Dimensionality Reduction and Interactive Visualization of Multivariate Data — Methods, Tools, Applications

Abstract

A plethora of technical problems are characterized by sets of high-dimensional data. Significance, correlations, redundancy, or irrelevancy of the variables _{v i} with regard to the given application are a priori unknown. The extraction of underlying knowledge or the reliable automatic classification for cognitive systems requires the reduction of the initial data set to the essential information and the corresponding variables. Thus, dimensionality reduction is an ubiquituous problem and together with multivariate data visualization a topic of interdisciplinary research interest for more than three decades. Recently, high economic interest applications, e.g., data mining and knowledge discovery applications, give renewed strong incentive to the field. This tutorial, gives a focused survey of relevant methods from past to present based on an elaborated taxonomy. Quantitative and qualitative assessment and comparison of the methods in an unifying approach will be carried out. Enhancements and benefits of interactive visualization will be introduced. Dedicated tools based on the introduced method spectrum will be presented and key applications will serve for further elucidation of the approach and its potential. The most practical methods and tools from the tutorial as well as a comprehensive sets of slides are available from http://www.iee.et.tu-dresden.de/^~koeniga/QuickCog.html as free demo software version of the QuickCog system.