Discrete Bidirectional Associative Memory Research Articles

Discrete Bidirectional Associative Memory Neural Networks of the Cohen–Grossberg Type for Engineering Design Symmetry Related Problems: Practical Stability of Sets Analysis

In recent years, artificial intelligence techniques have become fundamental parts of various engineering research activities and practical realizations. The advantages of the neural networks, as one of the main artificial intelligence methods, make them very appropriate for different engineering design problems. However, the qualitative properties of the neural networks’ states are extremely important for their design and practical performance. In addition, the variety of neural network models requires the formulation of appropriate qualitative criteria. This paper studies a class of discrete Bidirectional Associative Memory (BAM) neural networks of the Cohen–Grossberg type that can be applied in engineering design. Due to the nature of the proposed models, they are very suitable for symmetry-related problems. The notion of the practical stability of the states with respect to sets is introduced. The practical stability analysis is conducted by the method of the Lyapunov functions. Examples are presented to verify the proposed criteria and demonstrate the efficiency of the results. Since engineering design is a constrained processes, the obtained stability of the sets’ results can be applied to numerous engineering design tasks of diverse interest.

Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach

This paper is interested in the problem of asymptotic stability analysis of Bidirectional Associative Memory (BAM) neural networks with time-varying delays via delta operator approach. The delays are assumed to exist in the nonlinear synaptic connection between different neural fields. Based on the Lyapunov–Krasovskii functional in delta domain, a new delay-dependent criterion for analyzing the asymptotic stability of BAM neural networks is obtained. Some previous results of continuous and discrete BAM systems are unified into the delta operator system framework due to the favorable numerical properties and the quasi-continuous performance of delta operator approach at high sampling rates. Since the sampling period is an explicit parameter in the results, it can be regulated to analyze the stability of systems. Numerical examples are presented to demonstrate the effectiveness of the developed theoretical results.

Bifurcation analysis in a discrete BAM network model with delays

In this paper, a discrete bidirectional associative memory network model consisting of three neurons is considered. We study the stability of the equilibria of the system by analysing the distribution of the eigenvalues. It is found that there are three kinds of bifurcations: Pitchfork bifurcation, Period-Doubling bifurcation and Neimark–Sacker bifurcation. The direction and stability of the Neimark–Sacker are determined by using normal forms and centre manifold theory. Some numerical simulations are carried out to illustrate the analytical results.

Stability and bifurcation of a discrete BAM neural network model with delays

A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results.

DCBAM: A discrete chainable bidirectional associative memory

A two-layer discrete chainable bidirectional associative memory, DCBAM, is proposed in this paper. As an extension of Kosko's Discrete Bidirectional Associative Memory (DBAM), the proposed DCBAM possesses many advantages such as small correlation matrix; tolerance to noisy, partial and distorted inputs; and convergence within a small number of retrieval cycles. Moreover, the additional chaining feedbacks make the proposed DCBAM capable of multistep retrieval-chaining. That is, given the stored association pairs (A, B), (B, C) and an initial input pattern A, the proposed DCBAM can automatically find the directly-associated pattern B and the sparsely-associated pattern C, which is indirectly related to pattern A, without any prior knowledge of the structures and relationships between these stored association pairs. This is generally realized in previous neural networks by stratifying them into a compound network based on prior knowledge. Extensive experimental results and analysis are presented for discussion.

Adaptation of the relaxation method for learning in bidirectional associative memory

An iterative learning algorithm called PRLAB is described for the discrete bidirectional associative memory (BAM). Guaranteed recall of all training pairs is ensured by PRLAB. The proposed algorithm is significant in many ways. Unlike many existing iterative learning algorithms, PRLAB is not based on the gradient descent technique. It is a novel adaptation from the well-known relaxation method for solving a system of linear inequalities. The algorithm is very fast. Learning 200 random patterns in a 200-200 BAM takes only 20 epochs on the average. PRLAB is highly insensitive to learning parameters and the initial configuration of a BAM. It also offers high scalability for large applications by providing the same high performance when the number of training patterns are increased in proportion to the size of the BAM. An extensive performance analysis of the new learning algorithm is included.

Two coding strategies for bidirectional associative memory

Enhancements of the encoding strategy of a discrete bidirectional associative memory (BAM) reported by B. Kosko (1987) are presented. There are two major concepts in this work: multiple training, which can be guaranteed to achieve recall of a single trained pair under suitable initial conditions of data, and dummy augmentation, which can be guaranteed to achieve recall of all trained pairs if attaching dummy data to the training pairs is allowable. In representative computer simulations, multiple training has been shown to lead to an improvement over the original Kosko strategy for recall of multiple pairs as well. A sufficient condition for a correlation matrix to make the energies of the training pairs be local minima is discussed. The use of multiple training and dummy augmentation concepts are illustrated, and theorems underlying the results are presented.