Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Private Spectral Analysis

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_552-1

Years and Authors of Summarized Original Work

  • 2014; Dwork, Talwar, Thakurta, Zhang

  • 2014; Hardt, Price

Problem Definition

Spectral analysis refers to a family of popular and effective methods that analyze an input matrix by exploiting information about its eigenvectors or singular vectors. Applications include principal component analysis, low-rank approximation, and spectral clustering. Many of these applications are commonly performed on data sets that feature sensitive information such as patient records in a medical study. In such cases privacy is a major concern. Differential privacy is a powerful general-purpose privacy definition. This entry explains how differential privacy may be applied to task of approximately computing the top singular vectors of a matrix.

Generally speaking, the input is a real-valued matrix \(A \in \mathbb{R}^{m\times n}\)


Differential privacy Spectral analysis Singular value decomposition Power method 
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Recommended Reading

  1. 1.
    Blum A, Dwork C, McSherry F, Nissim K (2005) Practical privacy: the SuLQ framework. In: Proceedings of the 24th PODS. ACM, pp 128–138Google Scholar
  2. 2.
    Dwork C, Talwar K, Thakurta A, Zhang L (2014) Analyze gauss: optimal bounds for privacy-preserving principal component analysis. In: Proceedings of the 46th symposium on theory of computing (STOC). ACM, pp 11–20Google Scholar
  3. 3.
    Hardt M, Price E (2014) The noisy power method: A meta algorithm with applications. CoRR abs/1311.2495v2. http://arxiv.org/abs/1311.2495
  4. 4.
    Hardt M, Roth A (2012) Beating randomized response on incoherent matrices. In: Proceedings of the 44th symposium on theory of computing (STOC). ACM, pp 1255–1268Google Scholar
  5. 5.
    Hardt M, Roth A (2013) Beyond worst-case analysis in private singular vector computation. In: Proceedings of the 45th Symposium on Theory of Computing (STOC). ACMGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.IBM Research – AlmadenSan JoseUSA