Amalgams: data-driven amalgamation for the reference-free dimensionality reduction of zero-laden compositional data

In the health sciences, many data sets produced by next-generation sequencing (NGS) only contain relative information because of biological and technical factors that limit the total number of nucleotides observed for a given sample. As mutually dependent elements, it is not possible to interpret any component in isolation, at least without normalization. The field of compositional data analysis (CoDA) has emerged with alternative methods for relative data based on log-ratio transforms. However, NGS data often contain many more features than samples, and thus require creative new ways to reduce the dimensionality of the data without sacrificing interpretability. The summation of parts, called amalgamation, is a practical way of reducing dimensionality, but can introduce a non-linear distortion to the data. We exploit this non-linearity to propose a powerful yet interpretable dimension reduction method. In this report, we present data-driven amalgamation as a new method and conceptual framework for reducing the dimensionality of compositional data. Unlike expert-driven amalgamation which requires prior domain knowledge, our data-driven amalgamation method uses a genetic algorithm to answer the question, "What is the best way to amalgamate the data to achieve the user-defined objective?". We present a user-friendly R package, called amalgam, that can quickly find the optimal amalgamation to (a) preserve the distance between samples, or (b) classify samples as diseased or not. Our benchmark on 13 real data sets confirm that these amalgamations compete with the state-of-the-art unsupervised and supervised dimension reduction methods in terms of performance, but result in new variables that are much easier to understand: they are groups of features added together.