Estimating the number of pure chemical components in a mixture by maximum likelihood

This paper addresses the problem of determining the number of pure chemical components in a mixturebyapplying themaximumlikelihoodestimator (MLE)of intrinsicdimension.Theapplication here is to Raman spectroscopy data, although the method is general and can be applied to any type of data from a chemical mixture. We show that the MLE produces superior results compared to other methods on both simulated and real chemicalmixtures, and is accurate evenwhenminor components are present. Even if the signal-to-noise (SN) ratio is very low, accurate estimates can still be obtained by smoothing the data before applying the estimator, this approach is illustrated on two real datasets with high noise levels. Since the MLE is computed locally at every data point, we also show how the local estimates canbeused for other applications, such as segmenting the specimen intohomogeneous regions. Copyright© 2007 John Wiley & Sons, Ltd.