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We use a recently developed synchronous Spiking Neural Network (SNN) model to study the problem of learning hierarchically-structured concepts. We introduce an abstract data model that describes simple hierarchical concepts. We define a feed-forward layered SNN model, with learning modeled using Oja's local learning rule, a well known biologically-plausible rule for adjusting synapse weights. We define what it means for such a network to recognize hierarchical concepts; our notion of recognition is robust, in that it tolerates a bounded amount of noise. Then, we present a learning algorithm by which a layered network may learn to recognize hierarchical concepts according to our robust definition. We analyze correctness and performance rigorously; the amount of time required to learn each concept, after learning all of the sub-concepts, is approximately O 1 η k ℓmax log (k) + 1 ɛ + b log (k) , where k is the number of sub-concepts per concept, ℓmax is the maximum hierarchical depth, η is the learning rate, ɛ describes the amount of uncertainty allowed in robust recognition, and b describes the amount of weight decrease for "irrelevant" edges. An interesting feature of this algorithm is that it allows the network to learn sub-concepts in a highly interleaved manner. This algorithm assumes that the concepts are presented in a noise-free way; we also extend these results to accommodate noise in the learning process. Finally, we give a simple lower bound saying that, in order to recognize concepts with hierarchical depth two with noise-tolerance, a neural network should have at least two layers. The results in this paper represent first steps in the theoretical study of hierarchical concepts using SNNs. The cases studied here are basic, but they suggest many directions for extensions to more elaborate and realistic cases. [ABSTRACT FROM AUTHOR]

Find the global optimal solution of the model is one promising research topic in computational intelligent community. Dependent on analogies to natural processes, the evolutionary swarm intelligent algorithms are widely used for solving global optimization problems which directed by the fitness values. In this paper, we propose one efficient fractional global learning machine (Fragmachine) which includes two stages (descending and ascending) to determine the optimal search path. The neural network model is used to approach the given fitness value. Specifically, for the descending stage, the integer gradient of the network output with respect the current location is employed to find the next descending point, while for the ascending stage, the fractional gradient is implemented to climb and escape from the local optimal point. We further propose one adaptive learning rate during training which relies on both the current gradient (integer or fractional) information and the fitness value. Finally, a series of numerical experiments verify the effectiveness of the proposed algorithm, Fragmachine. [ABSTRACT FROM AUTHOR]

Abstract: The focus of this paper is to propose a hybrid neural network model for associative recall of analog and digital patterns. This hybrid model consists of self-feedback neural network structures (SFNN) in parallel with generalized regression neural networks (GRNN). Using a new one-shot learning algorithm developed in the paper, pattern representations are first stored as the asymptotically stable fixed points of the SFNN. Then in the retrieving process, each pattern is applied to the GRNN to make the corresponding initial condition and to initiate the dynamical equations of the SFNN that should in turn output the corresponding representation. In this way, the corresponding stored patterns are retrieved even under high noise degradation. Moreover, contrary to many associative memories, the proposed hybrid model is without any spurious attractors and can store both binary and real-value patterns without any preprocessing. Several simulations confirm the theoretical analyses of the model. Results indicate that the performance of the hybrid model is better than that of recurrent associative memory and competitive with other classes of networks. [Copyright &y& Elsevier]

This paper considers the loopy belief propagation (LBP) algorithm applied to Gaussian graphical models. It is known for Gaussian belief propagation that, if LBP converges, LBP computes the exact posterior means but incorrect variances. In this paper, we analytically derive the posterior variances for some special structured graphs and clarify the accuracy of LBP. For the graphs of a single cycle, we derive a rigorous solution for the posterior variances and thereby find the quantity that determines the accuracy of LBP. Based on this result, we state a necessary condition for LBP convergence. The quantity above also plays an important role in graphs of a single cycle with arbitrary trees. For arbitrary topological graphs, we consider the situation where correlations between any pair of nodes are comparatively small and show analytically the principal values that determine the accuracy of LBP. [Copyright &y& Elsevier]

Abstract: Selection of the optimal neural architecture to solve a pattern classification problem entails to choose the relevant input units, the number of hidden neurons and its corresponding interconnection weights. This problem has been widely studied in many research works but their solutions usually involve excessive computational cost in most of the problems and they do not provide a unique solution. This paper proposes a new technique to efficiently design the MultiLayer Perceptron (MLP) architecture for classification using the Extreme Learning Machine (ELM) algorithm. The proposed method provides a high generalization capability and a unique solution for the architecture design. Moreover, the selected final network only retains those input connections that are relevant for the classification task. Experimental results show these advantages. [Copyright &y& Elsevier]

Abstract: This paper introduces a granular neural network framework for evolving fuzzy system modeling from fuzzy data streams. The evolving granular neural network (eGNN) is able to handle gradual and abrupt parameter changes typical of nonstationary (online) environments. eGNN builds interpretable multi-sized local models using fuzzy neurons for information fusion. An online incremental learning algorithm develops the neural network structure from the information contained in data streams. We focus on trapezoidal fuzzy intervals and objects with trapezoidal membership function representation. More precisely, the framework considers triangular, interval, and numeric types of data to construct granular fuzzy models as particular arrangements of trapezoids. Application examples in classification and function approximation in material and biomedical engineering are used to evaluate and illustrate the neural network usefulness. Simulation results suggest that the eGNN fuzzy modeling approach can handle fuzzy data successfully and outperforms alternative state-of-the-art approaches in terms of accuracy, transparency and compactness. [Copyright &y& Elsevier]

Abstract: Data mining is based on data files which usually contain errors in the form of missing values. This paper focuses on a methodological framework for the development of an automated data imputation model based on artificial neural networks. Fifteen real and simulated data sets are exposed to a perturbation experiment, based on the random generation of missing values. These data set sizes range from 47 to 1389 records. A perturbation experiment was performed for each data set where the probability of missing value was set to 0.05. Several architectures and learning algorithms for the multilayer perceptron are tested and compared with three classic imputation procedures: mean/mode imputation, regression and hot-deck. The obtained results, considering different performance measures, not only suggest this approach improves the quality of a database with missing values, but also the best results are clearly obtained using the Multilayer Perceptron model in data sets with categorical variables. Three learning rules (Levenberg–Marquardt, BFGS Quasi-Newton and Conjugate Gradient Fletcher–Reeves Update) and a small number of hidden nodes are recommended. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to study loss functions in multiclass classification. In classification problems, the decision function is estimated by minimizing an empirical loss function, and then, the output label is predicted by using the estimated decision function. We propose a class of loss functions which is obtained by a deformation of the log-likelihood loss function. There are four main reasons why we focus on the deformed log-likelihood loss function: (1) this is a class of loss functions which has not been deeply investigated so far, (2) in terms of computation, a boosting algorithm with a pseudo-loss is available to minimize the proposed loss function, (3) the proposed loss functions provide a clear correspondence between the decision functions and conditional probabilities of output labels, (4) the proposed loss functions satisfy the statistical consistency of the classification error rate which is a desirable property in classification problems. Based on (3), we show that the deformed log-likelihood loss provides a model of mislabeling which is useful as a statistical model of medical diagnostics. We also propose a robust loss function against outliers in multiclass classification based on our approach. The robust loss function is a natural extension of the existing robust loss function for binary classification. A model of mislabeling and a robust loss function are useful to cope with noisy data. Some numerical studies are presented to show the robustness of the proposed loss function. A mathematical characterization of the deformed log-likelihood loss function is also presented. [Copyright &y& Elsevier]

Abstract: Minor subspace analysis (MSA) is a statistical method for extracting the subspace spanned by all the eigenvectors associated with the minor eigenvalues of the autocorrelation matrix of a high-dimension vector sequence. In this paper, we propose a self-stabilizing neural network learning algorithm for tracking minor subspace in high-dimension data stream. Dynamics of the proposed algorithm are analyzed via a corresponding deterministic continuous time (DCT) system and stochastic discrete time (SDT) system methods. The proposed algorithm provides an efficient online learning for tracking the MS and can track an orthonormal basis of the MS. Computer simulations are carried out to confirm the theoretical results. [Copyright &y& Elsevier]

Abstract: A comparison of behavior-based and planning approaches of robot control is presented in this paper. We focus on miniature mobile robotic agents with limited sensory abilities. Two reactive control mechanisms for an agent are considered—a radial basis function neural network trained by evolutionary algorithm and a traditional reinforcement learning algorithm over a finite agent state space. The control architecture based on localization and planning is compared to the former method. [Copyright &y& Elsevier]

Abstract: In this paper we propose a boosting approach to random subspace method (RSM) to achieve an improved performance and avoid some of the major drawbacks of RSM. RSM is a successful method for classification. However, the random selection of inputs, its source of success, can also be a major problem. For several problems some of the selected subspaces may lack the discriminant ability to separate the different classes. These subspaces produce poor classifiers that harm the performance of the ensemble. Additionally, boosting RSM would also be an interesting approach for improving its performance. Nevertheless, the application of the two methods together, boosting and RSM, achieves poor results, worse than the results of each method separately. In this work, we propose a new approach for combining RSM and boosting. Instead of obtaining random subspaces, we search subspaces that optimize the weighted classification error given by the boosting algorithm, and then the new classifier added to the ensemble is trained using the obtained subspace. An additional advantage of the proposed methodology is that it can be used with any classifier, including those, such as nearest neighbor classifiers, that cannot use boosting methods easily. The proposed approach is compared with standard AdaBoost and RSM showing an improved performance on a large set of 45 problems from the UCI Machine Learning Repository. An additional study of the effect of noise on the labels of the training instances shows that the less aggressive versions of the proposed methodology are more robust than AdaBoost in the presence of noise. [Copyright &y& Elsevier]