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.

中文翻译：

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自组织图和关系透视图可用于高维高光谱数据的精确可视化。

我们提出了一种环形自组织图（SOM）算法的优化，用于高光谱数据的精确可视化。这代表了我们先前工作的重大进步，其中我们展示了使用环形SOM来可视化飞行时间二次离子质谱（ToF-SIMS）成像数据。先前我们已经表明，可以在无监督的情况下使用环形SOM来生成分析区域的多色相似图，在该图中，具有相似质谱的像素被分配相似的颜色。在这里，我们使用一种附加的算法，即关系透视映射（RPM），以产生更准确的高光谱数据可视化效果。SOM输出用作RPM算法的输入，这是一种非线性降维技术，旨在产生高维数据的二维图。使用SOM提供的拓扑信息，RPM提供补充的距离信息。结果是一种配色方案，可以更准确地反映数据中像素之间的局部光谱距离。我们使用来自小鼠肿瘤组织切片的ToF-SIMS成像数据来举例说明SOM-RPM。将产生的相似度图与质谱成像领域中两种领先的高光谱可视化技术产生的相似度图进行比较：t分布随机邻域嵌入（t-SNE）和均匀流形逼近和投影（UMAP）。我们定性和定量地评估每种技术的性能，调查模型中的距离与数据中的距离之间的相关性。根据我们的评估，SOM-RPM与t-SNE和UMAP相比具有明显的竞争力。此外，神经网络的使用在数据表征方面提供了明显的优势，我们将对此进行讨论。我们还展示了如何使用线性判别分析进一步分析从SOM-RPM识别的感兴趣区域提取的光谱，以验证和表征表面化学性质。