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A new algorithm for self-modeling curve resolution (SMCR) that yields improved results by incorporating soft constraints is described. The method uses least squares penalty functions to implement constraints in an alternating least squares algorithm, including nonnegativity, unimodality, equality, and closure constraints. By using least squares penalty functions, soft constraints are formulated rather than hard constraints. Significant benefits are (obtained using soft constraints, especially in the form of fewer distortions due to noise in resolved profiles. Soft equality constraints can also be used to introduce incomplete or partial reference information into SMCR solutions. Four different examples demonstrating application of the new method are presented, including resolution of overlapped HPLC-DAD peaks, flow injection analysis data, and batch reaction data measured by UV/visible and near-infrared spectroscopy (NIR). Each example was selected to show one aspect of the significant advantages of soft constraints over traditionally used hard constraints. Incomplete or partial reference information into self-modeling curve resolution models is described. The method offers a substantial improvement in the ability to resolve time-dependent concentration profiles from mixture spectra recorded as a function of time.

26) Shaka, A. J.; Keeler, J.; Frenklel, T.; Freeman, R. J. Magn. Res. (27) Guiilou, C.; Trlerweiler, M.; Martin, G. J. Mgn. Reson. Chem. 1988, (28) Martln, 0. J.; Naulet, N. Fresenlus' 2. Anal. Chem. 1988. 332, (29) Craig, H. Geochlm. Cos". Acta 1957, 12, 133-149. (30) Rauschenbach, P.; Simon, H.; Stichler, W.; Moser, H. Z. Mturforsch. (31) Misselhorn, K.; Bruckner, H.; MussigZuflka, M.; Grafahrend, W. 1990, 94. 8303-8309.ThkmMlecrlptdescdbwmethodsfor detecting and modeling nonlinear regions of spectral response In multivariate, multicomponent spectroscopic assays. Slmuiated data and ex-parimenta1 UV/vklble data were used to 8tudy the capablilty of multivariate Ilnear models to approximate nonlinear response. Tho sources of real and apparent noniinearlty dmulated Included nonilnear Instrument response functions (e.g. dray light), concentrationdependent wavelength shifts, and concentratlon dependent absorption bandwidth changes. A weighting algorithm was devised to reduce the Influence of nonlnear spectral reglons in principal component regresdon (PCR) caiibratlons, thereby improvlng the performance of muitivariate linear calibration models. Secondorder caiibrat h methods using quadratic principal component scores and nonilnear calibration methods using artlficlal neural networks were compared to unwelghted and welghted i h a r callbration methods. Orthogonal transformation of the input variables was used to dgnlficantly improve neural network trainlng speed and reduce callbration error. Some conditions where wc-r and nonitnear calibration techniques outperform Ilnear callbration techniques have been ldentlfled and are dercribod.

Self-modeling curve resolution (SMCR) describes a set of mathematical tools for estimating pure-component spectra and composition profiles from mixture spectra. The source of mixture spectra may be overlapped chromatography peaks, composition profiles from equilibrium studies, kinetic profiles from chemical reactions and batch industrial processes, depth profiles of treated surfaces, and many other types of materials and processes. Mathematical solutions are produced under the assumption that pure-component profiles and spectra should be nonnegative and composition profiles should be unimodal. In many cases, SMCR may be the only method available for resolving the composition profiles and pure-component spectra from these measurements. Under ideal circumstances, the SMCR results are accurate quantitative estimates of the true underlying profiles. Although SMCR tools are finding wider use, it is not widely known or appreciated that, in most circumstances, SMCR techniques produce a family of solutions that obey nonnegativity constraints. In this paper, we present a new method for computation of the range of feasible solutions and use it to study the effect of chromatographic resolution, peak height, spectral dissimilarity, and signal-to-noise ratios on the magnitude of feasible solutions. An illustration of its use in resolving composition profiles from a batch reaction is also given.

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SUMMARYOne of the major applications of factor analysis in the chemical literature, self-modeling curve resolution (SMCR), is covered in this review, including a historical account of the methods derived from Lawton and Sylvestre's original method. Papers treating the theory or applications of SMCR are included. Qualitative and quantitative applications are described where appropriate.

A method for testing raw materials has been developed by using S1MCA (soft Independent modeling of class analogy) analysis of near-infrared reflectance spectra. Samples are classified as acceptable or unacceptable based on probability levels obtained from an F test. Over 400 first derivative spectra of six types of pharmaceutical raw materials were tested. The method had an overall recognition rate of 95 % for acceptable samples and a 99 % rejection rate for unacceptable samples. The single unacceptable sample classified Incorrectly differed from the "tralnlng,' samples only In particle size distribution. Minor levels (ca. 1 %) of contaminates were detected. Materials rejected during the manufacturing process by manual testing were detected. Subclustering with respect to suppliers was Investigated. Sources of variation In the spectra were analyzed, including short-term and longterm Instrumental variation, variation due to cell repacking, and variation between production lots.