275 research outputs found
Robust Recovery of Subspace Structures by Low-Rank Representation
In this work we address the subspace recovery problem. Given a set of data
samples (vectors) approximately drawn from a union of multiple subspaces, our
goal is to segment the samples into their respective subspaces and correct the
possible errors as well. To this end, we propose a novel method termed Low-Rank
Representation (LRR), which seeks the lowest-rank representation among all the
candidates that can represent the data samples as linear combinations of the
bases in a given dictionary. It is shown that LRR well solves the subspace
recovery problem: when the data is clean, we prove that LRR exactly captures
the true subspace structures; for the data contaminated by outliers, we prove
that under certain conditions LRR can exactly recover the row space of the
original data and detect the outlier as well; for the data corrupted by
arbitrary errors, LRR can also approximately recover the row space with
theoretical guarantees. Since the subspace membership is provably determined by
the row space, these further imply that LRR can perform robust subspace
segmentation and error correction, in an efficient way.Comment: IEEE Trans. Pattern Analysis and Machine Intelligenc
Subspace Clustering via Optimal Direction Search
This letter presents a new spectral-clustering-based approach to the subspace
clustering problem. Underpinning the proposed method is a convex program for
optimal direction search, which for each data point d finds an optimal
direction in the span of the data that has minimum projection on the other data
points and non-vanishing projection on d. The obtained directions are
subsequently leveraged to identify a neighborhood set for each data point. An
alternating direction method of multipliers framework is provided to
efficiently solve for the optimal directions. The proposed method is shown to
notably outperform the existing subspace clustering methods, particularly for
unwieldy scenarios involving high levels of noise and close subspaces, and
yields the state-of-the-art results for the problem of face clustering using
subspace segmentation
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