Two Novel Methods For The Determination Of The Number Of Components In Independent Components Analysis Models

Independent Components Analysis is a Blind Source Separation method that aims to find the pure source signals mixed together in unknown proportions in the observed signals under study. It does this by searching for factors which are mutually statistically independent. It can thus be classified among the latent-variable based methods. Like other methods based on latent variables, a careful investigation has to be carried out to find out which factors are significant and which are not. Therefore, it is important to dispose of a validation procedure to decide on the optimal number of independent components to include in the final model. This can be made complicated by the fact that two consecutive models may differ in the order and signs of similarly-indexed ICs. As well, the structure of the extracted sources can change as a function of the number of factors calculated. Two methods for determining the optimal number of ICs are proposed in this article and applied to simulated and real datasets to demonstrate their performance

Genetic algorithms (GA) applied to the orthogonal projection approach (OPA) for variable selection

Multivariate curve resolution (MCR) and especially the orthogonal projection approach (OPA) can be applied to spectroscopic data and were proved to be suitable for process monitoring. To improve the quality of the on-line monitoring of batch processes, it is interesting to get as many as possible spectra in a given period of time. Nevertheless, hardware limitations could lead to the fact that it is not possible to acquire more than a certain number of spectra in this given period of time. Wavelength selection could be a good way to limit this problem since it decreases size, and consequently the acquisition time, of each recorded spectrum. This paper details an industrial application of genetic algorithms (GA) coupled with a curve resolution method (OPA) for such purpose.</p

Determination of the number of components during mixture analysis using the Durbin-Watson criterion in the Orthogonal Projection Approach and in the SIMPLe-to-use Interactive Self-modelling Mixture Analysis approach

The Orthogonal Projection Approach (OPA) and the SIMPLe-to-use Interactive Self-modelling Mixture Analysis approach (SIMPLISMA) are widely employed during process monitoring to obtain concentration profiles and/or pure spectra of a mixture. In the first step of these methods, it is extremely important to select the right number of components present in the mixture. This selection is not always obvious, and in this paper, the Durbin-Watson criterion was applied to dissimilarity values in OPA and to purity values in SIMPLISMA as a tool for the decision of the number of components. It is shown that this yields more objective results than visual interpretation.</p

Use of the orthogonal projection approach (OPA) to monitor batch processes

The orthogonal projection approach (OPA) and multivariate curve resolution (MCR) are presented as a way to monitor batch processes using spectroscopic data. Curve resolution allows one to look within a batch and predict on-line real concentration profiles of the different species appearing during reactions. Taking into account the variations of the process by using an augmented matrix of complete batches, the procedure explained here calculates some prediction coefficients that can afterwards be applied for a new batch.</p

Causal and Interpretable Rules for Time Series Analysis

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Determining orthogonal and similar chromatographic systems from the injection of mixtures in liquid chromatography-diode array detection and the interpretation of correlation coefficients color maps

Generic orthogonal chromatographic systems might be helpful tools as potential starting points in the development of methods to separate impurities and the active substance in drugs with unknown impurity profiles. The orthogonality of 38 chromatographic systems was evaluated from weighted-average-linkage dendrograms and color maps, both based on the correlation coefficients between the retention factors on the different systems. On each chromatographic system, 68 drug substances were injected as mixtures of three or four components to increase the throughput. The (overlapping) peaks were identified and resolved with a peak purity algorithm, orthogonal projection approach (OPA). The visualization techniques applied allowed a simple evaluation of orthogonal and (groups of) similar systems.</p

An evaluation of the PoLiSh smoothed regression and the Monte Carlo Cross-Validation for the determination of the complexity of a PLS model

A crucial point of the PLS algorithm is the selection of the right number of factors or components (i.e., the determination of the optimal complexity of the system to avoid overfitting). The leave-one-out cross-validation is usually used to determine the optimal complexity of a PLS model, but in practice, it is found that often too many components are retained with this method. In this study, the Monte Carlo Cross-Validation (MCCV) and the PoLiSh smoothed regression are used and compared with the better known adjusted Wold's R criterion.</p