973 research outputs found
Neural Collaborative Subspace Clustering
We introduce the Neural Collaborative Subspace Clustering, a neural model
that discovers clusters of data points drawn from a union of low-dimensional
subspaces. In contrast to previous attempts, our model runs without the aid of
spectral clustering. This makes our algorithm one of the kinds that can
gracefully scale to large datasets. At its heart, our neural model benefits
from a classifier which determines whether a pair of points lies on the same
subspace or not. Essential to our model is the construction of two affinity
matrices, one from the classifier and the other from a notion of subspace
self-expressiveness, to supervise training in a collaborative scheme. We
thoroughly assess and contrast the performance of our model against various
state-of-the-art clustering algorithms including deep subspace-based ones.Comment: Accepted to ICML 201
Robust Low-Rank Subspace Segmentation with Semidefinite Guarantees
Recently there is a line of research work proposing to employ Spectral
Clustering (SC) to segment (group){Throughout the paper, we use segmentation,
clustering, and grouping, and their verb forms, interchangeably.}
high-dimensional structural data such as those (approximately) lying on
subspaces {We follow {liu2010robust} and use the term "subspace" to denote both
linear subspaces and affine subspaces. There is a trivial conversion between
linear subspaces and affine subspaces as mentioned therein.} or low-dimensional
manifolds. By learning the affinity matrix in the form of sparse
reconstruction, techniques proposed in this vein often considerably boost the
performance in subspace settings where traditional SC can fail. Despite the
success, there are fundamental problems that have been left unsolved: the
spectrum property of the learned affinity matrix cannot be gauged in advance,
and there is often one ugly symmetrization step that post-processes the
affinity for SC input. Hence we advocate to enforce the symmetric positive
semidefinite constraint explicitly during learning (Low-Rank Representation
with Positive SemiDefinite constraint, or LRR-PSD), and show that factually it
can be solved in an exquisite scheme efficiently instead of general-purpose SDP
solvers that usually scale up poorly. We provide rigorous mathematical
derivations to show that, in its canonical form, LRR-PSD is equivalent to the
recently proposed Low-Rank Representation (LRR) scheme {liu2010robust}, and
hence offer theoretic and practical insights to both LRR-PSD and LRR, inviting
future research. As per the computational cost, our proposal is at most
comparable to that of LRR, if not less. We validate our theoretic analysis and
optimization scheme by experiments on both synthetic and real data sets.Comment: 10 pages, 4 figures. Accepted by ICDM Workshop on Optimization Based
Methods for Emerging Data Mining Problems (OEDM), 2010. Main proof simplified
and typos corrected. Experimental data slightly adde
Symmetric low-rank representation for subspace clustering
We propose a symmetric low-rank representation (SLRR) method for subspace
clustering, which assumes that a data set is approximately drawn from the union
of multiple subspaces. The proposed technique can reveal the membership of
multiple subspaces through the self-expressiveness property of the data. In
particular, the SLRR method considers a collaborative representation combined
with low-rank matrix recovery techniques as a low-rank representation to learn
a symmetric low-rank representation, which preserves the subspace structures of
high-dimensional data. In contrast to performing iterative singular value
decomposition in some existing low-rank representation based algorithms, the
symmetric low-rank representation in the SLRR method can be calculated as a
closed form solution by solving the symmetric low-rank optimization problem. By
making use of the angular information of the principal directions of the
symmetric low-rank representation, an affinity graph matrix is constructed for
spectral clustering. Extensive experimental results show that it outperforms
state-of-the-art subspace clustering algorithms.Comment: 13 page
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