**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…