rs-Sparse principal component analysis: A mixed integer nonlinear programming approach with VNS

Principal component analysis is a popular data analysis dimensionality reduction technique, aiming to project with minimum error for a given dataset into a subspace of smaller number of dimensions. In order to improve interpretability, different variants of the method have been proposed in the liter...

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Vydáno v:Computers & operations research Ročník 52; číslo Part B; s. 349 - 354
Hlavní autoři: Carrizosa, Emilio, Guerrero, Vanesa
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Elsevier Ltd 01.12.2014
Pergamon Press Inc
Témata:
Errors
Heuristic
Integer programming
Mathematical models
Mathematical problems
Mixed integer
Nonlinear mixed integer programming
Nonlinear programming
Numerical analysis
Operations research
Principal component analysis
Principal components analysis
Searching
Sparse principal component analysis
Sparsity
Studies
Subspaces
Variable neighborhood search
Nonlinear mixed integer programming
Sparse principal component analysis
Variable neighborhood search
ISSN:0305-0548, 1873-765X, 0305-0548
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Popis
Shrnutí:Principal component analysis is a popular data analysis dimensionality reduction technique, aiming to project with minimum error for a given dataset into a subspace of smaller number of dimensions. In order to improve interpretability, different variants of the method have been proposed in the literature, in which, besides error minimization, sparsity is sought. In this paper we formulate as a mixed integer nonlinear program the problem of finding a subspace with a sparse basis minimizing the sum of squares of distances between the points and their projections. Contrary to other attempts in the literature, with our model the user can fix the level of sparseness of the resulting basis vectors. Variable neighborhood search is proposed to solve the problem obtained this way. Our numerical experience on test sets shows that our procedure outperforms benchmark methods in the literature, both in terms of sparsity and errors.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2013.04.012