Efficient Online Minimization for Low-Rank Subspace Clustering

by   Jie Shen, et al.
Rutgers University

Low-rank representation (LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory footprint, in that the size of the nuclear norm regularized matrix is n-by-n (where n is the number of samples). In this paper, we thereby develop a fast online implementation of LRR that reduces the memory cost from O(n^2) to O(pd), with p being the ambient dimension and d being some estimated rank (d < p ≪ n). The crux for this end is a non-convex reformulation of the LRR program, which pursues the basis dictionary that generates the (uncorrupted) observations. We build the theoretical guarantee that the sequence of the solutions produced by our algorithm converges to a stationary point of the empirical and the expected loss function asymptotically. Extensive experiments on synthetic and realistic datasets further substantiate that our algorithm is fast, robust and memory efficient.


page 1

page 2

page 3

page 4


Subspace clustering based on low rank representation and weighted nuclear norm minimization

Subspace clustering refers to the problem of segmenting a set of data po...

Smoothed Low Rank and Sparse Matrix Recovery by Iteratively Reweighted Least Squares Minimization

This work presents a general framework for solving the low rank and/or s...

Efficient Rank Minimization via Solving Non-convexPenalties by Iterative Shrinkage-Thresholding Algorithm

Rank minimization (RM) is a wildly investigated task of finding solution...

Non-Convex Rank Minimization via an Empirical Bayesian Approach

In many applications that require matrix solutions of minimal rank, the ...

Practical Matrix Completion and Corruption Recovery using Proximal Alternating Robust Subspace Minimization

Low-rank matrix completion is a problem of immense practical importance....

Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs

The ability to compare and align related datasets living in heterogeneou...

Tensor Laplacian Regularized Low-Rank Representation for Non-uniformly Distributed Data Subspace Clustering

Low-Rank Representation (LRR) highly suffers from discarding the localit...

Please sign up or login with your details

Forgot password? Click here to reset