Exact methods for variable selection in principal component analysis: Guide functions and pre-selection

Joaquín Pacheco, Silvia Casado and Santiago Porras

Computational Statistics & Data Analysis, 2013, vol. 57, issue 1, 95-111

Abstract: A variable selection problem is analysed for use in Principal Component Analysis (PCA). In this case, the set of original variables is divided into disjoint groups. The problem resides in the selection of variables, but with the restriction that the set of variables that is selected should contain at least one variable from each group. The objective function under consideration is the sum of the first eigenvalues of the correlation matrix of the subset of selected variables. This problem, with no known prior references, has two further difficulties, in addition to that of the variable selection problem: the evaluation of the objective function and the restriction that the subset of selected variables should also contain elements from all of the groups. Two Branch & Bound methods are proposed to obtain exact solutions that incorporate two strategies: the first one is the use of “fast” guide functions as alternatives to the objective function; the second one is the preselection of variables that help to comply with the latter restriction. From the computational tests, it is seen that both strategies are very efficient and achieve significant reductions in calculation times.

Keywords: PCA; Variable selection; Branch & Bound methods; Guide functions; Filters (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947312002551
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:57:y:2013:i:1:p:95-111

DOI: 10.1016/j.csda.2012.06.014

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().