Uncoupled Cellular Neural Networks Research Articles

NXOR- or XOR-based robust template decomposition for cellular neural networks implementing an arbitrary Boolean function via support vector classifiers

Robust template design for cellular neural networks (CNNs) implementing an arbitrary Boolean function is currently an active research area. If the given Boolean function is linearly separable, a single robust uncoupled CNN can be designed preferably as a maximal margin classifier to implement the Boolean function. On the other hand, if the linearly separable Boolean function has a small geometric margin or the Boolean function is not linearly separable, a popular approach is to find a sequence of robust uncoupled CNNs implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are usually restricted to assume only a given finite set of integers. In this study, we try to remove this unnecessary restriction. NXOR- or XOR-based decomposition algorithm utilizing the soft margin and maximal margin support vector classifiers is proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

A new design for reconfigurable XOR function based on cellular neural networks

We have described a new method to construct the reconfigurable XOR logic circuit by using the modification of the standard uncoupled cellular neural network (CNN) cells. The modification of the cell is easier to implement in engineering applications. The scheme proposed in this paper, using the modification of standard uncoupled CNN cells, allows less hardware consumption in comparison to the utilisation of chaos computing system or harnessing piecewise-linear systems. The template parameters of the modified cell have been discussed, and the physical circuit implementing the reconfigurable two-input and three-input XOR function has also been presented.

Robust decomposition with guaranteed robustness for cellular neural networks implementing an arbitrary Boolean function

Given a general Boolean function, an algorithm is proposed in this paper to find a sequence of robust uncoupled cellular neural networks, with logic operators as the conjunctions, implementing the given Boolean function. Each resulting robust uncoupled cellular neural network in the decomposition has a margin greater than or equal to a pre-specified value. For reasonable robustness levels, the proposed algorithm usually requires lesser number of searching templates and provides faster execution than those by using other similar methods. Furthermore, a mechanism for practical tradeoff between the guaranteed robustness and the complexity in terms of the number of terms in the decomposition is provided in our proposed algorithm.

Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

ROBUST TEMPLATE DECOMPOSITION WITH RESTRICTED WEIGHTS FOR CELLULAR NEURAL NETWORKS IMPLEMENTING AN ARBITRARY BOOLEAN FUNCTION

In this paper, a general problem of the robust template decomposition with restricted weights for cellular neural networks (CNNs) implementing an arbitrary Boolean function is investigated. First, the geometric margin of a linear classifier with respect to a training data set is used to define the robustness of an uncoupled CNN implementing a linearly separable Boolean function. Second, maximal margin classifiers, i.e. robust CNNs, for such Boolean functions can be designed via support vector machines (SVMs). Third, some general properties of robust CNNs with or without restricted weights are discussed. Moreover, all robust CNNs with restricted weights are characterized. Finally, for an arbitrarily given Boolean function, we propose an algorithm, which is the generalized version of the well-known CFC algorithm, to find a sequence of robust uncoupled CNNs implementing the given Boolean function. Several illustrative examples demonstrate the efficiency of the proposed method. It will be seen that, in general, the tradeoff between the complexity regarding the number of terms in the decomposition and the guaranteed robustness regarding the geometric margins of the resulting CNNs must be made in the robust template decomposition with restricted weights.

A Recurrent Fuzzy Coupled Cellular Neural Network System With Automatic Structure and Template Learning

The cellular neural network (CNN) is a powerful technique to mimic the local function of biological neural circuits, especially the human visual pathway system, for real-time image and video processing. Recently, many studies show that an integrated CNN system can solve more complex high-level intelligent problems. In this brief, we extend our previously proposed multi-CNN integrated system, called recurrent fuzzy CNN (RFCNN) which considers uncoupled CNNs only, to automatically learn the proper network structure and parameters simultaneously of coupled CNNs, which is called recurrent fuzzy coupled CNN (RFCCNN). The proposed RFCCNN provides a solution to the current dilemma on the decision of templates and/or fuzzy rules in the existing integrated (fuzzy) CNN systems. For comparison, the capability of the proposed RFCCNN is demonstrated on the same defect inspection problems. Simulation results show that the proposed RFCCNN outperforms the RFCNN

REALIZATION OF BOOLEAN FUNCTIONS VIA CNN WITH VON NEUMANN NEIGHBORHOODS

Recently, an effective method for realizing linearly separable Boolean functions via Cellular Neural Networks (CNN), called the threshold bifurcation method, was introduced, with a CNN gene bank of four variables established [Chen & Chen, 2005]. Based on this success, the present paper is to further explore the realization of all linearly separable Boolean functions of five variables via CNN with von Neumann neighborhoods. This paper provides: (i) important and essential relations among the genes (or templates) and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set, (ii) a neat truth table of uncoupled CNN with five input variables, (iii) 94572 linearly separable Boolean functions (LSBF) in the family of 225 = 4.294967296 × 109 Boolean functions of five variables, realizable by a single CNN, and (iv) all 94572 CNN linearly separable Boolean genes (LSBG), which can be determined to form the CNN gene bank of five variables.

REALIZATION AND BIFURCATION OF BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS

In this work, we study the realization and bifurcation of Boolean functions of four variables via a Cellular Neural Network (CNN). We characterize the basic relations between the genes and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set. Based on the analysis, we have rigorously proved that there are exactly 1882 linearly separable Boolean functions of four variables, and found an effective method for realizing all linearly separable Boolean functions via an uncoupled CNN. Consequently, any kind of linearly separable Boolean function can be implemented by an uncoupled CNN, and all CNN genes that are associated with these Boolean functions, called the CNN gene bank of four variables, can be easily determined. Through this work, we will show that the standard CNN invented by Chua and Yang in 1988 indeed is very essential not only in terms of engineering applications but also in the sense of fundamental mathematics.

On locally regular cellular neural networks

Since their inception, cellular neural networks (CNNs) have been divided into two classes, namely the uncoupled CNNs which do not have intercell feedback and their coupled counterparts which have feedback. The uncoupled class is fully analytically tractable and well understood, whereas the coupled class may exhibit complex dynamics prohibiting an exact analysis. In this paper, the author proposes a different dichotomy by defining the class of locally regular (LR) CNNs which comprises uncoupled and the most commonly used coupled networks. He shows that there is a unifying theory for the design and analysis of this class, and that LR CNNs meet all the requirements for a successful implementation in analog VLSI hardware. In particular, they can be made highly robust against deviations of both template parameters and cells' time constants, and they operate correctly on different classes of CNN chips, including sampled-data implementations and networks with high-gain or hardlimiting output nonlinearity. Furthermore, they can be numerically simulated very efficiently, since the integration step size may be chosen as large as the cell's time constant.