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sparsely connected autoassociative fuzzy implicative memories and their application for the reconstruction of large gray-scale images

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NEUROCOMPUTING 2010年第1-3期74卷 343-353页

作者： Valle, Marcos Eduardo Univ Estadual Londrina Dept Math BR-86051990 Londrina PR Brazil

Autoassociative fuzzy implicative memories (AFIMs) are models that exhibit optimal absolute storage capacity and an excellent tolerance with respect to incomplete or eroded patterns As a consequence they can be effectively used for the reconstruction of gray-scale images In practice however applications of AFIMs are confined to Images of small size due to computational limitations In order to circumvent this computational overhead and motivated by the sparsity of biological neural networks this paper introduces the class of sparsely connected AFIMs (SCAFIMs) Such as the original AFIMs SCAFIMs exhibit optimal absolute storage capacity and tolerance with respect to Incomplete or eroded patterns By means of computational experiments we investigate the performance of SCAFIMs with different network topologies and compare the novel models with other techniques for the reconstruction of gray-scale images (C) 2010 Elsevier B V All rights reserved

关键词： Fuzzy associative memory Large gray scale images sparse encoding Storage capacity Noise tolerance

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An efficient string sorting algorithm for weighing matrices of small weight

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OPTIMIZATION LETTERS 2010年第1期4卷 29-36页

作者： Kotsireas, Ilias S. Koukouvinos, Christos Pardalos, Panos M. Wilfrid Laurier Univ Dept Phys & Comp Sci Waterloo ON N2L 3C5 Canada Natl Tech Univ Athens Dept Math GR-15773 Athens Greece Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

In this paper, we demonstrate that the search for weighing matrices of small weights constructed from two circulants can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. We also introduce a sparse encoding of the periodic autocorrelation function vector, based on concepts from Algorithmic Information Theory, also known as Kolmogorov complexity, that allows us to speed up the algorithm considerably. Finally, we use these ideas to find new weighing matrices W(2 center dot n, 9) constructed from two circulants, for many values of n in the range 100 a parts per thousand currency signA n a parts per thousand currency signA 300. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.

关键词： Weighing matrices Algorithm Pattern String sorting sparse encoding

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Memory capacity and information capacity of sparsely encoded associative memory with replacement units

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ARTIFICIAL LIFE AND ROBOTICS 2010年第3期15卷 291-295页

作者： Miyata, Ryota Muta, Shinnosuke Kurata, Koji Univ Ryukyus Grad Sch Engn & Sci 1 Senbaru Nishihara Okinawa 9030213 Japan Univ Ryukyus Fac Engn Okinawa Japan

We introduce sparse encoding into the autoassociative memory model with replacement units. Utilizing computer simulation, we search the optimal number of replacement units in two terms: the memory capacity and the information capacity of the network. We show that the optimal number of replacement units to maximize the memory capacity and the information capacity decreases as the fi ring ratio decreases, and that the difference in the memory capacity between sparse encoding and non-sparse encoding becomes small as the number of replacement units increases.

关键词： Autoassociative memory sparse encoding Catastrophic forgetting Rebirth neuron Memory capacity Information capacity

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sparsely Connected Autoassociative Fuzzy Implicative Memories for the Reconstruction of Large Gray-Scale Images

Sparsely Connected Autoassociative Fuzzy Implicative Memorie...

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Joint World Congress of International-Fuzzy-Systems-Association (IFSA)/European Conference of European-Society-for-Fuzzy-Logic-and-Technology (EUSFLAT)

作者： Valle, Marcos Eduardo Univ Londrina Dept Math Londrina Parana Brazil

ISBN: (纸本)9789899507968

Autoassociative fuzzy implicative memories (AFIMs) are models that exhibit optimal absolute storage capacity and an excellent tolerance with respect to incomplete or eroded patterns. Thus, they can be effectively used for the reconstruction of gray-scale images. In practice, however, applications of AFIMs are confined to images of small size due to computational limitations. This paper introduces a class of sparsely connected AFIMs (SCAFIMs) that circumvent this computational overhead and, therefore, can be used for the reconstruction of large images. We show that SCAFIMs exhibit optimal absolute storage capacity and tolerance with respect to incomplete or eroded patterns. Furthermore, we compare the performance of SCAFIMs with their corresponding fully connected AFIM both theoretically and by means of computational experiments.

关键词： Fuzzy associative memory reconstruction of large gray-scale images sparse encoding storage capacity tolerance with respect to noise

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A cascade associative memory model with a hierarchical memory structure

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NEURAL NETWORKS 2000年第1期13卷 41-50页

作者： Hirahara, M Oka, N Kindo, T Matsushita Res Inst Tokyo Inc Tama Ku Kawasaki Kanagawa 214 Japan Japan Sci & Technol Corp Kawaguchi 332 Japan

The introduction of a hierarchical memory structure into a cascade associative memory model for storing hierarchically correlated patterns improves the storage capacity and the size of the basins of attraction remarkably. A learning algorithm groups descendants (second-level patterns) according to their ancestors (first-level ones), and organizes the memory structure in a weight matrix where the groups are memorized separately. The weight matrix is, thus, in the form of a pile of covariance matrices, each of which is responsible for recalling only the descendants of each ancestor. Putting it simply, the model is multiplex associative memory. The recalling process proceeds as follows: the model first recalls the ancestor of a target descendant. Then, the dynamics with dynamic threshold combines the ancestor and the weight matrix to activate the covariance matrix for recalling only the descendants of the ancestor. This mechanism suppresses the cross-talk noise generated by the descendants of the other ancestors, and the recalling ability is enhanced. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： cascade associative memory hetero-associative memory hierarchical memory structure difference patterns sparse encoding dynamic threshold storage capacity basins of attraction

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Associative memory with a sparse encoding mechanism for storing correlated patterns

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NEURAL NETWORKS 1997年第9期10卷 1627-1636页

作者： Hirahara, M Oka, N Kindo, T Matsushita Res Inst Tokyo Inc Tama Ku Kawasaki Kanagawa 214 Japan

H. Gutfreund (Neural networks with hierarchically correlated patterns. Physical Review A, 37, 570-577, 1988) has proposed a model for storing hierarchically correlated patterns where ancestor patterns are correlated with descendant ones. However, there is a problem of small storage capacity. Furthermore, we must give ancestors in the learning phase, and determine the value of the parameter on which the capacity and the basins of attraction strongly depend. To overcome these problems, we present a model (CASM) consisting of the first associative memory to form ancestors from their descendants and the second associative memory to store sparse difference patterns which have only information on differences between the formed ancestors and the descendants. To evaluate the performance of CASM, extensive simulations are carried out. The results show that the capacity increases with increasing correlation between the ancestors and the descendants, and is as large as that of sparsely encoded associative memory. The basins of attraction become larger with decreasing correlation and do not depend on loading level. (C) 1997 Elsevier Science Ltd. All rights reserved.

关键词： associative memory cascade hierarchically correlated patterns difference patterns sparse encoding storage capacity basins of attraction ancestor formation

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Informational capacity and recall quality in sparsely encoded Hopfield-like neural network: Analytical approaches and computer simulation

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NEURAL NETWORKS 1997年第5期10卷 845-855页

作者： Frolov, AA Husek, D Muraviev, IP ACAD SCI CZECH REPUBL INST COMP SCIPRAGUE 18207CZECH REPUBLIC RUSSIAN ACAD SCI INST HIGHER NERVOUS ACT & NEUROPHYSIOLMOSCOW 117901RUSSIA

A sparsely encoded Hopfield-like attractor neural network is investigated analytically and by computer simulation. informational capacity and recall quality are evaluated. Three analytical approaches are used: replica method (RM);method of statistical neurodynamics (SN);and single-step approximation (SS). Computer simulation confirmed the good accuracy of RIM and SN for all levels of network activity. SS is accurate only for large sparseness. It is shown that informational capacity monotonically increases when sparseness increases, while recall quality changes nonmonotonically: initially it decreases and then increases. Computer simulation revealed the main features of network behaviour near the saturation which are not predicted by the used analytical approaches. (C) 1997 Elsevier Science Ltd.

关键词： Hopfield-like network information capacity recall quality sparse encoding

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LEARNING AND RECALL ALGORITHM FOR OPTICAL ASSOCIATIVE MEMORY USING A BISTABLE SPATIAL LIGHT-MODULATOR

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APPLIED OPTICS 1995年第17期34卷 3145-3151页

作者： TOYODA, H ISHIKAWA, M UNIV TOKYO BUNKYO KUTOKYO 113JAPAN

A learning and recall algorithm for optical associative memory based on the conventional correlation-learning method with three effective improvements (sparse-encoding method, constant-total-activity method, and binary memory) is proposed from a viewpoint of practical implementation It is shown that the algorithm is suitable for implementation with a bistable spatial light modulator such as a ferroelectric liquid-crystals spatial light modulator, which has high resolution and a fast response time. The results of theoretical analysis and simulations indicate that the algorithm permits an associative-memory system with a large memory capacity to be realized. An example of an optical system for executing this algorithm is proposed. To determine the performance specifications that are required for the various optical components within the system, we simulate and evaluate the effect of noise (which is caused by nonideal components) on system performance. These results show that the system is robust in the presence of predicted noise levels.

关键词： OPTICAL COMPUTING NEURAL NETWORK ASSOCIATIVE MEMORY CORRELATION LEARNING BISTABLE SPATIAL LIGHT MODULATOR sparse encoding

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CORRECTIVE MEMORY BY A SYMMETRICAL sparseLY ENCODED NETWORK

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IEEE TRANSACTIONS ON INFORMATION THEORY 1994年第2期40卷 429-438页

作者： BARAM, Y NASA AMES RES CTRMOFFETT FIELDCA 94035

A neural network that retrieves stored binary vectors, when probed by possibly corrupted versions of them, is presented. It employs sparse ternary internal coding and autocorrelation (Hebbian) storage. It is symmetrically structured and, consequently, can be folded into a feedback configuration. Bounds on the network parameters are derived from probabilistic considerations. It is shown that when the input dimension is n, the proportional activation radius is rho and the network size is 2nun With nu > 1 - h2(rho), the equilibrium capacity is at least 2alphan/8nrho(1 - rho) for any alpha < 1 - h2 (rho), where h2 (.) is the binary entropy. A similar capacity bound is derived for the correction of errors of proportional size rho or less, when rho less-than-or-equal-to 0.3. The performance of a finite-size symmetric network is examined by simulation and found to exceed, at the cost of higher connectivity, that of the Kanerva model, operating as a content addressable memory.

关键词： NEURAL NETWORKS CORRECTIVE MEMORY ASSOCIATIVE MEMORY sparse encoding

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STATISTICAL-ANALYSIS OF THE DYNAMICS OF A sparse ASSOCIATIVE MEMORY

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NEURAL NETWORKS 1992年第4期5卷 645-661页

作者： GIBSON, WG ROBINSON, J The University of Syndney Australia

A theoretical treatment of the dynamics of a recurrent autoassociative network is given. The network consists of randomly connected excitatory neurons, together with an inhibitory interneuron that sets their thresholds. Both the degree of connectivity between the neurons and the level of firing in the stored memories can be set arbitrarily. The memories are stored via a two-valued Hebbian, and evolution from an arbitrary initial state is by discrete, synchronous steps. The theory takes into account both spatial correlations between the learned connection strengths and temporal correlations between the state of the system and these connection strengths. Good qualitative and quantitative agreement with computer simulations is obtained for both the intermediate states and the final equilibrium state. Recall is studied as a function of initial state and of threshold parameters. The capacity of the network is investigated both numerically and analytically;there is a large increase in capacity as the level of firing decreases and also as the connectivity increases.

关键词： ASSOCIATIVE MEMORY RECALLING PROCESS EQUILIBRIUM STATES MEMORY CAPACITY sparse encoding LOW CONNECTIVITY THRESHOLD SETTING STATISTICAL NEURODYNAMICS

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