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Many literature apply Principal Component Analysis (PCA) as either preliminary visualization or variable construction methods or both. Focus of PCA can be on the samples (R-mode PCA) or variables (Q-mode PCA). Traditionally, R-mode PCA has been the usual approach to reduce high-dimensionality data before the application of Linear Discriminant Analysis (LDA), to solve classification problems. Output from PCA composed of two new matrices known as loadings and scores matrices. Each matrix can then be used to produce a plot, i.e. loadings plot aids identification of important variables whereas scores plot presents spatial distribution of samples on new axes that are also known as Principal Components (PCs). Fundamentally, the scores matrix always be the input variables for building classification model. A recent paper uses Q-mode PCA but the focus of analysis was not on the variables but instead on the samples. As a result, the authors have exchanged the use of both loadings and scores plots in which clustering of samples was studied using loadings plot whereas scores plot has been used to identify important manifest variables. Therefore, the aim of this study is to statistically validate the proposed practice. Evaluation is based on performance of external error obtained from LDA models according to number of PCs. On top of that, bootstrapping was also conducted to evaluate the external error of each of the LDA models. Results show that LDA models produced by PCs from R-mode PCA give logical performance and the matched external error are also unbiased whereas the ones produced with Q-mode PCA show the opposites. With that, we concluded that PCs produced from Q-mode is not statistically stable and thus should not be applied to problems of classifying samples, but variables. We hope this paper will provide some insights on the disputable issues. [ABSTRACT FROM AUTHOR]

Selection of the most significant variables, i.e. the wavenumber, from an infrared (IR) spectrum is always difficult to be achieved. In this preliminary paper, the feasibility of genetic algorithms (GA) in identifying most informative wavenumbers from 150 IR spectra of papers was investigated. The list of selected wavenumbers was then employed in Linear Discriminant Analysis (LDA). GA procedure was repeated 30 times to get different lists of variables. Then the performances of LDA models were estimated via leave-one-out cross-validation. A total of six to eight wavenumbers were identified to be valuable variables in the GA procedures. All the 30 LDA models achieve correct classification rates between 97.3% to 100.0%. Therefore the GA-LDA model could be a suitable tool for differentiating white papers that appeared to be highly similar in their IR fingerprints. [ABSTRACT FROM AUTHOR]

The infrared (IR) spectra of different white copy paper types tend to appear indifferent. Discrimination between white copy papers could lead to the solution of forgery cases. In this preliminary study, three varieties of white paper were purchased from local stationery shops in Kuala Lumpur, Malaysia. The papers were classified according to their manufacturers using Partial Least Squares-Discriminant Analysis (PLS-DA) and sparse PLS-DA (sPLS-DA) models. The error rate for the two models on the training and the test data sets were estimated and compared. Results show that the performance of the two models are comparable. By including the first six latent variables in both models, classification accuracy as high as 100% can be achieved. [ABSTRACT FROM AUTHOR]

Infrared (IR) spectral data are always influenced by undesired random and systematic variations. As such, preprocessing of spectral data is normally required before chemometric modeling. Two most widely used pre-processing techniques, i.e. scatter-correction methods and spectral derivatives, were used to pre-process 150 IR spectral data of paper. The algorithms investigated in this preliminary study are Standard Normal Variate (SNV), Multiplicative Scatter Correction (MSC), Savitzky-Golay (SG) and Gap-Segment (GS). The visual examination of the clustering among three studied varieties of paper, i.e. IK Yellow, One Paper and Save Pack, is accomplished via Principal Component Analysis (PCA). Overall, separation of the three varieties of paper is greatly enhanced after pre-processing. The most significant improvement is obtained with pre-processing via 1st derivative using SG algorithms. [ABSTRACT FROM AUTHOR]

Principal Component Analysis (PCA) is a commonly used unsupervised exploratory analysis technique. It is also frequently used in dimensionality reduction. This preliminary paper investigates the feasibility of three variants of PCA, i.e. independent PCA (iPCA), sparse PCA (sPCA), and sparse independent PCA (siPCA) on forensic classification of paper based on their IR spectral data. After that, Linear Discriminant Analysis (LDA) models were built using the Principal Components (PCs) produced by the PCA and the three aforementioned variants. The performances of all these four LDA models, i.e. PCA-DA, iPCA-DA, sPCA-DA and siPCA-DA, were evaluated via leave-one-out cross-validation on the data set. The results obtained show that iPCA-DA and siPCA-DA are the most effective models with 100.0% classification accuracy. Then, the effectiveness of siPCA and iPCA models was evaluated based on posterior probability used for predictions of class membership that were derived from leave-one-out cross-validation. As a conclusion, siPCA is identified as the best classification model. [ABSTRACT FROM AUTHOR]

Until recently, normal mode analysis (NMA) was limited to small proteins, not only because the required energy minimization is a computationally exhausting task, but also because NMA requires the expensive diagonalization of a 3Na x 3Na matrix with Na the number of atoms. A series of simplified models has been proposed, in particular the Rotation-Translation Blocks (RTB) method by Tama et al. for the simulation of proteins. It makes use of the concept that a peptide chain or protein can be seen as a subsequent set of rigid components, i.e. the peptide units. A peptide chain is thus divided into rigid blocks with six degrees of freedom each. Recently we developed the Mobile Block Hessian (MBH) method, which in a sense has similar features as the RTB method. The main difference is that MBH was developed to deal with partially optimized systems. The position/orientation of each block is optimized while the internal geometry is kept fixed at a plausible - but not necessarily optimized - geometry. This reduces the computational cost of the energy minimization. Applying the standard NMA on a partially optimized structure however results in spurious imaginary frequencies and unwanted coordinate dependence. The MBH avoids these unphysical effects by taking into account energy gradient corrections. Moreover the number of variables is reduced, which facilitates the diagonalization of the Hessian. In the original implementation of MBH, atoms could only be part of one rigid block. The MBH is now extended to the case where atoms can be part of two or more blocks. Two basic linkages can be realized: (1) blocks connected by one link atom, or (2) by two link atoms, where the latter is referred to as the hinge type connection. In this work we present the MBH concept and illustrate its performance with the crambin protein as an example. [ABSTRACT FROM AUTHOR]

The reflectance spectrum of one member of the garnet family, Mn3Al2Si3O12 spessartine, was computed at the ab initio level with an all electron Gaussian type basis set and the B3LYP Hamiltonian. The static high frequency dielectric constant was obtained by applying the Coupled Perturbed Kohn Sham scheme as implemented in the CRYSTAL code; the Hessian matrix was evaluated numerically starting from the analytical gradients of the total energy with respect to the Cartesian coordinates of the atoms; the oscillator strengths were computed from well localized Wannier functions. An excellent agreement was obtained with the corresponding experimental spectrum, the exception being the very low frequency region. [ABSTRACT FROM AUTHOR]

The single crystals of L-Alaninium oxalate are grown by slow evaporation method and vibrational spectral analysis is carried out using FT IR and FT Raman spectral data to study the vibrational interactions of the molecule. The vibrational spectra confirm the presence of NH3+ in the crystal. [ABSTRACT FROM AUTHOR]