Evaluation of Distance Metrics and Spatial Autocorrelation in Uniform Manifold Approximation and Projection Applied to Mass Spectrometry Imaging Data

In this work, uniform manifold approximation and projection (UMAP) is applied for nonlinear dimensionality reduction and visualization of mass spectrometry imaging (MSI) data. We evaluate the performance of the UMAP algorithm on MSI data sets acquired in mouse pancreas and human lymphoma samples and compare it to those of principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE), and the Barnes-Hut (BH) approximation of t-SNE. Furthermore, we compare different distance metrics in (BH) t-SNE and UMAP and propose the use of spatial autocorrelation as a means of comparing the resulting low-dimensional embeddings. The results indicate that UMAP is competitive with t-SNE in terms of visualization and is well-suited for the dimensionality reduction of large (>100 000 pixels) MSI data sets. With an almost fourfold decrease in runtime, it is more scalable in comparison with the current state-of-the-art: t-SNE or the Barnes-Hut approximation of t-SNE. In what seems to be the first application of UMAP to MSI data, we assess the value of applying alternative distance metrics, such as the correlation, cosine, and the Chebyshev metric, in contrast to the traditionally used Euclidean distance metric. Furthermore, we propose "histomatch" as an additional custom distance metric for the analysis of MSI data.