Innovation Pursuit: A New Approach To Subspace Clustering

Keywords

Big Data; Innovation Pursuit; Linear Programming; Subspace Clustering; Subspace Learning; Unsupervised learning

Abstract

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on their relative novelties. We present two frameworks in which the idea of innovation pursuit is used to distinguish the subspaces. Underlying the first framework is an iterative method that finds the subspaces consecutively by solving a series of simple linear optimization problems, each searching for a direction of innovation in the span of the data potentially orthogonal to all subspaces except for the one to be identified in one step of the algorithm. A detailed mathematical analysis is provided establishing sufficient conditions for iPursuit to correctly cluster the data. The proposed approach can provably yield exact clustering even when the subspaces have significant intersections. It is shown that the complexity of the iterative approach scales only linearly in the number of data points and subspaces, and quadratically in the dimension of the subspaces. The second framework integrates iPursuitwith spectral clustering to yield a new variant of spectral-clustering-based algorithms. The numerical simulations with both real and synthetic data demonstrate that iPursuit can often outperform the stateof-the-art subspace clustering algorithms, more so for subspaces with significant intersections, and that it significantly improves the state-of-the-art result for subspace-segmentation-based face clustering.

Publication Date

12-1-2017

Publication Title

IEEE Transactions on Signal Processing

Volume

65

Issue

23

Number of Pages

6276-6291

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TSP.2017.2749206

Socpus ID

85029170322 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85029170322

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