New Theory and Algorithms for Scalable Data Fusion
Abstract
New mathematical theory and algorithms were developed for querying functions and data sets in high dimensions. This was accomplished in both the deterministic setting as well as the stochastic setting with noise. Since high dimensional problems suffer from the curse of dimensionality, new model classes were introduced based on the notions of sparsity and variable reductions. These model classes were shown to fit real world problems and yet be amenable to realistic computational methods for querying in high dimensions. The new algorithms were developed using sophisticated adaptive methods. They utilize the most judicious deterministic point clouds in high dimension such as those based on discrepancy theory (Halton sequences) and perfect hashing. The resulting algorithms were shown to have optimal performance on the proposed model classes. Thus, they have provided the most efficient algorithms for querying high dimensional data under the model assumptions. Results were also developed and proved for classification of data. These stochastic algorithms were shown to have optimal performance on various model classes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 20, 2013
- Accession Number
- ADA587535
Entities
People
- Ronald A. Dvore
Organizations
- Texas A&M University