We reported that a competitive learning neural network had the ability of self-organization in the classification of questionnaire survey data. In this letter, its self-organized learning was evaluated by means of mutual information. Mutual information may be useful to find efficently the network which can give optimal classification.

In this paper, I investigate a property of self-organizing feature map (SOFM) in terms of reference vector density q(x) when probability density function of input signal fed into SOFM is p(x). Difficulty of general analysis on this property is briefly discussed. Then, I employ an assumption (conformal map assumption) to evaluate this property, and it is shown that for equilibrium state, q(x)p(x)s holds. By giving Lyapunov functioin for time evolution of reference vector density q(x) in SOFM, the equilibrium state is proved to be stable in terms of distribution. Comparison of the result with one which is based on different assumption reveals that there is no unique result of a simple form, such as conjectured by Kohonen. However, as there are cases in which these assumptions hold, these results suggest that we can consider a range of the property of SOFM. On the basis of it, we make comparison on this property between SOFM and fundamental adaptive vector quantization algorithm, in terms of the exponent s of the relation q(x)p(x)s. Difference on this property between SOFM and fundamental adaptive vector quantization algorithm, and propriety of mean squared quantization error for a performance measure of SOFM, are discussed.

This paper proposes a multi-layer cellular network in which a self-organizing method is implemented. The network is developed for the purpose of data clustering and recognition. A multi-layer structure is presented to realize the sophisticated combination of several sub-spaces which are spanned by given input characteristic data. A self-organizing method is useful for evaluating the set of clusters for input data without a supervisor. Thus, using these techniques this network can provide good clustering ability as an example for image/pattern data which have complicated and structured characteristics. In addition to the development of this algorithm, this paper also presents a parallel VLSI architecture for realizing the mechanism with high efficiency. Since the locality can be kept among all processing elements on every layer, the system is easily designed without large global data communication.

The mechanism of environment-dependent self-organization of "positional information" in a coupled nonlinear oscillator system is proposed as a new principle of realtime coordinative control in biological distributed system. By modeling the pattern formation in tactic response of Physarum plasmodium, it is shown that a global phase gradient pattern self-organized by mutual entrainment encodes not only the positional relationship between subsystems and the total system but also the relative relationship between internal state of the system and the environment.

The self-organization rule of planar neural networks has been proposed for learning of 2D distributions. However, it cannot be applied to 3D objects. In this paper, we propose a new model for global representation of the 3D objects. Based on this model, global topology reserving self-organization is achieved using parallel local competitive learning rule such as Kohonen's maps. The proposed model is able to represent the objects distributively and easily accommodate local features.