Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Clustering of Affine Subspaces   Subspace clustering is an important problem in machine learning with many
applications in computer vision and pattern recognition. Prior work has studied
this problem using algebraic, iterative, statistical, low-rank and sparse
representation techniques. While these methods have been applied to both linear
and affine subspaces, theoretical results have only been established in the
case of linear subspaces. For example, algebraic subspace clustering (ASC) is
guaranteed to provide the correct clustering when the data points are in
general position and the union of subspaces is transversal. In this paper we
study in a rigorous fashion the properties of ASC in the case of affine
subspaces. Using notions from algebraic geometry, we prove that the
homogenization trick, which embeds points in a union of affine subspaces into
points in a union of linear subspaces, preserves the general position of the
points and the transversality of the union of subspaces in the embedded space,
thus establishing the correctness of ASC for affine subpaces.

0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph