A New Algorithm for Sequential Minor Component Analysis

Principal component analysis (PCA) and minor component analysis (MCA) are two important statistical tools which have many applications in the fields of signal processing and data analysis. PCA and MCA neural networks (NNs) can be used to online extract principal component and minor component from input data. It is interesting to develop generalized learning algorithms of PCA and MCA NNs. Some novel generalized PCA and MCA learning algorithms are proposed in this paper. Convergence of PCA and MCA learning algorithms is an essential issue in practical applications. Traditionally, the convergence is studied via deterministic continuous-time (DCT) method. The DCT method requires the learning rate of the algorithms to approach to zero, which is not realistic in many practical applications. In this paper, deterministic discrete-time (DDT) method is used to study the dynamical behaviors of the proposed algorithms. The DDT method is more reasonable for the convergence analysis since it does not require constraints as that of the DCT method. It is proven that under some mild conditions, the weight vector in these proposed algorithms will converge exponentially to principal or minor component. Simulation results are further used to illustrate the theoretical results.

Convergence analysis of a simple minor component analysis algorithm

Generalized eigenvector plays an essential role in the signal processing field. In this paper, we present a novel neural network learning algorithm for estimating the generalized eigenvector of a Hermitian matrix pencil. Differently from some traditional algorithms, which need to select the proper values of learning rates before using, the proposed algorithm does not need a learning rate and is very suitable for real applications. Through analyzing all of the equilibrium points, it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil, the proposed algorithm reaches to convergence status. By using the deterministic discretetime (DDT) method, some convergence conditions, which can be satisfied with probability 1, are also obtained to guarantee its convergence. Simulation results show that the proposed algorithm has a fast convergence speed and good numerical stability. The real application demonstrates its effectiveness in tracking the optimal vector of beamforming.

A unified learning algorithm to extract principal and minor components

An adaptive quasi-Newton algorithm is first developed to extract a single minor component corresponding to the smallest eigenvalue of a stationary sample covariance matrix. A deflation technique instead of the commonly used inflation method is then applied to extract the higher-order minor components. The algorithm enjoys the advantage of having a simpler computational complexity and a highly modular and parallel structure for efficient implementation. Simulation results are given to demonstrate the effectiveness of the proposed algorithm for extracting multiple minor components adaptively.

A self-stabilizing MSA algorithm in high-dimension data stream

Algorithms that extract the principal or minor components of a signal are widely used in signal processing and control applications. This paper explores new frameworks for generating learning rules for iteratively computing the principal and minor components (or subspaces) of a given matrix. Stability analysis using Lyapunov theory and La Salle invariance principle is provided to determine regions of attraction of these learning rules. Among many derivations, it is specifically shown that Oja's rule and many variations of it are asymptotically globally stable. Lyapunov stability theory is also applied to weighted learning rules. Some of the essential features for the proposed MCA/PCA learning rules are that they are self normalized and can be applied to non-symmetric matrices. Exact solutions for some nonlinear dynamical systems are also provided

The minor component analysis is widely used in many fields, such as signal processing and data analysis, so it has very important theoretical significance and practical values for the convergence analysis of these algorithms. In this paper we seek the convergence condition for Feng’s MCA learning algorithm in deterministic discrete time system. Finally numerical experiments show the correctness of our theory.KeywordsMCA learning algorithmDDT systemeigenvalueeigenvectorinvariant sets

This brief deals with the problem of minor component analysis (MCA). Artificial neural networks can be exploited to achieve the task of MCA. Recent research works show that convergence of neural networks based MCA algorithms can be guaranteed if the learning rates are less than certain thresholds. However, the computation of these thresholds needs information about the eigenvalues of the autocorrelation matrix of data set, which is unavailable in online extraction of minor component from input data stream. In this correspondence, we introduce an adaptive learning rate into the OJAn MCA algorithm, such that its convergence condition does not depend on any unobtainable information, and can be easily satisfied in practical applications.

SUMMARY The LQ+ problem, i.e. the finite-horizon linear quadratic optimal control problem with nonnegative state constraints, is studied for positive linear systems in continuous time and in discrete time. Necessary and sufficient optimality conditions are obtained by using the maximum principle. These conditions lead to a computational method for the solution of the LQ+ problem by means of a corresponding Hamiltonian system. In addition, the necessary and sufficient conditions are proved for the LQ+-optimal control to be given by the standard LQ-optimal state feedback law. Then sufficient conditions are established for the positivity of the LQ-optimal closed-loop system. In particular, such conditions are obtained for the problem of minimal energy control with penalization of the final state. Moreover, a positivity criterion for the LQ-optimal closed-loop system is derived for positive discrete-time systems with a positively invertible (dynamics) generator. The main results are illustrated by numerical examples. Copyright q 2010 John Wiley & Sons, Ltd.

Differences in amino acid composition and heme electronic structure of the multiple monomeric hemoglobin components of Glycera dibranchiata

physiological systems are characterized by multiple interdependent components that collectively subserve various processes and functions. In seeking better understanding of the performance of such complex systems, we must identify and evaluate alternative ways and operating schemes, comparing their

A multifunctional platform by controlling of carbon nitride in the core-shell structure: From design to construction, and catalysis applications

Global energy and environmental crises are among the most pressing challenges facing humankind. To overcome these challenges, recent years have seen an upsurge of interest in the development and production of renewable chemical fuels as alternatives to the nonrenewable and high-polluting fossil fuels. Photocatalysis, photoelectrocatalysis, and electrocatalysis provide promising avenues for sustainable energy conversion. Single- and dual-component catalytic systems based on nanomaterials have been intensively studied for decades, but their intrinsic weaknesses hamper their practical applications. Multicomponent nanomaterial-based systems, consisting of three or more components with at least one component in the nanoscale, have recently emerged. The multiple components are integrated together to create synergistic effects and hence overcome the limitation for outperformance. Such higher-efficiency systems based on nanomaterials will potentially bring an additional benefit in balance-of-system costs if they exclude the use of noble metals, considering the expense and sustainability. It is therefore timely to review the research in this field, providing guidance in the development of noble-metal-free multicomponent nanointegration for sustainable energy conversion. In this work, we first recall the fundamentals of catalysis by nanomaterials, multicomponent nanointegration, and reactor configuration for water splitting, CO2 reduction, and N2 reduction. We then systematically review and discuss recent advances in multicomponent-based photocatalytic, photoelectrochemical, and electrochemical systems based on nanomaterials. On the basis of these systems, we further laterally evaluate different multicomponent integration strategies and highlight their impacts on catalytic activity, performance stability, and product selectivity. Finally, we provide conclusions and future prospects for multicomponent nanointegration. This work offers comprehensive insights into the development of cost-competitive multicomponent nanomaterial-based systems for sustainable energy-conversion technologies and assists researchers working toward addressing the global challenges in energy and the environment.

Edible oil analysis by high-resolution nuclear magnetic resonance spectroscopy: recent advances and future perspectives