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This paper presents a collaborative neurodynamic approach to Boolean matrix factorization. Based on a binary optimization formulation to minimize the Hamming distance between a given data matrix and its low-rank reconstruction, the proposed approach employs a population of Boltzmann machines operating concurrently for scatter search of factorization solutions. In addition, a particle swarm optimization rule is used to re-initialize the neuronal states of Boltzmann machines upon their local convergence to escape from local minima toward global solutions. Experimental results demonstrate the superior convergence and performance of the proposed approach against six baseline methods on ten benchmark datasets. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter . In the latter case, dilution is introduced in pattern entries, in such a way that a fraction of them is blank. Then, we merge these two extensions to obtain a system able to retrieve several patterns in parallel and the quality of retrieval, encoded by the set of Mattis magnetizations , is reminiscent of the correlation among patterns. By tuning the parameters and , qualitatively different outputs emerge, ranging from highly hierarchical to symmetric. The investigations are accomplished by means of both numerical simulations and statistical mechanics analysis, properly adapting a novel technique originally developed for spin glasses, i.e. the Hamilton–Jacobi interpolation, with excellent agreement. Finally, we show the thermodynamical equivalence of this associative network with a (restricted) Boltzmann machine and study its stochastic dynamics to obtain even a dynamical picture, perfectly consistent with the static scenario earlier discussed. [Copyright &y& Elsevier]

Abstract: A specific type of neural networks, the Restricted Boltzmann Machines (RBM), are implemented for classification and feature detection in machine learning. They are characterized by separate layers of visible and hidden units, which are able to learn efficiently a generative model of the observed data. We study a “hybrid” version of RBMs, in which hidden units are analog and visible units are binary, and we show that thermodynamics of visible units are equivalent to those of a Hopfield network, in which the visible units are the neurons and the hidden units are the learned patterns. We apply the method of stochastic stability to derive the thermodynamics of the model, by considering a formal extension of this technique to the case of multiple sets of stored patterns, which may act as a benchmark for the study of correlated sets. Our results imply that simulating the dynamics of a Hopfield network, requiring the update of neurons and the storage of synapses, can be accomplished by a hybrid Boltzmann Machine, requiring the update of neurons but the storage of only synapses. In addition, the well known glass transition of the Hopfield network has a counterpart in the Boltzmann Machine: it corresponds to an optimum criterion for selecting the relative sizes of the hidden and visible layers, resolving the trade-off between flexibility and generality of the model. The low storage phase of the Hopfield model corresponds to few hidden units and hence a overly constrained RBM, while the spin-glass phase (too many hidden units) corresponds to unconstrained RBM prone to overfitting of the observed data. [Copyright &y& Elsevier]