Extending compositional data analysis from a graph signal processing perspective
本文将成分数据分析与图信号处理联系起来，扩展了Aitchison几何，使其只考虑特定变量间的对数比，保留了尺度不变性和成分一致性，并通过生物信息学实例展示其用途。
Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is known that a relationship only exists between very specific variables (e.g. for metabolomic pathways), while for other pairs a relationship does not exist. Modeling absence or presence of relationships is done in graph theory, where the vertices represent the variables, and the connections refer to relations. This paper links compositional data analysis with graph signal processing, and it extends the Aitchison geometry to a setting where only selected log-ratios can be considered. The presented framework retains the desirable properties of scale invariance and compositional coherence. A real data example from bioinformatics underlines the usefulness of this approach.