One-Dimensional Cluster Analysis and its Application to Chemistry

Clustering of data is often observed in spectroscopy. The notion of clustering is made mathematically rigorous by first fixing the number of clusters, defining the cluster average, and then minimizing the sum of squared deviations between the data and the cluster average to calculate the error. By analyzing some model data, criteria for identifying the best number of clusters to use are identified that correspond to intuitive notions. These are then applied to the proton NMR spectra of ethyl ethanoate, the IR spectrum of carbon dioxide, and the microwave spectra of CsI, CsBr, RbI, RbBr, and KI. For the NMR and IR spectra presented, the primary features are identified. For the microwave spectra presented, the cluster analysis (usually) allows for assignment of the rotational and vibrational quantum numbers of the transitions, to separate isotopologues, and to identify a putative printing error.