Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Sample Complexity of Subspace Learning   A large number of algorithms in machine learning, from principal component
analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral
embedding and support estimation methods, rely on estimating a linear subspace
from samples. In this paper we introduce a general formulation of this problem
and derive novel learning error estimates. Our results rely on natural
assumptions on the spectral properties of the covariance operator associated to
the data distribu- tion, and hold for a wide class of metrics between
subspaces. As special cases, we discuss sharp error estimates for the
reconstruction properties of PCA and spectral support estimation. Key to our
analysis is an operator theoretic approach that has broad applicability to
spectral learning methods.

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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
2
The categories of this paper are: math