Testing for Multivariate Normality in Mass Spectrometry Imaging Data: A Robust Statistical Approach for Clustering Evaluation and the Generation of Synthetic Mass Spectrometry Imaging Data Sets

Spatial clustering is a powerful tool in mass spectrometry imaging (MSI) and has been demonstrated to be capable of differentiating tumor types, visualizing intratumor heterogeneity, and segmenting anatomical structures. Several clustering methods have been applied to mass spectrometry imaging data, but a principled comparison and evaluation of different clustering techniques presents a significant challenge. We propose that testing whether the data has a multivariate normal distribution within clusters can be used to evaluate the performance when using algorithms that assume normality in the data, such as k-means clustering. In cases where clustering has been performed using the cosine distance, conversion of the data to polar coordinates prior to normality testing should be performed to ensure normality is tested in the correct coordinate system. In addition to these evaluations of internal consistency, we demonstrate that the multivariate normal distribution can then be used as a basis for statistical ...