Decomposition of Data Matrices by Factors

Wolfgang Karl Härdle and Zdeněk Hlávka
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Wolfgang Karl Härdle: Humboldt-Universität zu Berlin, C.A.S.E. Centre f. Appl. Stat. & Econ. School of Business and Economics
Zdeněk Hlávka: Charles University in Prague, Faculty of Mathematics and Physics Department of Statistics

Chapter Chapter 10 in Multivariate Statistics, 2015, pp 167-181 from Springer

Abstract: Abstract In this chapter, we take a descriptive perspective and show how using a geometrical approach can be a good way to reduce the dimension of a data matrix. We derive the interesting projections with respect to a least-squares criterion. The results will be low-dimensional graphical pictures of the data matrix. This involves the decomposition of the data matrix into factors. These factors will be sorted in decreasing order of importance. The approach is very general and is the core idea of many multivariate techniques. We deliberately use the word “factor” here as a tool or transformation for structural interpretation in an exploratory analysis. Factor

Keywords: Singular Value Decomposition; Data Matrix; Factorial Variable; Spectral Decomposition; Professional Activity (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-36005-3_10

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DOI: 10.1007/978-3-642-36005-3_10

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