An exact and direct analytical method for the design of optimally robust CNN templates

Abstract

In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.Index Terms-Cellular neural networks (CNN's), robustness, template design.

Image-Based Quantitative Analysis of Gold Immunochromatographic Strip via Cellular Neural Network Approach

“…Unfortunately, it is still very difficult to choose the best optimal template parameters which results in limiting the performance of the CNN [10]. Thus, it is clear from (13)- (14) that what we need to do is to find a way to optimize the template parameters: a 1 , a 2 , a 5 , b 1 , b 2 , b 5 , I.…”

“…However, by analyzing the dynamic properties of CNN, we are only able to get the range of the template parameters. At this stage, it is still very difficult to obtain the best (optimal) template parameters that would give rise to optimal performance of the CNN [10]. Thus, we hope to find an approach in this paper to optimize the template parameters of the CNN for improving its performance.…”

Template design methods for binary stable cellular neural networks

“…As we already pointed out in the Introduction, most of the templates have been designed so far through direct derivation References [23,29], i.e. by imposing the number of active cells according to suitable local rules.…”

“…The major drawback of this method is that, apart from uncoupled networks, some kind of unidirectional templates Reference [23], and the monotonic templates References [25][26][27][28], we do not know the class of templates for which the knowledge of the initial derivative allows to rigorously predict the asymptotic dynamics of the network: this step is essential for ensuring that the local rules are correctly implemented by the CNN. However, despite some disadvantages, the techniques based on the direct template derivation appear to be more suitable for CNN design, because they allow to understand the network spatio-temporal dynamics and to develop methods for robust design References [29,30].…”

Robustness oriented design tool for multilayer DTCNN applications

“…For the class of bipolar CNN, analytical methods have been proposed [13] that ÿnd optimally robust template parameters. However, for greyscale input applications there is an inÿnite set of possible input combinations which makes the exhaustive evaluation of Equation (3) unapproachable.…”