Principal Components Analysis
Principal components analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data’s variation. Instead of investigating thousands of original variables, the first few components containing the majority of the data’s variation are explored. The visualization and statistical analysis of these new variables, the principal components, can help to find similarities and differences between samples. Important original variables that are the major contributors to the first few components can be discovered as well.
This chapter seeks to deliver a conceptual understanding of PCA as well as a mathematical description. We describe how PCA can be used to analyze different datasets, and we include practical code examples. Possible shortcomings of the methodology and ways to overcome these problems are also discussed.
Key wordsPrincipal components analysis Multivariate data analysis Metabolite profiling Codon usage Dimensionality reduction
- 15.Kriegel HP, Kröger P, Schubert E, Zimek A (2008) A general framework for increasing the robustness of PCA-based correlation clustering algorithms. In: Ludäscher B, Mamoulis N (eds) Scientific and statistical database management. Springer, BerlinGoogle Scholar
- 16.Todorov V, Filzmoser P (2009) An object-oriented framework for robust multivariate analysis. J Stat Softw 32:1–47Google Scholar
- 20.Baek K, Draper BA, Beveridge JR, She K (2002) PCA vs. ICA: a comparison on the feret data set. In Proc of the 4th Intern Conf on Computer Vision, ICCV 20190, pp 824–827Google Scholar
- 22.Marchini JL, Heaton C, Ripley BD (2009) fastICA: FastICA algorithms to perform ica and projection pursuit. http://cran.r-project.org/web/packages/fastICA
- 26.Hotelling H (1936) Relations between two sets of variates. Biometrika 28:321–377Google Scholar
- 27.de Leeuw J, Mair P (2009) Simple and canonical correspondence analysis using the R package anacor. J Stat Softw 31:1–18Google Scholar