FFT Calculation of the L1-norm Principal Component of a Data Matrix

2021 ◽  
pp. 108286
Author(s):  
Stefania Colonnese ◽  
Panos P. Markopoulos ◽  
Gaetano Scarano ◽  
Dimitris A. Pados
Keyword(s):  
Principal Component ◽  
Data Matrix ◽  
L1 Norm

Principal component analysis of substituent constants

1990 ◽  
Vol 55 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Drahomír Hnyk
Keyword(s):  
Principal Component Analysis ◽  
Inductive Effect ◽  
Resonance Effect ◽  
Principal Component ◽  
Component Analysis ◽  
Total Variance ◽  
Data Matrix ◽  
Cumulative Proportion ◽  
Two Factors ◽  
Substituent Constants

The principal component analysis has been applied to a data matrix formed by 7 usual substituent constants for 38 substituents. Three factors are able to explain 99.4% cumulative proportion of total variance. Several rotations have been carried out for the first two factors in order to obtain their physical meaning. The first factor is related to the resonance effect, whereas the second one expresses the inductive effect, and both together describe 97.5% cumulative proportion of total variance. Their mutual orthogonality does not directly follow from the rotations carried out. With the help of these factors the substituents are divided into four main classes, and some of them assume a special position.

Development and Validation of Chemometric-Assisted Spectrophotometric Methods for Simultaneous Determination of Phenylephrine Hydrochloride and Ketorolac Tromethamine in Binary Combinations

2016 ◽  
Vol 99 (5) ◽  
pp. 1247-1251 ◽  
Author(s):  
Hamed M Elfatatry ◽  
Mokhtar M Mabrouk ◽  
Sherin F Hammad ◽  
Fotouh R Mansour ◽  
Amira H Kamal ◽  
...  
Keyword(s):  
Least Squares ◽  
Simultaneous Determination ◽  
Principal Component Regression ◽  
Principal Component ◽  
Data Matrix ◽  
Ketorolac Tromethamine ◽  
Concentration Data ◽  
Phenylephrine Hydrochloride ◽  
Spectrophotometric Methods

Abstract The present work describes new spectrophotometric methods for the simultaneous determination of phenylephrine hydrochloride and ketorolac tromethamine in their synthetic mixtures. The applied chemometric techniques are multivariate methods including classical least squares, principal component regression, and partial least squares. In these techniques, the concentration data matrix was prepared by using the synthetic mixtures containing these drugs dissolved in distilled water. The absorbance data matrix corresponding to the concentration data was obtained by measuring the absorbances at 16 wavelengths in the range 244–274 nm at 2 nm intervals in the zero-order spectra. The spectrophotometric procedures do not require any separation steps. The accuracy, precision, and linearity ranges of the methods have been determined, and analyzing synthetic mixtures containing the studied drugs has validated them. The developed methods were successfully applied to the synthetic mixtures and the results were compared to those obtained by a reported HPLC method.

scholarly journals SVD-based principal component analysis of geochemical data

2005 ◽  
Vol 3 (4) ◽  
pp. 731-741 ◽  
Author(s):  
Petr Praus
Keyword(s):  
Principal Component Analysis ◽  
Euclidean Distance ◽  
Principal Component ◽  
Component Analysis ◽  
Data Matrix ◽  
Geochemical Data ◽  
Average Group ◽  
Testing Data ◽  
Value Decomposition ◽  
Geochemical Variables

AbstractPrincipal Component Analysis (PCA) was used for the mapping of geochemical data. A testing data matrix was prepared from the chemical and physical analyses of the coals altered by thermal and oxidation effects. PCA based on Singular Value Decomposition (SVD) of the standardized (centered and scaled by the standard deviation) data matrix revealed three principal components explaining 85.2% of the variance. Combining the scatter and components weights plots with knowledge of the composition of tested samples, the coal samples were divided into seven groups depending on the degree of their oxidation and thermal alteration.The PCA findings were verified by other multivariate methods. The relationships among geochemical variables were successfully confirmed by Factor Analysis (FA). The data structure was also described by the Average Group dendrogram using Euclidean distance. The found sample clusters were not defined so clearly as in the case of PCA. It can be explained by the PCA filtration of the data noise.

scholarly journals Liquid Chromatographic and Spectrophotometric Determination of Diflucortolone Valerate and Isoconazole Nitrate in Creams

2011 ◽  
Vol 94 (1) ◽  
pp. 128-135 ◽  
Author(s):  
Elif Karacan ◽  
Mehmet Gokhan Çaġlayan ◽  
İsmail Murat Palabiyik ◽  
Feyyaz Onur
Keyword(s):  
Principal Component Regression ◽  
Principal Component ◽  
Derivative Spectrophotometry ◽  
Data Matrix ◽  
Concentration Data ◽  
Spectrophotometric Methods ◽  
First Derivative ◽  
First Derivative Spectrophotometry ◽  
Liquid Chromatographic

Abstract A new RP-LC method and two new spectrophotometric methods, principal component regression (PCR) and first derivative spectrophotometry, are proposed for simultaneous determination of diflucortolone valerate (DIF) and isoconazole nitrate (ISO) in cream formulations. An isocratic system consisting of an ACE® C18 column and a mobile phase composed of methanol–water (95+5, v/v) was used for the optimal chromatographic separation. In PCR, the concentration data matrix was prepared by using synthetic mixtures containing these drugs in methanol–water (3+1, v/v). The absorbance data matrix corresponding to the concentration data matrix was obtained by measuring the absorbances at 29 wavelengths in the range of 242–298 nm for DIF and ISO in the zero-order spectra of their combinations. In first derivative spectrophotometry, dA/dλ values were measured at 247.8 nm for DIF and at 240.2 nm for ISO in first derivative spectra of the solution of DIF and ISO in methanol–water (3+1, v/v). The linear ranges were 4.00–48.0 μg/mL for DIF and 50.0–400 μg/mL for ISO in the LC method, and 2.40–40.0 μg/mL for DIF and 60.0–260 μg/mL for ISO in the PCR and first derivative spectrophotometric methods. These methods were validated by analyzing synthetic mixtures. These three methods were successfully applied to two pharmaceutical cream preparations.

Determination of the moisture content of paprika (Capsicum annuum) powders: a comparative study/ Determinación de la humedad del pimentón (Capsicum annuum): estudio comparativo

1996 ◽  
Vol 2 (1) ◽  
pp. 23-27 ◽  
Author(s):  
E. Forgács ◽  
V. Kiss ◽  
T. Cserháti ◽  
J. Holló
Keyword(s):  
Principal Component Analysis ◽  
Moisture Content ◽  
Capsicum Annuum ◽  
Near Infrared ◽  
Principal Component ◽  
Peak Height ◽  
Data Matrix ◽  
Drying Method ◽  
Electric Oven

The moisture content of 25 different paprika powders was determined by an electronic moisture analyzer at 40, 50, 60, 70, 80, 90, 100 and 105°C by near infrared spectroscopy, using both peak area and peak height for the water; and by the traditional drying method, using an electric oven at 100°C for 1, 2 and 3 h. The data matrix was evaluated by principal component analysis. It was established that the moisture content of paprika powders can be equally determined by each method. The use of the NIR method has been proposed because it is both rapid and accurate, and the presence of other volatile compounds does not influence the reliability of the determination of the moisture content.

Disinfection by-products in drinking water – a case study on Calgary, Alberta, Canada

2011 ◽  
Vol 46 (3) ◽  
pp. 200-210 ◽  
Author(s):  
Mei Chen ◽  
Klas Ohman ◽  
Jason Sinclair ◽  
Darcy Petkau ◽  
Raymond Yau ◽  
...  
Keyword(s):  
Drinking Water ◽  
Water Treatment ◽  
Distribution System ◽  
Principal Component ◽  
Data Matrix ◽  
Key Factor ◽  
Chlorine Demand ◽  
Public Health Protection ◽  
By Products

Disinfection by-products (DBPs) have been monitored in Calgary's drinking water for approximately 15 years. The variability of the DBPs has typically exhibited similar patterns over the period of monitoring. Due to the nature of the surface waters supplying the water treatment plants, the level of DBPs was largely influenced by surface runoff events where the level of natural organic matter (NOM) increased, which was characterized by a relatively high total organic carbon (TOC) content. Principal component analysis (PCA) was utilized for this study to quickly identify the key underlying correlations present within the very large, complex multivariate data matrix. Apart from TOC, chlorine demand, chlorine residual and temperature were observed to correlate with the formation of DBPs in the finished drinking water. In addition to TOC, PCA also indicates that pH and temperature in the distribution system could have an influence on the variability of DBPs in Calgary's drinking water. It was apparent that upgrades to the water treatment systems in Calgary have resulted in an improved removal of DBP precursors such as NOM prior to chlorination, which is a key factor in reducing the DBP levels in the drinking water, thereby providing an enhanced level of public health protection.

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