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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]

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]