Orthogonal transformation component analysis

An often-overlooked issue is the inherent non-orthogonality of coordinate systems used to portray data points. Almost universally a Euclidean coordinate system is used. This assumes that the original variables are orthogonal, that is, are uncorrelated, when it is well known that this is generally not the case. Typically, principal component analysis (PCA) is performed to generate a putative orthogonal coordinate system each of whose axes correspond to directions of maximum variance in the transformed space. This, however, is not quite cor-... 

Principle components analysis (PCA), a form of factor analysis (FA), is one of the most common unsupervised methods used in the analysis of NMR data. Also known as Eigenanalysis or principal factor analysis (PEA), this method involves the transformation of data matrix D into an orthogonal basis set which describes the variance within the data set. The data matrix D can be described as the product of a scores matrix T, and a loading matrix P,... 

On the other hand, successful identification of bacterial spores has been demonstrated by using Fourier transform infrared photoacoustic and transmission spectroscopy " in conjunction with principal component analysis (PCA) statistical methods. In general, PCA methods are used to reduce and decompose the spectral data into orthogonal components, or factors, which represent the most coimnon variations in all the data. As such, each spectrum in a reference library has an associated score for each factor. These scores can then be used to show clustering of spectra that have common variations, thus forming a basis for group member classification and identification. 

These are autocovariances and cross-covariances calculated from sequential data with the aim of transforming them into uniform-length descriptors suitable for QSAR modeling. ACC transforms were originally proposed to describe peptide sequences [Wold, Jonsson et al, 1993 Sjbstrbm, Rannar et al., 1995 Andersson, Sjostrom et al., 1998 Nystrom, Andersson et al., 2000]. To calculate ACC transforms, each amino acid position in the peptide sequence is defined in terms of three orthogonal z-scores, derived from a Principal Component Analysis (PC A) of 29 physico-chemical properties of the 20 coded amino acids. 

To calculate ACC transforms of peptide sequences, each amino acid in the peptide sequence was described by three orthogonal z-scores (Table B3), derived from a —> Principal Component Analysis on 29 physico-chemical properties of the 20 coded amino a.cids (Hellberg,... 

People working in chemometrics will be familiar with another kind of basis transformation principal component analysis (PCA). They may be puzzled by the differences between PCA and orthogonal polynomials. Therefore we will compare the two. 

Generation of new orthogonal features can be carried out by a principal component analysis. A Karhunen-Loeve transformation (Chapter 8.2) gives new non-correlated vector components. 

Principal component analysis Principal component analysis (PCA) [8,40-41] takes as its input a set of vectors described by partially cross-correlated variables and transforms it into one described by a smaller number of orthogonal variables... 

PCA is a statistical technique that has been used ubiquitously in multivariate data analysis." Given a set of input vectors described by partially cross-correlated variables, the PCA will transform them into a set that is described by a smaller number of orthogonal variables, the principle components, without a significant loss in the variance of the data. The principle components correspond to the eigenvectors of the covariance matrix, m, a symmetric matrix that contains the variances of the variables in its diagonal elements and the covariances in its off-diagonal elements (15) ... 

---