On the construction of sparse matrices from expander graphs
Abstract
We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these matrices, precisely $d = \mathcal{O}\left(\log_s(N/s) \right)$; as opposed to the standard $d = \mathcal{O}\left(\log(N/s) \right)$. This gives insights into why using small $d$ performed well in numerical experiments involving such matrices. Furthermore, we derive quantitative sampling theorems for our constructions which show our construction outperforming the existing state-of-the-art. We also used our results to compare performance of sparse recovery algorithms where these matrices are used for linear sketching.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.09212
- arXiv:
- arXiv:1804.09212
- Bibcode:
- 2018arXiv180409212B
- Keywords:
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- Computer Science - Information Theory;
- 15B52
- E-Print:
- 28 pages, 4 figures