Topological dimensionality determination and dimensionality reduction based on minimum spanning trees

In the design of multidimensional systems for the analysis of complex data, an intelligent reduction of the data dimensionality is needed to enable its efficient and accurate processing without much loss of information. The underlying data transformation process can be implemented by nonlinearly mapping the high-dimensional data space onto a low-dimensional feature space where the mapping preserves the topological structure of the transformed data in the feature space as much as possible. This method is often referred to as Multidimensional Scaling (MDS). This paper describes a new MDS approach for feature extraction purposes. It consists of a fast hierachical Minimal-Spanning-Tree-based method which minimizes the Sammon´s criteria with a genetic algorithm. Results presented show that this new approach is promising for several applications