Publication Type

Conference Proceeding Article

Version

submittedVersion

Publication Date

12-2015

Abstract

Subspace clustering is an unsupervised learning problem that aims at grouping data points into multiple “clusters” so that data points in a single cluster lie approximately on a low-dimensional linear subspace. It is originally motivated by 3D motion segmentation in computer vision, but has recently been generically applied to a wide range of statistical machine learning problems, which often involves sensitive datasets about human subjects. This raises a dire concern for data privacy. In this work, we build on the framework of differential privacy and present two provably private subspace clustering algorithms. We demonstrate via both theory and experiments that one of the presented methods enjoys formal privacy and utility guarantees; the other one asymptotically preserves differential privacy while having good performance in practice. Along the course of the proof, we also obtain two new provable guarantees for the agnostic subspace clustering and the graph connectivity problem which might be of independent interests.

Discipline

Theory and Algorithms

Publication

NIPS'15 Proceedings of the 28th International Conference on Neural Information Processing Systems

First Page

1000

Last Page

1008

Publisher

ACM

Copyright Owner and License

LARC

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