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

Abstract

This paper addresses the problem of determining the number of pure chemical components in a mixture by applying the maximum likelihood estimator (MLE) of intrinsic dimension. The application 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 chemical mixtures, and is accurate even when minor 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 can be used for other applications, such as segmenting the specimen into homogeneous regions. Copyright © 2007 John Wiley & Sons, Ltd.