Extending Applicability of Cluster Based Pattern Recognition with Efficient Approximation Techniques

The fundamental goal of this research has been to improve computational efficiency of the Visually Empirical Region of Influence (VERI) 1 based clustering and pattern recognition (PR) algorithms we developed in previous work. The original clustering algorithm, when applied to data sets with N points, ran in time proportional to N 3 (denoted with the notation O (N 3)), which limited the size of data sets it could find solutions for. Results generated from our original clustering algorithm were superior to commercial clustering packages. These results warranted our efforts to improve the runtimes of our algorithms. This report describes the new algorithms, advances and obstacles met in their development. The report gives qualitative and quantitative analysis of the improved algorithms' performances. With the information in this report, an interested user can determine which algorithm is best for a given problem in clustering (2-D) or PR (K-D), and can estimate how long it will run using the runtime plots of the algorithms before using any software. 1. Introduction Clustering and PR algorithms are not new algorithms. One purpose of a clustering algorithm is to determine (or impose) an order on an unknown set of points in a data set. After a data set has been clustered, and depending on the quality of the clustering result, the data will be ordered into clusters. The clustering algorithm used determines how or why the points in a cluster are related to each other. In a PR algorithm we utilize a training set of known information, and a test set with unknown classes of points. The training set contains experimental examples of each class to be identified, and these class data are used to develop criteria for automatically identifying future examples (test points) of these classes. For each of the test points we want to examine where it spatially occurs in the classified training points and assign a class to the test point based on the class criteria established.