Sparse principal balances. (April 2015)

• Record Type: Journal Article
• Authors: Mert, Mehmet Can; Filzmoser, Peter; Hron, Karel
• Other Names: Filzmoser Peter guest-editor.; Hron Karel guest-editor.
• Is Part Of: Statistical modelling. Volume 15:Number 2(2015)
• Page Start: 159
• Page End: 174
• Publication Date: 2015-04
• Subjects: principal component analysis -- compositional data -- isometric logratio transformation -- sparseness; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X14535525
• Languages: English
• ISSNs: 1471-082X

Abstract

Compositional data analysis deals with situations where the relevant information is contained only in the ratios between the measured variables, and not in the reported values. This article focuses on high-dimensional compositional data (in the sense of hundreds or even thousands of variables), as they appear in chemometrics (e.g., mass spectral data), proteomics or genomics. The goal of this contribution is to perform a dimension reduction of such data, where the new directions should allow for interpretability. An approach named principal balances turned out to be successful for low dimensions. Here, the concept of sparse principal component analysis is proposed for constructing principal directions, the so-called sparse principal balances. They are sparse (contain many zeros), build an orthonormal basis in the sample space of the compositional data, are efficient for dimension reduction and are applicable to high-dimensional data.