Surface analysis insight note: An example of a cluster analysis of spectra from an X-ray photoelectron spectroscopy image

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.