Private Spectral Analysis

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 mindividuals. The goal of the...