Intelligent Classification in Huge Heterogeneous Data Sets.

摘要

This research effort sought to develop basic mathematical models and algorithms to perform classification and pattern recognition on large, heterogeneous data sets. To handle the large amounts of data, the principal investigator employed sparse representations to a two - fold effect. First, the effective dimensionality of the data is greatly reduced, allowing the discovery of meaningful connections among disparate data which is essential for classification. Second, the data dimension reduction technique used lends itself well to fast processing and accurate algorithms. To this end, several research directions were pursued. An efficient algorithm for approximating Dantzig selectors, which provide sparse minimal l1 - norm vectors solving a linear regression problem, is presented. The Dantzig selector model and algorithm is then extended to incorporate overcomplete dictionaries, which allows one to explore data separation, classification, and pattern recognition in heterogeneous data sets. Finally, new research is presented approximating high dimensional generalized Fourier series with a focus upon using the series for a novel method to perform rotational invariant pattern recognition in images.