In this paper, an FPGA (Field Programmable Gate Array)-implementable digital chaos circuit with nonlinear mapping function learning ablility is proposed. The features of this circuit are user-programmability of the mapping functions by on-chip supervised learning, robustness of chaos signal generation based on digital processing, and high-speed and low-cost thanks to its FPGA implementation. The circuit design and analysis are presented in detail. The learning dynamics of the circuit and the quantitization effect to the quasi-chaos generation are analyzed by numerical simulations. The proposed circuit is designed by using an FPGA CAD tool, Verilog-HDL. This confirmed that the one-dimensional chaos circuit block (except for SRAM's) is implementable on a single FPGA chip and can generate quasi-chaos signals in real time.

A new current-mode sampled-data chaos circuit is proposed. The proposed circuit is composed of an operation block, a parameter block, and a delay block. The nonlinear mapping functions of this circuit are generated in the neuro-fuzzy based operation block. And these functions are determined by supervised learning. For the proposed circut, the dynamics of the learning and the state of the chaos are analyzed by computer simulations. The design conditions concerning the bifurcation diagram and the nonlinear mapping function are presented to clarify the chaos generating conditions and the effect of nonidealities of the proposed circuit. The simulation results showed that the nonlinear mapping functions can be realized with the precision of the order of several percent and that different kinds of bifurcation modes can be generated easily.

A structure of neural network suitable for clustering and deinterleaving radar pulses is proposed. The proposed structure consists of two networks, one for intrinsic features of pluses and the other for PRIs (pulse repetition intervals). The unsupervised learning method which adjusts the number of nodes for clusters adaptively is adopted for these two networks to learn patterns. These two networks are connected by a set of links. According to the weights of these links, the clusters categorized by the network for features can be refined further by merging or partitioning. The main defect of the unsupervised network with an adaptive number of nodes for clusters is that the result of classification closely depends on the learning sequence of patterns. This defect can be improved by the proposed refinement algorithm. In addition to the proposed structure and learning algorithms, simulation results have also been discussed.

A learning algorithm is presented for nearest neighbor pattern classifiers for the cases where mixed supervised and unsupervised training data are given. The classification rule includes rejection of outlier patterns and fuzzy classification. This partially supervised learning problem is formulated as a multiobjective program which reduces to purely super-vised case when all training data are supervised or to the other extreme of fully unsupervised one when all data are unsupervised. The learning, i. e. the solution process of this program is performed with a gradient method for searching a saddle point of the Lagrange function of the program.

A new arithmetic multiple-valued algebra with functional completeness is introduced. The algebra is called Neuro-Algebra for it has very similar formula and architecture to neural networks. Two canonical forms of multiple-valued functions of this Neuro-Algebra are presented. Since the arithmetic operations of the Neuro-Aglebra are basically a weighted-sum and a piecewise linear operations, their implementations are very simple and straightforward. Furthermore, the multiple-valued networks based on the Neuro-Algebra can be trained by the traditional back-propagation learning algorithm directly.

To investigate necessary conditions for the object recognition by simulations using neural network models is one of ways to acquire suggestions for understanding the neuronal representation of objects in the brain. In the present study, we trained a three layered neural network to form a geometrical feature representation in its output layer using back-propagation algorithm. After training using 73 learning examples, 65 testing patterns made by various combinations of above features could be recognized with the network at a rate of 95.3% appropriate response. We could classify four types of hidden layer units on the basis of effects on the output layer.