10,101 research outputs found
Distributed Low-rank Subspace Segmentation
Vision problems ranging from image clustering to motion segmentation to
semi-supervised learning can naturally be framed as subspace segmentation
problems, in which one aims to recover multiple low-dimensional subspaces from
noisy and corrupted input data. Low-Rank Representation (LRR), a convex
formulation of the subspace segmentation problem, is provably and empirically
accurate on small problems but does not scale to the massive sizes of modern
vision datasets. Moreover, past work aimed at scaling up low-rank matrix
factorization is not applicable to LRR given its non-decomposable constraints.
In this work, we propose a novel divide-and-conquer algorithm for large-scale
subspace segmentation that can cope with LRR's non-decomposable constraints and
maintains LRR's strong recovery guarantees. This has immediate implications for
the scalability of subspace segmentation, which we demonstrate on a benchmark
face recognition dataset and in simulations. We then introduce novel
applications of LRR-based subspace segmentation to large-scale semi-supervised
learning for multimedia event detection, concept detection, and image tagging.
In each case, we obtain state-of-the-art results and order-of-magnitude speed
ups
New Guarantees for Blind Compressed Sensing
Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS)
where the optimal sparsifying dictionary is assumed to be unknown and subject
to estimation (in addition to the CS sparse coefficients). Since the emergence
of BCS, dictionary learning, a.k.a. sparse coding, has been studied as a matrix
factorization problem where its sample complexity, uniqueness and
identifiability have been addressed thoroughly. However, in spite of the strong
connections between BCS and sparse coding, recent results from the sparse
coding problem area have not been exploited within the context of BCS. In
particular, prior BCS efforts have focused on learning constrained and complete
dictionaries that limit the scope and utility of these efforts. In this paper,
we develop new theoretical bounds for perfect recovery for the general
unconstrained BCS problem. These unconstrained BCS bounds cover the case of
overcomplete dictionaries, and hence, they go well beyond the existing BCS
theory. Our perfect recovery results integrate the combinatorial theories of
sparse coding with some of the recent results from low-rank matrix recovery. In
particular, we propose an efficient CS measurement scheme that results in
practical recovery bounds for BCS. Moreover, we discuss the performance of BCS
under polynomial-time sparse coding algorithms.Comment: To appear in the 53rd Annual Allerton Conference on Communication,
Control and Computing, University of Illinois at Urbana-Champaign, IL, USA,
201
Unsupervised Feature Selection with Adaptive Structure Learning
The problem of feature selection has raised considerable interests in the
past decade. Traditional unsupervised methods select the features which can
faithfully preserve the intrinsic structures of data, where the intrinsic
structures are estimated using all the input features of data. However, the
estimated intrinsic structures are unreliable/inaccurate when the redundant and
noisy features are not removed. Therefore, we face a dilemma here: one need the
true structures of data to identify the informative features, and one need the
informative features to accurately estimate the true structures of data. To
address this, we propose a unified learning framework which performs structure
learning and feature selection simultaneously. The structures are adaptively
learned from the results of feature selection, and the informative features are
reselected to preserve the refined structures of data. By leveraging the
interactions between these two essential tasks, we are able to capture accurate
structures and select more informative features. Experimental results on many
benchmark data sets demonstrate that the proposed method outperforms many state
of the art unsupervised feature selection methods
- …