approach, two cooperating recurrent neural networks are used. The first approach employs two Tank-Hopfield networks for linear programming. The second approach employs two two-layer recurrent neural networks for quadratic programming and linear programming, respectively. Both the minimal 2-norm and infinity-norm of joint velocity vector can be obtained from the output of the recurrent neural networks. Simulation results demonstrate that the proposed approaches are effective with the second approach being better in terms of accuracy and optimality.
6599744
A multilayer recurrent neural network for solving continuous-time algebraic Riccati equations
A multilayer recurrent neural network is proposed for solving continuous-time algebraic matrix Riccati equations in real time. The proposed recurrent neural network consists of four bidirectionally connected layers. Each layer consists of an array of neurons. The proposed recurrent neural network is shown to be capable of solving algebraic Riccati equations and synthesizing linear-quadratic control systems in real time. Analytical results on stability of the recurrent neural network and solvability of algebraic Riccati equations by use of the recurrent neural network are discussed. The operating characteristics of the recurrent neural network are also demonstrated through three illustrative examples.
492137
Blind source extraction in various ill-conditioned cases
The paper discusses blind source extraction in various ill-conditioned cases based on a simple extraction network model. Extractability is first analyzed for the following ill-conditioned cases: the mixing matrix is square but-singular; the number of sensors is smaller than that of sources; the number of sensors is larger than that of sources, but the column rank of the mixing matrix is deficient; the number of sources is unknown and the column rank of the mixing matrix is deficient. A necessary and sufficient condition for extractability is obtained. A cost function and an unsupervised learning algorithm for the extraction network model are developed. Simulation results are also presented to show the validity of the theoretical results and the performance and characteristics of the learning algorithm.
61565821
Modelling and stability of FAST TCP
We introduce a discrete-time model of FAST TCP that fully captures the effect of self-clocking and compare it with the traditional continuous-time model. While the continuous-time model predicts instability for homogeneous sources sharing a single link when feedback delay is large, experiments suggest otherwise. Using the discrete-time model, we prove that FAST TCP is locally asymptotically stable in general networks when all sources have a common round-trip feedback delay, no matter how large the delay is. We also prove global stability for a single bottleneck link in the absence of feedback delay. The techniques developed here are new and applicable to other protocols.
14306866
Differences in gene expression between B-cell chronic lymphocytic leukemia and normal B cells: a meta-analysis of three microarray studies
MOTIVATION
A major focus of current cancer research is to identify genes that can be used as markers for prognosis and diagnosis, and as targets for therapy. Microarray technology has been applied extensively for this purpose, even though it has been reported that the agreement between microarray platforms is poor. A critical question is: how can we best combine the measurements of matched genes across microarray platforms to develop diagnostic and prognostic tools related to the underlying biology?


RESULTS
We introduce a statistical approach within a Bayesian framework to combine the microarray data on matched genes from three investigations of gene expression profiling of B-cell chronic lymphocytic leukemia (CLL) and normal B cells (NBC) using three different microarray platforms, oligonucleotide arrays, cDNA arrays printed on glass slides and cDNA arrays printed on nylon membranes. Using this approach, we identified a number of genes that were consistently differentially expressed between CLL and NBC samples.
5318094
Fast approximation of centrality
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized approximation algorithm for centrality in weighted graphs. For graphs exhibiting the small world phenomenon, our method estimates the centrality of all vertices with high probability within a (1 + ∈) factor in near-linear time.
12107864
Kernel Trick Embedded Gaussian Mixture Model
In this paper, we present a kernel trick embedded Gaussian Mixture Model (GMM), called kernel GMM. The basic idea is to embed kernel trick into EM algorithm and deduce a parameter estimation algorithm for GMM in feature space. Kernel GMM could be viewed as a Bayesian Kernel Method. Compared with most classical kernel methods, the proposed method can solve problems in probabilistic framework. Moreover, it can tackle nonlinear problems better than the traditional GMM. To avoid great computational cost problem existing in most kernel methods upon large scale data set, we also employ a Monte Carlo sampling technique to speed up kernel GMM so that it is more practical and efficient. Experimental results on synthetic and real-world data set demonstrate that the proposed approach has satisfing performance.
863373
A validity-guided support vector clustering algorithm for identification of optimal cluster configuration
This paper presents a validity-guided support vector clustering (SVC) algorithm for identifying an optimal cluster configuration. Since the SVC is a kernel based clustering approach, the parameter of kernel functions plays a crucial role in the clustering result. Without a priori knowledge of data sets, a validity measure, based on a ratio of overall cluster compactness to separation, has been developed to automatically determine a suitable parameter of the kernel functions. Using this parameter, the SVC algorithm is capable of identifying the optimal cluster number with compact and smooth arbitrary-shaped cluster boundaries. Computer simulations have been conducted to demonstrate the effectiveness of the proposed validity-guided SVC algorithm.