Establishment of generalized theory of self-organizing maps and its applications

本项目的目的是建立广义自组织映射理论，并将其应用于各种实际任务。在资助期间，我们取得了以下成果。(1)Kohonen的自组织映射（SOM）的一般理论建立了各种数据类型。该理论是通过采用各种模块化结构代替传统SOM的矢量单元来实现的，我们称之为模块化网络SOM（mnSOM）。在多层感知器模块的情况下，利用函数空间中的勒让德展开证明了理论等价性。我们还建立了SOM的高阶理论，称之为SOM^n。通过使用SOM^n，一组数据分布由纤维丛建模。(2)我们将mn SOM和SOM^应用于自适应控制、纹理分类、三维物体分类、人脸图像识别、手写字母识别等实际任务中，并将其应用于移动的机器人中，成功地获得了外部环境的内部模型。(3)我们开发了一些扩展架构的基础上，这些广义的SOM。自我进化（self-evolving）自生长）模块化网络应用于移动的机器人组织外部世界的图形表示。

The purpose of this project is to establish the theory of generalized self-organizing maps and to apply it to various practical tasks. During the grant, we obtained the following results.(1) The generalized theory of Kohonen's self-organizing map (SOM) was established for various data types. The theory was realized by adopting various module architectures as the replacement of the vector units of the conventional SOM, which we called mn SOM (modular network SOM). In the case of multi-layer perceptron module, theoretical equivalence was proved by using Legendre expansion in function space. We also established the theory of the higher-rank of SOM, that is called SOM^n. By using SOM^n, a set of data distributions are modeled by a fiber bundle.(2) We applied the mn SOM and the SOM^n various practical tasks, such as adaptive control, texture classification, 3D object classification, face image recognition, hand written letter recognition and so on. We also applied them to mobile robots, and the robots succeeded to acquire an inner model of the outer environment.(3) We developed some extended architectures based on these generalized SOMs. The self-evolving (i.e., self-growing) modular network was applied to mobile robots to organize a graph-base representation of the outer world.