Dimensionality Reduction and Visualization in Principal Component Analysis

Abstract

Many modern applications of analytical chemistry involve the collection of large megavariate data sets and subsequent processing with multivariate analysis techniques (MVA), two of the more common goals being data analysis (also known as data mining and exploratory data analysis) and classification. Classification attempts to determine variables that can distinguish known classes allowing unknown samples to be correctly assigned, whereas data analysis seeks to uncover and understand or confirm relationships between the samples and the variables. An important part of analysis is visualization which allows analysts to apply their expertise and knowledge and is often easier for the samples than the variables since there are frequently far more of the latter. Here we describe principal component variable grouping (PCVG), an unsupervised, intuitive method that assigns a large number of variables to a smaller number of groups that can be more readily visualized and understood. Knowledge of the source or nature of the variables in a group allows them all to be appropriately treated, for example, removed if they result from uninteresting effects or replaced by a single representative for further processing.