ARO Statistical Foundations for Analyzing Large Collections of Network-Data Objects

Abstract

In this work we investigated new ways to use concepts from geometry, probability and statistics on manifolds in order to analyze and categorize classes of data objects. This project progressed along the following three thrusts: 1. It associated classes of data objects with submanifolds and singular quotient spaces of Euclidean spaces through their adjacency matrices and (combinatorial) Laplacians. Techniques of differential geometry enabled mathematical characterization of these novel spaces and of appropriate notions of averaging of objects in these spaces. 2. Concepts from probability and statistics on manifolds were extended to adapt to the high-dimensional and geometrically complex nature of these data spaces. An appropriate probabilistic framework was developed for describing the statistical behavior of such averages. 3. From this probabilistic foundation, a variety of statistical methodologies were constructed and tested for analyzing large collections of data objects.

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Document Details

Document Type
Technical Report
Publication Date
Oct 31, 2018
Accession Number
AD1068368

Entities

People

  • Eric D. Kolaczyk

Organizations

  • Boston University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computer Science
  • Covariance
  • Data Analysis
  • Data Mining
  • Data Science
  • Differential Geometry
  • Gaussian Processes
  • Geometry
  • Information Processing
  • Information Science
  • Mathematics
  • Network Science
  • Probability
  • Standards
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Distributed Systems and Data Platform Development
  • Graph Algorithms and Convex Optimization.
  • Regression Analysis.

Technology Areas

  • Space
  • Space - Space Objects