Living Reference Work Entry

Encyclopedia of Algorithms

pp 1-5

Date: Latest Version

Private Spectral Analysis


Differential privacy Spectral analysis Singular value decomposition Power method

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 \(A \in \mathbb{R}^{m\times n}\) and a parameter \(k \in \mathbb{N}\). We think of the input matrix as specifying n attributes for m individuals. The goal of the algorithm ...

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