The pioneering contribution of this paper is to design and implement a Neural Network (NN) that demonstrates chaotic Pattern Recognition (PR) properties, and where the network in and of itself is a “small-world” or “scale-free” network. The foundational NN that we employ for this is the Adachi Neural Network (AdNN). The latter is a fascinating NN which has been shown to possess chaotic properties, and to also demonstrate Associative Memory (AM) and PR, while variants of the AdNN have also been used to obtain other PR phenomena, and even blurring. The problem with the Adachi NN is that it is a fully-connected network requiring quadratic computations for the training. Our aim in this paper is to reduce the computations needed for the training significantly. The motivation for this is the fact that most “physical” networks including biological NNs and Internet networks have the properties of complex small-world or scale-free networks. To place the paper in the right perspective, we mention that in [1] we managed to reduce the AdNN's computational cost significantly by merely using a linear number of computations by enforcing a Maximum Spanning Tree topology and a gradient search method. However, from the perspective of a network's structure, very few real-life networks have a tree-shaped linearly-connected topology. The question we consider in this paper is whether we can reduce the degree of connections of each node to mimic the small-world or scale-free phenomena, more akin to “real” NNs. Simultaneously, we shall also attempt to ensure that the newly-obtained network still possesses strong PR characteristics. To achieve this, we first construct a small-world network by means of the so-called N-W model. We then address the problem of computing the weights for the new NN. This is done in such a manner that the modified small-world connection-based NN has approximately the same input-output characteristics, and thus the new weights are themselves calculated using a gradient-based algorithm. By a detailed experimental analysis, we show that the new small-world AdNN-like network possesses PR properties for appropriate settings. As far as we know, such a small-world AdNN has not been reported, and the results given here are novel.

Additional Metadata
Keywords Adachi-like Neural Networks, Chaotic Neural Networks, Chaotic Pattern Recognition, Small-world Networks
Conference 7th International Conference on Chaotic Modeling and Simulation, CHAOS 2014
Citation
Qin, K. (Ke), & Oommen, J. (2019). Chaotic pattern recognition using the Adachi neural network modified in a small-world way. In CHAOS 2014 - Proceedings: 7th Chaotic Modeling and Simulation International Conference (pp. 391–398).