Using Topology Preservation Measures for Multidimensional Intelligent Data Analysis in the Reduced Feature Space

摘要

This paper investigates a possibility of supplementing standard dimensionality reduction procedures, used in the process of knowledge extraction from multidimensional datasets, with topology preservation measures. This approach is based on an observation that not all elements of an initial dataset are equally preserved in its low-dimensional embedding space representation. The contribution first overviews existing topology preservation measures, then their inclusion in the classical methods of exploratory data analysis is being discussed. Finally, some illustrative examples of presented approach in the tasks of cluster analysis and classification are being given.