Identification of similar and dissimilar spectra is an important part of analyzing X-ray photoelectron spectroscopy (XPS) images. Cluster analysis (CA) is a commonly used exploratory data analysis (EDA) method that groups similar spectra in a data set. CA can be performed in either an agglomerative fashion, for example, using Ward's method, which involves successively linking together/clustering the most similar spectra in a data set, or in a divisive fashion, for example, using the K-means approach, which involves partitioning all the data into a specified number of clusters. In this note, we show the application of CA to an XPS image dataset. The use of Ward's method identified two major clusters in the image, where one of the clusters appeared as two subclusters. The K-means image based on two clusters agrees well with previous analyses of the same image. The average spectra corresponding to clusters helped confirm the assignments made by the CA algorithms, as did a multivariate curve resolution (MCR) analysis of the interior region identified in our cluster analysis. “Elbow” plots can help determine the number of clusters to keep in K-means clustering. The combination of the agglomerative and divisive forms of CA, where the first informs the second, can be effective in revealing the structures of XPS image datasets. The Procrustean bed is a metaphor for overfitting and underfitting in EDA.

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表面分析洞察笔记：X 射线光电子能谱图像光谱聚类分析示例

相似和不相似光谱的识别是分析 X 射线光电子能谱 (XPS) 图像的重要组成部分。聚类分析 (CA) 是一种常用的探索性数据分析 (EDA) 方法，它将数据集中的相似光谱进行分组。CA 可以以凝聚方式（例如，使用 Ward 方法）执行，该方法涉及将数据集中最相似的光谱连续链接在一起/聚类，也可以以分裂方式（例如，使用 K 均值方法）执行，其中涉及将所有数据划分为指定数量的簇。在本文中，我们展示了 CA 在 XPS 图像数据集上的应用。使用沃德方法识别出图像中的两个主要簇，其中一个簇显示为两个子簇。基于两个聚类的 K 均值图像与之前对同一图像的分析非常吻合。与簇相对应的平均光谱有助于确认 CA 算法所做的分配，就像我们的簇分析中识别的内部区域的多元曲线分辨率 (MCR) 分析一样。“肘部”图可以帮助确定 K 均值聚类中要保留的聚类数量。CA 的凝聚形式和分裂形式的组合（前者通知后者）可以有效地揭示 XPS 图像数据集的结构。Procrustean 床是 EDA 中过拟合和欠拟合的隐喻。