A Deterministic Analysis of Noisy Sparse Subspace Clustering for Dimensionality-reduced Data
نویسندگان
چکیده
Subspace clustering groups data into several lowrank subspaces. In this paper, we propose a theoretical framework to analyze a popular optimization-based algorithm, Sparse Subspace Clustering (SSC), when the data dimension is compressed via some random projection algorithms. We show SSC provably succeeds if the random projection is a subspace embedding, which includes random Gaussian projection, uniform row sampling, FJLT, sketching, etc. Our analysis applies to the most general deterministic setting and is able to handle both adversarial and stochastic noise. It also results in the first algorithm for privacy-preserved subspace clustering.
منابع مشابه
A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data
Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the dimensionality of data points to be clustered are compressed due to constraints of measurement, computation or privacy. In this paper, we study the theoretical properties...
متن کاملA Deterministic Analysis of Noisy Sparse Subspace Clustering for Dimensionality-reduced Data
Appendix A contains proofs for our main results. The proofs are sorted in the order that their corresponding statements appear in the paper. Appendix B formalizes our claims in the paper about attribute privacy and the corresponding utility theorem and includes additional discussions on the difficulty of a stronger user-level privacy claim. Appendix C contains numerical simulations on the perfo...
متن کاملDimensionality-reduced subspace clustering
Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from undersampling due to complexity and speed constraints on the acquisition device o...
متن کاملGraph Connectivity in Noisy Sparse Subspace Clustering
Subspace clustering is the problem of clustering data points into a union of lowdimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work [4, 19, 24, 20] provided strong theoretical guarantee for sparse subspace clustering [4], the state-of-the-art algorithm for subspace clu...
متن کاملClustering Consistent Sparse Subspace Clustering
Subspace clustering is the problem of clustering data points into a union of lowdimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work [4, 19, 24, 20] provided strong theoretical guarantee for sparse subspace clustering [4], the state-of-the-art algorithm for subspace clu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015