Fast and simple methods for the optimization of kurtosis used as a projection pursuit index.

As a powerful method for exploratory data analysis, projection pursuit (PP) often outperforms principal component analysis (PCA) to discover important data structure. PP was proposed in 1970s but has not been widely used in chemistry largely because of the difficulty in the optimization of projection indices. In this work, new algorithms, referred as "quasi-power methods", are proposed to optimize kurtosis as a projection index. The new algorithms are simple, fast, and stable, which makes the search for the global optimum more efficient in the presence of multiple local optima. Maximization of kurtosis is helpful in the detection of outliers, while minimization tends to reveal clusters in the data, so the ability to search separately for the maximum and minimum of kurtosis is desirable. The proposed algorithms can search for either with only minor changes. Unlike other methods, no optimization of step size is required and sphering or whitening of the data is not necessary. Both univariate and multivariate kurtosis can be optimized by the proposed algorithms. The performance of the algorithms is evaluated using three simulated data sets and its utility is demonstrated with three experimental data sets relevant to analytical chemistry.

Interpretation of analysis of variance models using principal component analysis to assess the effect of a maternal anticancer treatment on the mineralization of rat bones.

The goal of the present study is to assess the effects of anticancer treatment with cyclophosphamide and cytarabine during pregnancy on the mineralization of mandible bones in 7-, 14- and 28-day-old rats. Each bone sample was described by its X-ray fluorescence spectrum characterizing the mineral composition. The data collected are multivariate in nature and their structure is difficult to visualize and interpret directly. Therefore, methods like analysis of variance-principal component analysis (ANOVA-PCA) and ANOVA-simultaneous component analysis (ASCA), which are suitable for the analysis of highly correlated spectral data and are able to incorporate information about the underlined experimental design, are greatly valued. In this study, the ASCA methodology adapted for unbalanced data was used to investigate the impact of the anticancer drug treatment during pregnancy on the mineralization of the mandible bones of newborn rats and to examine any changes in the mineralization of the bones over time. The results showed that treatment with cyclophosphamide and cytarabine during pregnancy induces a decrease in the K and Zn levels in the mandible bones of newborns. This suppresses the development of mandible bones in rats in the early stages (up to 14 days) of formation. An interesting observation was that the levels of essential minerals like K, Mg, Na and Ca vary considerably in the different regions of the mandible bones.

Three-way analysis of fluorescence spectra of polycyclic aromatic hydrocarbons with quenching by nitromethane.

The application of trilinear decomposition (TLD) to the analysis of fluorescence excitation-emission matrices of mixtures of polycyclic aromatic hydrocarbons (PAHs) is described. The variables constituting the third-order tensor are excitation wavelength, emission wavelength, and concentration of a fluorescence quencher (nitromethane). The addition of a quencher to PAH mixtures selectively reduces the fluorescence intensity of mixture components according to the Stern-Volmer equation. TLD allows the three-way matrix to be decomposed to give unique solutions for the excitation spectrum, emission spectrum, and quenching profiles for each component. The availability of spectra and calculated Stern-Volmer constants can aid in the identification of unknown components. Preprocessing of the data to correct for Rayleigh/Raman scatter and primary absorption by the quencher is necessary. Both three-component (anthracene, pyrene, 1-methylpyrene) and four-component (fluoranthene, anthracene, pyrene, 2,3-benzofluorene) synthetic mixtures are successfully resolved by TLD using quencher concentrations up to 100 mM. Results are compared using both alternating least-squares and direct trilinear decomposition algorithms. The reproducibility of extracted Stern-Volmer constants is determined from replicate experiments. To illustrate the application of TLD to a real sample, a chromatographic cut from the analysis of a light gas oil sample was used. Analysis of the TLD extracted spectra and quenching constants suggests the presence of three classes of polycyclic aromatic hydrocarbons consistent with data from a second dimension of chromatography and mass spectrometry.

Maximum likelihood multivariate calibration.

Two new approaches to multivariate calibration are described that, for the first time, allow information on measurement uncertainties to be included in the calibration process in a statistically meaningful way. The new methods, referred to as maximum likelihood principal components regression (MLPCR) and maximum likelihood latent root regression (MLLRR), are based on principles of maximum likelihood parameter estimation. MLPCR and MLLRR are generalizations of principal components regression (PCR), which has been widely used in chemistry, and latent root regression (LRR), which has been virtually ignored in this field. Both of the new methods are based on decomposition of the calibration data matrix by maximum likelihood principal component analysis (MLPCA), which has been recently described (Wentzell, P. D.; et al. J. Chemom., in press). By using estimates of the measurement error variance, MLPCR and MLLRR are able to extract the optimum amount of information from each measurement and, thereby, exhibit superior performance over conventional multivariate calibration methods such as PCR and partial least-squares regression (PLS) when there is a nonuniform error structure. The new techniques reduce to PCR and LRR when assumptions of uniform noise are valid. Comparisons of MLPCR, MLLRR, PCR, and PLS are carried out using simulated and experimental data sets consisting of three-component mixtures. In all cases of nonuniform errors examined, the predictive ability of the maximum likelihood methods is superior to that of PCR and PLS, with PLS performing somewhat better than PCR. MLLRR generally performed better than MLPCR, but in most cases the improvement was marginal. The differences between PCR and MLPCR are elucidated by examining the multivariate sensitivity of the two methods.

Acoustic flame detector for gas chromatography.

A novel gas chromatography detector is described that uses acoustic signals from a partly premixed hydrogen-air flame burning on top of a capillary. The device, referred to as the acoustic flame detector (AFD), is based on the measurement of the frequency of acoustic transients generated at the burner under a range of operating conditions. The presence of trace amounts of analyte in the flame was found to increase the frequency of these sonic bursts from the baseline level of ∼100 Hz. The response of the AFD for n-dodecane, measured as the shift in frequency, was determined to be linear over ∼3 orders of magnitude, with a minimum detectable level of about 1-5 ng C/s using the current system. The sensitivity correlates roughly with carbon content, except for certain organometallics (Sn, Mn), which gave substantially enhanced signals. Some tailing was observed but became serious only for particular types of organometallics. The noise of the system was predominantly of the 1/f type. The effects of flow conditions, burner geometry, and flame gas constituents were investigated. The oscillations could be followed by acoustic, visual, electrical, and optical means. The AFD mechanism is shown to involve oscillatory chemical kinetics, in which the flame front (the inner cone) temporarily enters a few millimeters into the capillary during each cycle, thereby creating the acoustic signal.

Evolving projection analysis of multicomponent mixtures.

The application of evolving projection analysis (EPA) to second-order bilinear data sets consisting of more than two components is described. EPA is a method for rank analysis of ordered data matrices where the components appear sequentially as a function of time or some other ordinal variable. It was found that extension of the method to mixtures of more than two components was best accomplished using principal components analysis to preprocess the data. The algorithm is demonstrated using simulated four-component chromatographic data, and experimental data from liquid chromatography (three- and four-component mixtures) and a spectrophotometric titration (four components), both employing UV-visible diode array detection.

Spectrophotometric determination of palladium with sulfochlorophenolazorhodanine by flow injection.

Sulfochlorophenolazorhodanine (as its sodium salt) has been used in the automated development of a sensitive flow-injection procedure for the spectrophotometric determination of palladium. The resulting method has high sample throughput, good precision, and low consumption of both sample and reagents. The optimum pH for the reaction is 5.0 and the response is constant at pH between 4.7 and 5.3. The sensitivity (calibration slope) of the procedure is 4.4 x 10(3) l./mole. The linear dynamic range is 0.045-30.0 mug/ml. The sample throughput is at least 120/hr. An automated procedure for optimization of analytical variables is described and a two-variable response surface for the system is given. Interference studies on 19 metal ions show that the method has good selectivity.

Computer-controlled apparatus for automated development of continuous flow methods.

An automated apparatus to assist in the development of analytical continuous flow methods is described. The system is capable of controlling and monitoring a variety of pumps, valves, and detectors through an IBM PC-AT compatible computer. System components consist of two types of peristaltic pumps (including a multiple pump unit), syringe pumps, electrically and pneumatically actuated valves, and an assortment of spectrophotometric and electrochemical detectors. Details of the interface circuitry are given where appropriate. To demonstrate the utility of the system, an automatically generated response surface is presented for the flow injection determination of iron(II) by its reaction with 1,10-phenanthroline.