Visualization of multidimensional image data sets using a neural network

TL;DR: The Kohonen map is introduced, that orders its neurons according to topological features of the data sets to be trained with, that can be called a topology-preserving feature map and can be used to solve general visualization problems of data mapping into a lower dimensional representation.

Abstract: This paper describes the application of self-organizing neural networks on the analysis and visualization of multidimensional data sets. First, a mathematical description of cluster analysis, dimensionality reduction, and topological ordering is given taking these methods as problems of discrete optimization. Then, the Kohonen map is introduced, that orders its neurons according to topological features of the data sets to be trained with. For this reason, it can also be called a topology-preserving feature map.