Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Solutions for Sparse Principal Component Analysis   Given a sample covariance matrix, we examine the problem of maximizing the
variance explained by a linear combination of the input variables while
constraining the number of nonzero coefficients in this combination. This is
known as sparse principal component analysis and has a wide array of
applications in machine learning and engineering. We formulate a new
semidefinite relaxation to this problem and derive a greedy algorithm that
computes a full set of good solutions for all target numbers of non zero
coefficients, with total complexity O(n^3), where n is the number of variables.
We then use the same relaxation to derive sufficient conditions for global
optimality of a solution, which can be tested in O(n^3) per pattern. We discuss
applications in subset selection and sparse recovery and show on artificial
examples and biological data that our algorithm does provide globally optimal
solutions in many cases.

23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ