Non-negative principal component analysis for NMR-based metabolomic data analysis

a r t i c l e i n f o Keywords: Non-negative principal component analysis Local feature representation k + 1 rule NMR-based metabolomics Multivariate data analysis Proton nuclear magnetic resonance (1 H-NMR) spectroscopy is one of the major analytical platforms used in metabolomics. The data acquired from NMR experiments are frequently processed using multivariate statistical methods such as principal component analysis (PCA) and partial least squares (PLS) to extract biologically meaningful information from complex spectra. Conventionally, these methods produce components with both positive and negative loadings, which contradict with the non-negativity of Fourier-transformed NMR spectra. In recent years, there is an increasing interest in incorporating non-negative constraints into multivariate methods. In the current study, a non-negative principal component analysis (NPCA) algorithm was introduced for the analysis of NMR-based metabolomic data. Using a simulated dataset, we showed that NPCA could reveal interesting local features in multivariate dataset, which are hidden in conventional PCA model. Notably, simulated peaks arising from a single compound were extracted by a same component in NPCA model. The current results also highlighted NPCA to be less susceptible to noise as compared to PCA. Furthermore, a supervised version of NPCA (sNPCA) was developed for class discrimination analysis, and it was used to identify urinary metabolites that distinguished hyperthyroid patients from healthy volunteers. Our results demonstrated that both NPCA and sNPCA could produce easily interpretable results and provide additional information to that of conventional projection methods. Proton nuclear magnetic resonance (1 H-NMR) spectroscopy and mass spectrometry (MS) constitute the leading profiling technologies in metabolomics. In general, MS-based methods offer a higher detection sensitivity and broader coverage of metabolome. The main advantage of using NMR is due to its nondestructive nature, which requires minimal sample preparation. Throughout the years, NMR-based metabolomics has found wide applications, for example in physiological evaluation [1], drug safety assessment [2,3], characterisation of animal models of disease [4], diagnosis of disease [5], and drug therapy monitoring [6]. NMR metabolomic data is characterised by very high dimensional-ities. However, it is generally accepted that only a small set of metab-olites are important for biological interpretation. Many feature selection algorithms have been used to reduce the dimensionality of metabolomic data, including principal component analysis (PCA) [7], partial least squares (PLS), independent component analysis (ICA) [8–10], nonnegative matrix factorisation (NMF) [11], as well as their variants [12–14]. Among these methods, PCA is regarded as the de facto standard …