Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured Sparse Subspace Clustering: A Joint Affinity Learning and
  Subspace Clustering Framework   Subspace clustering refers to the problem of segmenting data drawn from a
union of subspaces. State-of-the-art approaches for solving this problem follow
a two-stage approach. In the first step, an affinity matrix is learned from the
data using sparse or low-rank minimization techniques. In the second step, the
segmentation is found by applying spectral clustering to this affinity. While
this approach has led to state-of-the-art results in many applications, it is
sub-optimal because it does not exploit the fact that the affinity and the
segmentation depend on each other. In this paper, we propose a joint
optimization framework --- Structured Sparse Subspace Clustering (S$^3$C) ---
for learning both the affinity and the segmentation. The proposed S$^3$C
framework is based on expressing each data point as a structured sparse linear
combination of all other data points, where the structure is induced by a norm
that depends on the unknown segmentation. Moreover, we extend the proposed
S$^3$C framework into Constrained Structured Sparse Subspace Clustering
(CS$^3$C) in which available partial side-information is incorporated into the
stage of learning the affinity. We show that both the structured sparse
representation and the segmentation can be found via a combination of an
alternating direction method of multipliers with spectral clustering.
Experiments on a synthetic data set, the Extended Yale B data set, the Hopkins
155 motion segmentation database, and three cancer data sets demonstrate the
effectiveness of our approach.

2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio