Self-Organizing Map and Relational Perspective Mapping for the Accurate Visualization of High-Dimensional Hyperspectral Data

Abstract

We present an optimization of the toroidal self-organizing map (SOM) algorithm for the accurate visualization of hyperspectral data. This represents a significant advancement on our previous work, in which we demonstrated the use of toroidal SOMs for the visualization of time-of-flight secondary ion mass spectrometry (ToF-SIMS) imaging data. We have previously shown that the toroidal SOM can be used, unsupervised, to produce a multicolor similarity map of the analysis area, in which pixels with similar mass spectra are assigned a similar color. Here, we use an additional algorithm, relational perspective mapping (RPM), to produce more accurate visualizations of hyperspectral data. The SOM output is used as an input for the RPM algorithm, which is a nonlinear dimensionality reduction technique designed to produce a two-dimensional map of high-dimensional data. Using the topological information provided by the SOM, RPM provides complementary distance information. The result is a color scheme that more accurately reflects the local spectral distances between pixels in the data. We exemplify SOM-RPM using ToF-SIMS imaging data from a mouse tumor tissue section. The similarity maps produced are compared with those produced by two leading hyperspectral visualization techniques in the field of mass spectrometry imaging: t-distributed stochastic neighborhood embedding (t-SNE) and uniform manifold approximation and projection (UMAP). We evaluate the performance of each technique both qualitatively and quantitatively, investigating the correlations between distances in the models and distances in the data. SOM-RPM is demonstrably highly competitive with t-SNE and UMAP, according to our evaluations. Furthermore, the use of a neural network offers distinct advantages in data characterization, which we discuss. We also show how spectra extracted from regions of interest identified by SOM-RPM can be further analyzed using linear discriminant analysis for the validation and characterization of the surface chemistry.

Understanding mass spectrometry images: complexity to clarity with machine learning

“…Pixels in the original image are then assigned the color of their winning neuron to produce the similarity map. Some content adapted with permission from Gardner et al, [14] Figure 5. Copyright 2020 American Chemical Society F I G U R E 2 Analysis of a MALDI rat brain imaging data set using manual, PCA and various machine learning approaches.…”

“…Recently, we adjusted the RPM algorithm such that force calculations are performed on the surface of a 3D toroid, rather than a 2D plane with continuous boundaries. [14] We then applied the modified RPM to the output of a toroidal SOM, using their weights for the distance calculations. In short, this allows the neurons to be colored according to their relative distances in high-dimensional space, producing a more accurate similarity map.…”

“…This methodology and the modified RPM algorithm are discussed in depth in our recent work. [14] We compared the SOM-RPM similarity maps with those produced by t-SNE and UMAP, using ToF-SIMS images of a mouse model of breast cancer tumor cryosection (Figure 13). [14] Based on the suggestion of using alternate distance metrics by Smets et al, [49] we also compared Euclidean and Cosine distance metrics.…”

“…[14] We compared the SOM-RPM similarity maps with those produced by t-SNE and UMAP, using ToF-SIMS images of a mouse model of breast cancer tumor cryosection (Figure 13). [14] Based on the suggestion of using alternate distance metrics by Smets et al, [49] we also compared Euclidean and Cosine distance metrics. Rather than relying on a subjective comparison of the three techniques, which tended to identify similar features in the data, we suggested an objective measure of how well the similarity maps captured the distance information in the data (Figure 13B).…”

“…Perhaps most notable of the latter has been the application of non-linear machine and deep learning methods to MSI data. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] These methods have become crucial tools in enabling a deeper and more objective understanding of MSI data, while also reducing experimenter bias and allowing more robust data processing workflows.…”