We show that simultaneous perturbation can be used as an algorithm for on-line learning, and we report our theoretical investigation on generalization performance obtained with a statistical mechanical method. Asymptotic behavior of generalization error using this algorithm is on the order of t to the minus one-third power, where t is the learning time or the number of learning examples. This order is the same as that using well-known perceptron learning.

In this paper, we describe an implementation of analog neural network system with on-line learning capability. A learning rule using the simultaneous perturbation is adopted. Compared with usage of the ordinary back-propagation method, we can easily implement the simultaneous perturbation learning rule. The neural system can monitor weight values and an error value. The exclusive OR problem and a simple function problem are shown.

Weight perturbation learning was proposed as a learning rule in which perturbation is added to the variable parameters of learning machines. The generalization performance of weight perturbation learning was analyzed by statistical mechanical methods and was found to have the same asymptotic generalization property as perceptron learning. In this paper we consider the difference between perceptron learning and AdaTron learning, both of which are well-known learning rules. By applying this difference to weight perturbation learning, we propose adaptive weight perturbation learning. The generalization performance of the proposed rule is analyzed by statistical mechanical methods, and it is shown that the proposed learning rule has an outstanding asymptotic property equivalent to that of AdaTron learning.

This letter proposes a numerical method for approximating the location of and dynamics on a class of chaotic saddles. In contrast to the conventional strategy of maximizing the escape time, our proposal is to impose a zero-expansion condition along transversely repelling directions of chaotic saddles. This strategy exploits the existence of skeleton-forming unstable periodic orbits embedded in chaotic saddles, and thus can be conveniently implemented as a variant of subspace Newton-type methods. The algorithm is examined through an illustrative and another standard example.

The electroretinogram (ERG) is used to diagnose many kinds of eye diseases. Our final purpose in this paper is a detection of diabetic retinopathy by using only ERG. In this paper, we describe a method to examine whether presented ERG data belong to a group of diabetic retinopathy. The ERG mainly consists of the a-wave, the b-wave and the oscillatory potential (op-wave). It was known that the op-wave varies as progress of retinopathy. Thus, we use the latency, the amplitude and the peak frequency of the op-wave. First, we study these features of sample ERG data, statistically. It was clarified that some of these characteristics are significantly different between a normal group and a group of diabetic retinopathy. By using some of these characteristics, we classify unknown ERG data on the basis of the Mahalanobis' generalized distance or the linear discriminant function. The highest accuracy of this method for the unknown data is about 92.73%.