42505995
Erratum to "Adaptive Smoothing via Contextual and Local Discontinuities"
In the above titled paper (ibid., vol 27, no. 10, pp. 1552-1567, Oct 05), equation (9) contained a typographical error. The corrected equation is presented here.
6083596
Improved learning algorithms for mixture of experts in multiclass classification
Mixture of experts (ME) is a modular neural network architecture for supervised learning. A double-loop Expectation-Maximization (EM) algorithm has been introduced to the ME architecture for adjusting the parameters and the iteratively reweighted least squares (IRLS) algorithm is used to perform maximization in the inner loop [Jordan, M.I., Jacobs, R.A. (1994). Hierarchical mixture of experts and the EM algorithm, Neural Computation, 6(2), 181-214]. However, it is reported in literature that the IRLS algorithm is of instability and the ME architecture trained by the EM algorithm, where IRLS algorithm is used in the inner loop, often produces the poor performance in multiclass classification. In this paper, the reason of this instability is explored. We find out that due to an implicitly imposed incorrect assumption on parameter independence in multiclass classification, an incomplete Hessian matrix is used in that IRLS algorithm. Based on this finding, we apply the Newton-Raphson method to the inner loop of the EM algorithm in the case of multiclass classification, where the exact Hessian matrix is adopted. To tackle the expensive computation of the Hessian matrix and its inverse, we propose an approximation to the Newton-Raphson algorithm based on a so-called generalized Bernoulli density. The Newton-Raphson algorithm and its approximation have been applied to synthetic data, benchmark, and real-world multiclass classification tasks. For comparison, the IRLS algorithm and a quasi-Newton algorithm called BFGS have also been applied to the same tasks. Simulation results have shown that the use of the proposed learning algorithms avoids the instability problem and makes the ME architecture produce good performance in multiclass classification. In particular, our approximation algorithm leads to fast learning. In addition, the limitation of our approximation algorithm is also empirically investigated in this paper.
34883067
Personalized News Reading via Hybrid Learning
In this paper, we present a personalized news reading prototype where latest news articles published by various on-line news providers are automatically collected, categorized and ranked in light of a user’s habits or interests. Moreover, our system can adapt itself towards a better performance. In order to develop such an adaptive system, we proposed a hybrid learning strategy; supervised learning is used to create an initial system configuration based on user’s feedbacks during registration, while an unsupervised learning scheme gradually updates the configuration by tracing the user’s behaviors as the system is being used. Simulation results demonstrate satisfactory performance.
15908834
Ensemble Learning with Active Data Selection for Semi-Supervised Pattern Classification
Unlike traditional pattern classification, semi-supervised learning provides a novel technique to make use of both labeled and unlabeled data for improving the performance of classification. In general, there are two critical issues for semi-supervised learning of discriminative classifiers; i.e., how to create an initial classifier of a good generalization capability with the limited labeled data and the how to make an effective use of unlabeled data without degradation of the established classifier. To tackle two aforementioned problems, we propose an ensemble learning approach based on a recent active data selection strategy, where ensemble learning would yield good generalization and active data selection tends to choose the unlabeled data more likely resulting in an improvement during semi-supervised learning. By using an ensemble of K-NN classifiers, we demonstrate the effectiveness of our approach on a synthetic data classification and a facial expression recognition tasks.
41845464
Advances in Natural Computation, First International Conference, ICNC 2005, Changsha, China, August 27-29, 2005, Proceedings, Part I
15381679
A Modular Neural Network Architecture for Pattern Classification Based on Different Feature Sets
We propose a novel connectionist method for the use of different feature sets in pattern classification. Unlike traditional methods, e.g., combination of multiple classifiers and use of a composite feature set, our method copes with the problem based on an idea of soft competition on different feature sets developed in our earlier work. An alternative modular neural network architecture is proposed to provide a more effective implementation of soft competition on different feature sets. The proposed architecture is interpreted as a generalized finite mixture model and, therefore, parameter estimation is treated as a maximum likelihood problem. An EM algorithm is derived for parameter estimation and, moreover, a model selection method is proposed to fit the proposed architecture to a specific problem. Comparative results are presented for the real world problem of speaker identification.
16708333
MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Time-Varying Lyapunov Equation Solving
This paper presents a new kind of recurrent neural network proposed by Zhang et al.for solving online Lyapunov equation with time-varying coefficient matrices. Global exponential convergence could be achieved by such a recurrent neural network when solving the time-varying problems in comparison with gradient neural networks (GNN). MATLAB simulation of both neural networks for the real-time solution of time-varying Lyapunov equation is then investigated through several important techniques. Computer-simulation results substantiate the theoretical analysis and demonstrate the efficacy of such a Zhang neural network (ZNN) on time-varying Lyapunov equation solving, especially when using power-sigmoid activation functions.
122233994
An efficient method for evaluating the integral of a class of highly oscillatory functions
Highly oscillatory integrals require special techniques for their effective evaluation. Various studies have been conducted to find computational methods for evaluating such integrals. In this paper we present an efficient numerical method to evaluate a class of generalised Fourier integrals (on a line or a square) with integrands of the form f(x)e^i^k^g^(^x^), under the assumption that in the domain of integration, both f and g are sufficiently smooth and that g does not have any stationary/critical points. Numerical analysis and results are given to illustrate the effectiveness of our method for computing generalised Fourier integrals.
35419934
MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion
This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.
7778586
Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving
In view of the great potential in parallel processing and ready implementation via hardware, neural networks are now often employed to solve online matrix algebraic problems. Recently, a special kind of recurrent neural network has been proposed by Zhang et al, which could be generalized to solving online Lyapunov equation with time-varying coefficient matrices. In comparison with gradient-based neural networks (GNN), the resultant Zhang neural networks (ZNN) perform much better on solving these time-varying problems. This paper investigates the MATLAB Simulink modeling, simulative verification and comparison of ZNN and GNN models for time-varying Lyapunov equation solving. Computer-simulation results verify that superior convergence and efficacy could be achieved by such ZNN models when solving the time-varying Lyapunov matrix equation, as compared to the GNN models.
16722943
The Euclidean Orienteering Problem Revisited
We consider the rooted orienteering problem: Given a set $P$ of $n$ points in the plane, a starting point $r \in P$, and a length constraint $B$, one needs to find a path starting from $r$ that visits as many points of $P$ as possible and of length not exceeding $B$. We present a $(1-\varepsilon)$-approximation algorithm for this problem that runs in $n^{O(1/\varepsilon)}$ time; the computed path visits at least $ (1-\varepsilon)k_{\mathrm{opt}}$ points of $P$, where $k_{\mathrm{opt}}$ is the number of points visited by an optimal solution. This is the first polynomial time approximation scheme for this problem. The algorithm also works in higher dimensions.