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Chromatographic Fingerprints o/Twenty Salvia Species 515

performance liquid chromatography (HPLC), the second by use of head-space gas chromatography with mass spectrometric detection (HS-GS-MS). It is reveaied that - depending on the quality of the fingerprints - they may require different preprocessing (e.g., baseiine correction, denoising, signal alignment, etc.). For preprocessing and comparative analysis, the optimum set of chemometric approaches was selected and used.

Theory

In this section, we provide a short description of methods suitable for preprocessing and comparative analysis of chromatographic fingerprints. Fingerprints usually require background and noise removal, and peak alignment before comparative analysis.

Background Eliminadon

Many different approaches can be used to remove the background compo-nent from analytical signals; these include the penaiized asymmetric least-squares, PALS, approach proposed by Eilers [16]. It is an iterative procedurę, in which a signal baseiine, b, is fitted to the signal, x, in a least-squares sense. The key assumption is that each point of a signal has a different weight. In the course of procedurę, these weights are modified so that the points above an approximated baseiine receive very smali weights, and otherwise the weights are close to 1. The objective function, Q, minimized during the iterative procedurę, can be expressed as:

Q = Ż^wi(^xi -bj)² + x(A^dt>i)²    (1)

i=l

where w\ are weights, A is the so-called penalty term, d denotes the order of differences A, and n is the number of sampling points in a signal.

Two input quantities should be optimized - the order of differences and the penalty term. In most applications satisfactory baseiine approxima-tions are obtained when d = 2. The penalty term, which weighs the second term of eq. (1), is intended to control the smoothness of the signal baseiine. The larger the values of A, the smoother the baseiine obtained.