Semi-Orthogonally Associative Memory neural network model (SAM) uses the orthogonal vectors in Un = {-1, 1}n as its characteristic patterns. It is necessary to select the optimum characteristic parameter n so as to increase the efficiency of this model used. This paper investigates the dynamic behavior and error correcting capability of SAM by statistical neurodynamics, and demonstrates that there exists a convergence criterion in tis recalling processes. And then, making use of these results, its optimum characteristic parameter is deduced. It is proved that, in the statistical sense, its recalling outputs converge to the desired pattern when the initial similar probability is larger than the convergence criterion and not true otherwise. For a SAM with N neurons, when its characteristic parameter is optimum, its memory capacity is N/2 ln ln N, the information storage capacity per connection weight is larger than 9/23 (bits/weight) and the radius of attractive basin of non-spurious stable state is about 0.25N. Computer simulations are done on this model and the simulation results are consistent with the results of theoretical analyses.

In this paper we propose a new algorithm for recognizing 3-D objects from 2-D images. The algorithm takes the multiple view approach in which each 3-D object is modeled by a collection of 2-D projections from various viewing angles where each 2-D projection is called an object model. To select the candidates for the object model that has the best match with the input image, the proposed algorithm computes the surface matching score between the input image and each object model by using Hopfield nets. In addition, the algorithm gives the final matching error between the input image and each candidate model by the error of the pose-transform matrix proposed by Hong et al. and selects an object model with the smallest matching error as the best matched model. The proposed algorithm can be viewed as a combination of the algorithm of Lin et al. and the algorithm of Hong et al. However, the proposed algorithm is not a simple combination of these algorithms. While the algorithm of Lin et al. computes the surface matching score and the vertex matching score berween the input image and each object model to select the candidates for the best matched model, the proposed algorithm computes only the surface matching score. In addition, to enhance the accuracy of the surface matching score, the proposed algorithm uses two Hopfield nets. The first Hopfield net, which is the same as that used in the algorithm of Lin et al., performs a coarse matching between surfaces of an input image and surfaces of an object model. The second Hopfield net, which is the one newly proposed in this paper, establishes the surface correspondences using the compatibility measures between adjacent surface-pairs of the input image and the object model. the results of the experiments showed that the surface matching score obtained by the Hopfield net proposed in this paper is much more useful for the selectoin of the candidates for the best matched model than both the sruface matching score obtained by the first Hopfield net of Lin et al. and the vertex matching score obtained by the second Hopfield net of Lin et al. and, as the result, the object recognition algorithm of this paper can perform much more reliable object recognition than that obtained by simply combining the algorithm of Lin et al. and the algorithm of Hong et al.

A feedback pattern recognition method using an inverse recall neural network model is proposed. The feedback method can adjust processing parameter values adaptively to individual patterns so as to produce reliable recognition results. In order to apply an adaptive control technique to such pattern recognition processings, the evaluation value for recognition uncertainty is determined to be a function with regard to an input pattern and processing parameters. In its feedback phase, the input pattern is fixed and processing parameters are adjusted to decrease the recognition uncertainty. The proposed neural network model implements two functions in this feedback recognition method. One is a discrimination as a kind of multi-layer feedforward model. The other is to generate an input modification so as to decrease the recognition uncertainty. The modification values indicate parts which are important for more certain recognition but are missed in the original input to the nerwork. The proposed feedback method can adjust prcessing parameter values in order to detect the important parts shown by the inverse recall network model. As explained in this paper, feature extraction parameter values are adaptively adjusted by this feedback method. After the inverse recall model and the feedback function are implemented, features are extracted again by using the modified feature extraction parameter values. The feature is classified by the feedforward function of the network model. The feedforward and feedback processings are repeated until a certain recognition result is obtained. This method was examined for hadwritten alpha-numerics with rotation distortion. The feedback method was found to decrease the rejection ratio at the same substitution error ratio with high efficiency.

A new regularization cost function for generalization in real-valued function learning is proposed. This cost function is derived from the maximum likelihood method using a modified sample distribution, and consists of a sum of square errors and a stabilizer which is a function of integrated square derivatives. Each of the regularization parameters which gives the minimum estimation error can be obtained uniquely and non-empirically. The parameters are not constants and change in value during learning. Numerical simulation shows that this cost function predicts the true error accurately and is effective in neural network learning.

The problem of local minima is inevitable when solving combinatorial optimization problems by conventional methods such as the Hopfield network, relying on the minimization of an objective function E(X). Such a problem arises from the search mechanism in which only the local information about the objective function E(X) is used. In this paper we propose a new approach called the Single Minimum Method (SMM) which uses the global information in searching for the solutions to combinatorial optimization problems. In this approach, we add a function -TS(X) to the original objective function E(X) to construct the function F(X)=E(X)-TS(X) which has only one minimum, one which can be easily found by any general gradiet method including the Hopfield network. Based on an analogy between thermodynamic systems and neural networks, it is shown that the global information about the original objective function E(X) is included in the single minimum of the function F(X) and can be used for finding the global minimum of the objective function E(X). In order to show how to apply the Single Minimum Method to a combinatorial optimization problem we give an algorithm for the TSP problem based on our method. The simulation results show that the algorithm can almost always find the shortest or near shortest paths. Finally, a modified SMM, which has some great advantages for hardware implementation, is also given.

A discrete-time neuron model having a refractory period and containing a binary hysteresis output function is introduced. A detailed mathematical analysis of the output response is carried out and the necessary and sufficient condition which a sequence must satisfy in order to be designated as a periodic response of the neuron model under a constant or periodic stimulation is given.