Graph connection Laplacian and random matrices with random blocks

Published

Journal Article

© The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high-dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e. the case where there is no structure in the dataset under investigation. Developing this understanding is important in making sense of the output of the algorithms based on GCL. We hence develop a theory explaining the behavior of the spectral distribution of a large class of random matrices, in particular random matrices with random block entries of fixed size. Part of the theory covers the case where there is significant dependence between the blocks. Numerical work shows that the agreement between our theoretical predictions and numerical simulations is generally very good.

Full Text

Duke Authors

Cited Authors

  • Karoui, NE; Wu, HT

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 4 / 1

Start / End Page

  • 1 - 42

Electronic International Standard Serial Number (EISSN)

  • 2049-8772

Digital Object Identifier (DOI)

  • 10.1093/imaiai/iav001

Citation Source

  • Scopus