Elman Neural Networks and Time Integration for Object Recognition

We consider a system based on an Elman network for a categorization task. Four objects are investigated by an automa walking around in circles. The shapes are derived from four version of a cross: square, thick cross, critical cross and thin cross. Therefore, the input of the system is represented by the distance-wave relieved by the sensor at each step. We let several parameters vary: starting point and speed of the automa walk, radius of the circle and size of the shape. The system is trained using a back-propagation algorithm. We describe the complete setup of the parameters and noises, which the automa will have to face for the prediction/categorization task. INTRODUCTION In this paper we consider a model of an automa endowed with a distance sensor, which is able to walk around objects. On one hand, we are interested in the the capacity of that automa to categorize the object within a reasonable class of objects, and on the other hand robustness of such a capacity with respect to variations of the parameters involved in the entire setting, and with respect to noise parameters (see [10], [14], [9] and [13]). The model is reduced in our case to facing sequences of distance predictions, which correspond to special object contours. That task play a key role more in general in the autonomous robotics field, and namely in artificial active vision. Those distance sequences may be processed by an artificial neural network, which tries to reproduce biological neuron-like system. There are many different types of such networks; nevertheless we shall focus our attention on Elman neural networks (see [6], [3] and [2]). The Elman neural network we consider has the following architecture. It is a feed-forward network with two layers (see Figure 1 below). The activation functions for the hidden and the output layer are logistic functions Φσ(x) = 1 1+eσx , (1) where the parameter σ will be set to 1. The learning rule we use is the error back-propagation algorithm (see [11]). Moreover, the learning rate λ will be chosen later on. This type of network differs from conventional ones in that the input layer has a recurrent connection with the hidden one (denoted by the dashed lines in the Figure 1). Therefore, at each time step the output values of the hidden units are copied to the input ones, which store them and use them for the next time step. This process allows the network to memorize some information from the past, in such a way to better detect periodicity of the patterns (perception task). Since our network receives the distance from the pattern as input step by step, we are dealing with a passive perception (see [7], [16], [8], [5]). We neglect for the moment interaction with the patterns and active perception (see [12], [15], [1]). Anyway the predition is the main task we shall be involved with (see [4] and [17]). The object patterns we are interested in are cross-shaped objects with variable lengths in the arms and variable ratio between the longer and the shorter arm. We shall investigate which is the best class of such patterns to be categorized. Our experiments are split in two different periods. The first is the so-called learning phase, devoted to train the net and to update the weights. The second is the testing phase, devoted to test the answers of the net with the resulting fixed weights. Date: July 3, 2006. 2000 Mathematics Subject Classification. Primary: 92B20; Secondary: 68T10.