Visualize Highly-Dimensional Data Reference

Sammon projection

Abstract. An algorithm for the analysis of multivariate data is presented along with some experimental results. The algorithm is based upon a point mapping of N L- dimensional vectors from the L-space to a lower-dimensional space such that the inherent data “structure” is approximately preserved. Read more…

 

Self-Organizing Feature Map (SOM)

Abstract. This work contains a theoretical study and computer simulations of a new self-organizing process. The principal discovery is that in a simple network of adaptive physical elements which receives signals from a primary event space, the signal representations are

automatically mapped onto a set of output responses in such a way that the responses acquire the same topological order as that of the primary events. In other words, a principle has been discovered which facilitates the automatic formation of topologically correct maps of features of observable events. The basic self-organizing system is a one- or twodimensional array of processing units resembling a network of threshold-logic units, and characterized by short-range lateral feedback between neighbouring units. Several types of computer simulations are used to demonstrate the ordering process as well as the conditions under which it fails. Read more …

 

Molecular Dynamic – Multidimension Scaling

 

Abstract. We discuss a molecular dynamics approach to the problem of multidimensional scaling, which is a statistical method used for the visualization of dissimilarities in multidimensional data. Numerical estimates of dissimilarities between pairs of objects from a high dimensional data collection are approximated by distances between corresponding pairs of objects in a low dimensional visual representation. The quality of this approximation is expressed as an energy function, which yields the optimal arrangement at its minimum. We show how this optimal arrangement can be efficiently computed using the molecular dynamics approach. The numerical estimates show that the proposed molecular dynamics method is more accurate and about an order of magnitude faster than the simulated annealing method. Read more…