Multivariate Projection Techniques to Reduce Dimensionality in Large Datasets

Abstract

In this chapter, we review multivariate projection methods that can be used to reduce dimensionality when dealing with high-dimensional datasets. The methods we consider are Principal Component Analysis, Singular Value Decomposition, Correspondence Analysis, and Canonical Correlation Analysis. It is shown that these methods allow us to reduce dimensionality in an efficient way, to plot samples and variables in order to discover the underlying relationships, and to obtain descriptive and exploratory summaries when dealing with a large number of variables (possibly highly correlated) and few samples. The use of these techniques is illustrated with real applications to omic datasets.