Chaos Glial Network Connected to Multi-Layer Perceptron for Solving Two-Spiral Problem Chihiro Ikuta Dept. of Electrical and Electronic Eng., Tokushima University 2-1 Minami-Josanjima, Tokushima, Japan E-mail: ikuta@ee.tokushima-u.ac.jp Yoko Uwate University / ETH Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland, Email: yu001@ini.phys.ethz.ch Yoshifumi Nishio Dept. of Electrical and Electronic Eng., Tokushima University 2-1 Minami-Josanjima, Tokushima, Japan E-mail: nishio@ee.tokushima-u.ac.jp Abstract— Some methods using artificial neural network were proposed for solving to the Two-Spiral Problem (TSP). TSP is a problem which classifies two spirals drawn on the plane, and it is famous as the high nonlinear problem. In this paper, we propose a chaos glial network which connected to Multi-Layer Perceptron (MLP). The chaos glial network is inspired by astrocyte which is glial cell in the brain. By computer simulations for solving TSP, we confirmed that the proposed chaos glial network connected to MLP gains better performance than the conventional MLP. I. I NTRODUCTION Back Propagation (BP) was introduced by Rumelhart in 1986 [1]. BP is used for learning algorithm of MLP and the error propagates backwards in the network. MLP using BP al- gorithm is well known to perform for the pattern classification tasks. However, the solution of the network often falls into the local minimum, because BP uses the steepest descent method for the leaning process. Generally, if the solution of MLP falls into the local minimum, it can not escape. In order to avoid this problem, some methods to release the solution from the local minimum are required. Recently, the mechanism of astrocyte which is glial cell existing in the central nervous system of the brain has been attracting. Several research groups discovered that astrocytes affect to neurons with signal transduction [2]. We consider that astrocytes make good effects to neurons in the biological neural networks. In this study, we propose a chaos glial network which connects to MLP as shown in Fig. 1. We consider that glial cells produce chaotic oscillation which is affected to neurons. This view is motivated by investigations of the Hopfield network solving combinatorial optimization problems with the help of a chaotic input signal component, designed in order to avoid local minima. It appears, from computer simulations, that a chaotic input component may substantially enhance the capability of avoiding these local minima [3]-[5]. Hence, we believe that chaotic signals may be used to further enhance the efficiency of the proposed chaos glia neural network. Furthermore, chaotic oscillation generated from glial cells propagates to the neighbor glial cells. Namely, certain neuron in this network is affected from some of glial cells located at a nearby site. We apply the proposed chaos glial network connected to MLP for solving TSP and confirm the efficiency by computer simulations. Glial Cell Glial Network MLP Neuron Chaos Fig. 1. Conceptual chaos glial network. II. MULTI -LAYER PERCEPTRON MLP is a most famous feed forward neural network. This network is used for pattern recognition, pattern classification, and other tasks. MLP has some layers, it has mainly input layer, hidden layer, and output layer. Generally, it is known that MLP can solve a more difficult task if the number of layer or neuron is increased. We consider MLP which is composed of four layers (one input layer, two hidden layers and one output layer), and MLP has the chaos glial network in the second layer of the hidden layer. The proposed MLP with the chaos glial network structure (connected 2-20-40-1) is shown in Fig. 2. A. Neuron Updating Rule The updating rule of neurons in the input layer, the first hidden layer and the output layer is described by Eq. (1) which is conventional updating rule. x i (t + 1) = f ⎛ ⎝ n  j=1 w ij (t)x j (t) - θ i (t) ⎞ ⎠ , (1) In the chaos glial neural network, chaotic oscillation is added to neurons in the second hidden layer. This neuron’s 978-1-4244-5309-2/10/$26.00 ©2010 IEEE 1360