Simplex-structured matrix factorisation: application of soft clustering to metabolomic data.

Metabolomics is the measurement of metabolites in biological samples to reveal information on metabolic pathways and phenotypes. Cluster analysis is a popular multivariate technique employed in metabolomics to characterise observations with similar features. Previous work in the field has applied hard clustering approaches to group observations into distinct clusters. This approach can be overly restrictive in some practical applications. Therefore, there is a growing need for soft clustering methods that allow for the clustering of observations into more than one cluster. Simplex-structured matrix factorisation (SSMF) is proposed and applied in a simulation study and to a metabolomic dataset to demonstrate its utility for soft clustering. In the simulation study, the cluster prototypes and cluster memberships were well estimated. In the real data application to metabolomic data, the presence of four soft clusters was suggested by the gap statistic. Furthermore, the Shannon diversity index indicated that several observations have memberships in three clusters. Additionally, the introduction of the covariates sex, age and BMI revealed that sex and age mainly associated with the cluster memberships. The results indicate that a majority of men and young people were in the cluster predominantly characterised by high levels of amino acids and low levels of phosphatidylcholines and sphingomyelins. However, a high proportion of older people were characterised by low levels of amino acids, biogenic amines, acylcarnitines and lysophosphatidylcholines. The SSMF presented successfully estimates a soft clustering of the metabolomic data. It provides an interpretable representation of the data structure using the cluster prototypes combined with cluster memberships. A software package called MetabolSSMF has been developed, which is freely available as an R package, to facilitate the implementation of soft clustering in the field of metabolomics.