Signal recovery on graphs

Fundamental limits of sampling strategies

Siheng Chen, Rohan Varma, Aarti Singh, Jelena Kovacevic

Research output: Contribution to journalArticle

Abstract

This paper builds theoretical foundations for the recovery of a newly proposed class of smooth graph signals, approximately bandlimited graph signals, under three sampling strategies: uniform sampling, experimentally designed sampling, and active sampling. We then state minimax lower bounds on the maximum risk for the approximately bandlimited class under these three sampling strategies and show that active sampling cannot fundamentally outperform experimentally designed sampling. We propose a recovery strategy to compare uniform sampling with experimentally designed sampling. As the proposed recovery strategy lends itself well to statistical analysis, we derive the exact mean square error for each sampling strategy. To study convergence rates, we introduce two types of graphs and find that 1) the proposed recovery strategy achieves the optimal rates; and 2) the experimentally designed sampling fundamentally outperforms uniform sampling for Type-2 class of graphs. To validate our proposed recovery strategy, we test it on five specific graphs: a ring graph with k nearest neighbors, an Erd's-Rényi graph, a random geometric graph, a small-world graph, and a power-law graph and find that experimental results match the proposed theory well. This paper also presents a comprehensive explanation for when and why sampling for semi-supervised learning with graphs works.

Original languageEnglish (US)
Article number7581102
Pages (from-to)539-554
Number of pages16
JournalIEEE Transactions on Signal and Information Processing over Networks
Volume2
Issue number4
DOIs
StatePublished - Jan 1 2016

Fingerprint

Sampling
Recovery
Supervised learning
Mean square error
Statistical methods

Keywords

  • Active sampling
  • experimentally designed sampling
  • semi-supervised learning
  • signal processing on graphs
  • signal recovery

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Signal recovery on graphs : Fundamental limits of sampling strategies. / Chen, Siheng; Varma, Rohan; Singh, Aarti; Kovacevic, Jelena.

In: IEEE Transactions on Signal and Information Processing over Networks, Vol. 2, No. 4, 7581102, 01.01.2016, p. 539-554.

Research output: Contribution to journalArticle

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