This paper describes a visualization system which has been used as part of a data-mining effort to detect fraud and abuse within state medicare programs. The data-mining process generates a set of N attributes for each medicare provider and beneficiary in the state; these attributes can be numeric, categorical, or derived from the scoring proces of the data- mining routines. The attribute list can be considered as an N- dimensional space, which is subsequently partitioned into some fixed number of cluster partitions. The sparse nature of the clustered space provides room for the simultaneous visualization of more than 3 dimensions; examples in the paper will show 6-dimensional visualization. This ability to view higher dimensional data allows the data-mining researcher to compare the clustering effectiveness of the different attributes. Transparency based rendering is also used in conjunction with filtering techniques to provide selective rendering of only those data which are of greatest interest. Nonlinear magnification techniques are used to stretch the N- dimensional space to allow focus on one or more regions of interest while still allowing a view of the global context. The magnification can either be applied globally, or in a constrained fashion to expand individual clusters within the space.
T. Alan Keahey, T. Alan Keahey,
"Visualization of high-dimensional clusters using nonlinear magnification", Proc. SPIE 3643, Visual Data Exploration and Analysis VI, (25 March 1999); doi: 10.1117/12.342839; https://doi.org/10.1117/12.342839