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Mathematical Underpinnings of AnalyticsTheory and Applications$
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Peter Grindrod

Print publication date: 2014

Print ISBN-13: 9780198725091

Published to Oxford Scholarship Online: March 2015

DOI: 10.1093/acprof:oso/9780198725091.001.0001

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Similarity, graphs and networks, random matrices, and SVD

Similarity, graphs and networks, random matrices, and SVD

Chapter:
(p.12) 1 Similarity, graphs and networks, random matrices, and SVD
Source:
Mathematical Underpinnings of Analytics
Author(s):

Peter Grindrod CBE

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198725091.003.0002

This chapter considers how a range of ideas from linear algebra, nonnegative matrices, random matrices and modern graph theory may assist in the understanding of observed pairwise similarities and networks over a large population of people or objects. In particular it examines some well-known different types of network models and considers (inverse problems concerning) how best to represent any observed social and friendship networks within such classes. This provides methods for inverse problems and soft clustering. Example applications are given to social networks and to clinical data.

Keywords:   self-adjoint matrices, non-negative matrices, Perron-Frobenius theory, singular value decomposition, graph theory, similarity matrices, random matrices, clustering, range dependent networks, small world networks

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