Efficient Algorithms for Clustering and Interpolation of Large Spatial Data Sets

Categorizing, analyzing, and integrating large spatial data sets are of great importance in various areas such as image processing, pattern recognition, remote sensing, and life sciences. For example, NASA alone is faced with huge data sets gathered from around the globe on a daily basis to help scientists better understand our planet. Many approaches for accurately clustering, interpolating, and integrating these data sets are very computationally expensive. The focus of my PhD thesis is on the development of efficient implementations of data clustering and interpolation methods for large spatial data sets, and the application of these methods to geostatistics and remote sensing. In particular, I have developed fast implementations of ISODATA clustering and kriging interpolation algorithms. These implementations derive their efficiency through the use of both exact and approximate computational techniques from computational geometry and scientific computing. My work on the ISODATA clustering algorithm employs the kd-tree data structure and the filtering algorithm to speed up distance and nearest neighbor calculations. In the case of kriging interpolation, I applied techniques from scientific computing including iterative methods, tapering, fast multipole methods, and nearest neighbor searching techniques. I also present an application of kriging interpolation method to the problem of data fusion of remotely sensed data