19202214
A self-generating modular neural network architecture for supervised learning
Abstract In this paper, we present a self-generating modular neural network architecture for supervised learning. In the architecture, any kind of feedforward neural networks can be employed as component nets. For a given task, a tree-structured modular neural network is automatically generated with a growing algorithm by partitioning input space recursively to avoid the problem of pre-determined structure. Due to the principle of divide-and-conquer used in the proposed architecture, the modular neural network can yield both good performance and significantly faster training. The proposed architecture has been applied to several supervised learning tasks and has achieved satisfactory results.
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.
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.
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.
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.
41845464
Advances in Natural Computation, First International Conference, ICNC 2005, Changsha, China, August 27-29, 2005, Proceedings, Part I
15647217
Common Nature of Learning Exemplified by BP and Hopfield Neural Networks for Solving Online a System of Linear Equations
Many computational problems widely encountered in scientific and engineering applications could finally be transformed to the online linear-equations solving. Classic numerical methods for solving linear equations include Gaussian elimination and matrix factorization methods, which are usually of O(n3) operations. Being important parallel-computational models, both BP (back propagation) and Hopfield neural networks could be exploited for solving such linear equations. BP neural network is evidently different from Hopfield neural network in terms of network definition, architecture and learning pattern. However, both of these two neural networks could have a common nature of learning (i.e., governed by the same mathematical iteration formula) during the online solution of linear equations. In addition, computer-simulation results substantiate the theoretical analysis of both BP and Hopfield neural networks for solving online such a set of linear equations.
12408273
Multilevel algorithm for a Poisson noise removal model with total-variation regularization
Many commonly used models for the fundamental image processing task of noise removal can deal with Gaussian white noise. However, such Gaussian models are not effective in restoring images with Poisson noise, which is ubiquitous in certain applications. Recently, Le–Chartrand–Asaki derived a new data-fitting term in the variational model for Poisson noise. This paper proposes a multilevel algorithm for efficiently solving this variational model. As expected of a multilevel method, it delivers the same numerical solution many orders of magnitude faster than the standard single-level method of coordinate descent time-marching. Supporting numerical experiments on 2D gray scale images are presented.
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.
17434449
On Two Multigrid Algorithms for Modeling Variational Multiphase Image Segmentation
In this paper, we present two related multigrid algorithms for multiphase image segmentation. Algorithm I solves the model by Vese-Chan. We first generalize our recently developed multigrid method to this multiphase segmentation model (MG1); we also give a local Fourier analysis for the local smoother which leads to a new and more effective smoother. Although MG1 is found many magnitudes faster than the fast method of additive operator splitting (AOS), both algorithms are not robust with regard to the initial guess. To overcome this dependence on the initial guess, we consider a hierarchical segmentation model which achieves multiphase segmentation by repeated use of the Chan-Vese two-phase model; our algorithm II solves this model by a multigrid algorithm (MG2). Numerical experiments show that both algorithms are efficient and in particular MG2 is more robust than MG1 with respect to initial guesses. AMS subject classifications: 68U10, 65F10, 65K10.
15785287
A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration
Abstract
Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method (Chan et al., SIAM J. Sci. Comput. 20(6), 1964–1977, 1999) previously found reliable. Supporting numerical results are presented.
