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1

Binary associative memories with complemented operations

Gamino-Carranza Arturo

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 2

249--265

EN

Associative memories based on lattice algebra are of great interest in pattern recognition applications due to their excellent storage and recall properties. In this paper, a class of binary associative memory derived from lattice memories is presented, which is based on the definition of new complemented binary operations and threshold unary operations. The new learning method generates memories M and W; the former is robust to additive noise and the latter is robust to subtractive noise. In the recall step, the memories converge in a single step and use the same operation as the learning method. The storage capacity is unlimited, and in autoassociative mode there is perfect recall for the training set. Simulation results suggest that the proposed memories have better performance compared to other models.

2

Complex-valued associative memories with projection and iterative learning rules

Isokawa T., Yamamoto H., Nishimura H., Yumoto T., Kamiura N., Matsui N.

Journal of Artificial Intelligence and Soft Computing Research

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2018

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Vol. 8, No. 3

237--249

EN

In this paper, we investigate the stability of patterns embedded as the associative memory distributed on the complex-valued Hopfield neural network, in which the neuron states are encoded by the phase values on a unit circle of complex plane. As learning schemes for embedding patterns onto the network, projection rule and iterative learning rule are formally expanded to the complex-valued case. The retrieval of patterns embedded by iterative learning rule is demonstrated and the stability for embedded patterns is quantitatively investigated.

3

Minimum Number of Input Clues in Robust Information Retrieval

Junnila V., Laihonen T.

Fundamenta Informaticae

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2016

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Vol. 145, nr 3

243--256

EN

Information retrieval in associative memories was considered recently by Yaakobi and Bruck. In their model, a stored information unit is retrieved using input clues. In this paper, we study the problem where at most s (s ≥ 0) of the received input clues can be false and we still want to determine the sought information unit uniquely. We use a coding theoretical approach to estimate the maximum number of stored information units with respect to a given s. Moreover, optimal results for the problem are given, for example, in the infinite king grid. We also discuss the problem in the class of line graphs where a characterization and a connection to k-factors is given.

4

Optymalizacja statystycznych systemów uczących się

Jankowski S.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2012

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z. 183

3--107

PL

Dysertacja prezentuje wyniki badań w dziedzinie statystycznych systemów uczących się. W części l zostały opisane nowe, oryginalne idee rozszerzające zdolności przetwarzania informacji za pomocą wielkich nieliniowych układów dynamicznych. Opracowano uogólnienie pamięci asocjacyjnej Hopfielda w dziedzinie liczb zespolonych - system ma zdolność odtwarzania wzorców o stanach wielowartościowych reprezentujących odcienie szarości lub kolory dzięki zastosowaniu funkcji signum zespolone jako funkcji przetwarzania neuronów do kodowania fazowego wektorów wielowartościowych. Opisano nowy model zespolonej pamięci asocjacyjnej, która jest w stanie rozpoznawać obrazy inwariantnie względem przesunięcia. Wykazano, że pamięci asocjacyjne zbudowane z układów dynamicznych wyższego rzędu: oscylatorów drgań okresowych i oscylatorów drgań chaotycznych są zdolne do segmentacji (dekorelacji) wzorców złożonych. Przedstawiono implementacje programowalnych komórkowych sieci neuronowych do ultraszybkiego przetwarzania obrazów w postaci scalonego układu elektronicznego oraz implementację optoelektroniczną z wykorzystaniem tyrystorów optycznych. Część 2 rozprawy jest poświęcona prezentacji statystycznej teorii uczenia wybranych systemów statycznych przeznaczonych do uczenia nadzorowanego w zadaniach klasyfikacji i regresji: perceptron wielowarstwowy, maszyna wektorów nośnych, średniokwadratowa maszyna wektorów nośnych, maszyna wektorów istotnych. Opisano metody optymalizacji systemów na podstawie statystyki wpływu - wirtualnej skrajnej oceny krzyżowej. Przedstawiono wyniki zastosowania statystycznych systemów uczących się do badania struktury defektowej materiałów wysokorezystywnych i półizolujących. Zrealizowano koncepcję klasyfikacji transdukcyjnej - uczenia częściowo nadzorowanego do wspomagania diagnozy kardiologicznej.

EN

The dissertation presents the summary of research in the area of statistical learning systems. Part l is devoted to new, original ideas that enable extension of the ability of information processing by using large nonlinear dynamical systems. Generalization of the Hopfield associative memory in the complex number domain is able to retrieve multivalued patterns representing the gray-scaled and/ or colored images due to the application of complex signum neuron activation function to phasecoding of multivalued vectors. A new model of complex associative memory for shift invariant pattern recognition is presented. It was shown that associative memories composed of periodic and chaotic oscillating neurons are able to perform segmentation (decorrelation) of the composition of patterns. The implementations of programmable cellular neural networks for high speed image processing were presented in two forms: as an integrated electronic circuit and as an optoelectronic system based on optical thyristors. Part 2 presents the studies of statistical learning theory of selected static systems designed for supervised learning of classification and regression tasks: multilayer perceptron, support vector machine, least-square support vector machine, relevance vector machine. The optimization of these systems based on influential statistics - the virtual leave-one-out - was described. The original results of applications of statistical learning systems for analysis of defect structures of high resistive and semi-insulating materials were described. The idea of transductive classification – semisupervised learning system to computer-aided cardiologic diagnosis - was performed.

5

Improved storage capacity in correlation matrix memories storing fixed weight codes

Hobson S., Austin J.

Journal of Artificial Intelligence and Soft Computing Research

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2011

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Vol. 1, No. 2

97--102

EN

In this paper we introduce an improved binary correlation matrix memory (CMM) with better storage capacity when storing sparse fixed weight codes generated with the algorithm of Baum et al. [10]. We outline associative memory, and describe the binary correlation matrix memory— a specific example of a distributed associative memory. The importance of the representation used in a CMM for input and output codes is discussed, with specific regard to sparse fixed weight codes. We present an analysis of the benefits of an algorithm for the generation of fixed weight codes, originally given by Baum et al. [4]. The properties of this algorithm are briefly discussed, including possible thresholding functions which could be used when storing these codes in a CMM; L-max and L-wta. Finally, results generated from a series of simulations are used to demonstrate that the use of L-wta as a thresholding function provides an increase in storage capacity of around 15% over L-max.

6

On Characterization of Attractor Basins of Fuzzy Multiple Attractor Cellular Automata

Maji P.

Fundamenta Informaticae

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2008

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Vol. 86, nr 1-2

143-168

EN

Two new operators, namely, dependency vector (DV) and derived complement vector (DCV) are introduced in this paper to characterize the attractor basins of the additive fuzzy cellular automata (FCA) based associative memory, termed as fuzzy multiple attractor cellular automata (FMACA). The introduction of DV and DCV makes the complexity of the attractor basin identification algorithm linear in time. The characterization of the FMACA using DV and DCV establishes the fact that the FMACA provides both equal and unequal size of attractor basins. Finally, a set of algorithms is proposed to synthesize the FCA rules, attractors, and predecessors of attractors from the given DV and DCV in linear time complexity.

7

Image Recall Using a Large Scale Generalized Brain-state-in-a-box Neural Network

Oh Ch., Żak S. H.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 1

99-114

EN

An image recall system using a large scale associative memory employing the generalized Brain-State-in-a-Box (gBSB) neural network model is proposed. The gBSB neural network can store binary vectors as stable equilibrium points. This property is used to store images in the gBSB memory. When a noisy image is presented as an input to the gBSB network, the gBSB net processes it to filter out the noise. The overlapping decomposition method is utilized to efficiently process images using their binary representation. Furthermore, the uniform quantization is employed to reduce the size of the data representation of the images. Simulation results for monochrome gray scale and color images are presented. Also, a hybrid gBSB-McCulloch-Pitts neural model is introduced and an image recall system is built around this neural net. Simulation results for this model are presented and compared with the results for the system employing the gBSB neural model.

8

Duch W.

Control and Cybernetics

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2000

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Vol. 29, no 4

937-967

EN

Similarity-based methods (SBM) are a generalization of the minimal distance (MD) methods which form a basis of several machine learning and pattern recognition methods. Investigation of similarity leads to a fruitful framework in which many classification, approximation and association methods are accommodated. Probability p(C|X; M) of assigning class C to a vector X, given a classification model M, depends on adaptive parameters and procedures used in construction of the model. Systematic overview of choices available for model building is presented and numerous improvements suggested. Similarity-Based Methods have natural neural-network type realizations. Such neural network models as the Radial Basis Functions (RBF) and the Multilayer Perceptrons (MLPs) are included in this framework as special cases. SBM may also include several different submodels and a procedure to combine their results. Many new versions of similarity-based methods are derived from this framework. A search in the space of all methods belonging to the SBM framework finds a particular combination of parameterizations and procedures that is most appropriate for a given data. No single classification method can beat this approach. Preliminary implementation of SBM elements tested on a real-world datasets gave very good results.