Testing for Multivariate Normality in Mass Spectrometry Imaging Data: A Robust Statistical Approach for Clustering...

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 modeling of MSI data. This allows the generation of synthetic MSI data sets with known ground truth, providing a means of external clustering evaluation. To demonstrate this, reference data from seven anatomical regions of an MSI image of a coronal section of mouse brain were modeled. From this, a set of synthetic data based on this model was generated. Results of r² fitting of the chi-squared quantile-quantile plots on the seven anatomical regions confirmed that the data acquired from each spatial region was found to be closer to normally distributed in polar space than in Euclidean. Finally, principal component analysis was applied to a single data set that included synthetic and real data. No significant differences were found between the two data types, indicating the suitability of these methods for generating realistic synthetic data.