A generalized expression for the similarity of spectra: application to powder diffraction pattern classification

A generalized expression is given for the similarity of spectra, based on the normalized integral of a weighted crosscorrelation function. It is shown that various similarity and dissimilarity criteria previously described in literature can be written as special cases of this general expression. A new similarity criterion, based on this generalized expression, is introduced. The benefits of this criterion are that it properly recognizes shifted but otherwise similar details in spectra and that the resulting similarity measure is normalized. Moreover, the criterion can easily be adapted to specific properties of spectra resulting from various analytical methods. The new criterion is applied to the classification of a series of crystal structures of cephalosporin complexes, based on comparison of their calculated powder diffraction patterns. The results are compared with those obtained using previously described criteria. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 273–289, 2001