Stoichiometric identification with maximum likelihood principal component analysis

This study presents an effective procedure for the determination of a biologically inspired, black-box model of cultures of microorganisms (including yeasts, bacteria, plant and animal cells) in bioreactors. This procedure is based on sets of experimental data measuring the time-evolution of a few extracellular species concentrations, and makes use of maximum likelihood principal component analysis to determine, independently of the kinetics, an appropriate number of macroscopic reactions and their stoichiometry. In addition, this paper provides a discussion of the geometric interpretation of a stoichiometric matrix and the potential equivalent reaction schemes. The procedure is carefully evaluated within the stoichiometric identification framework of the growth of the yeast Kluyveromyces marxianus on cheese whey. Using Monte Carlo studies, it is also compared with two other previously published approaches.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

Multiple group principal component analysis and population differentiation

This paper explores the requirements and advantages of multiple group principal component analysis (MGPCA) when it is used to investigate population differentiation. A distinction is drawn between equality of orientation of the within-group axes and equality of variance along these axes. Several examples of the use of MGPCA are discussed and it is shown that MGPCA per se does not require equality of variance along the axes although it may be a requirement of some of the techniques subsequently used to analyse the component scores. MGPCA is simple and direct, being based on the mathematically well defined eigenvector analysis of a symmetric positive definite (pooled within-group covariance) matrix and it can be thought of as a step in the computation of canonical variate analysis (CVA). It can be used with CVA (which is the most popular method of biometrically assessing population affinities) to assess the contribution of within-group components to among-group discrimination. It is also one of a range of appropriate techniques that can be used to define (and delete if required) within-group growth effects and is particularly suitable when CVA is being used to assess the population affinities. When used in this way it has the advantage of being more influenced by the groups with the greatest growth range.     

Ordination of vegetation change in Guadalupe Mountains,New Mexico,USA

Vegetation change over a nine-year period was studied in Guadalupe Mountains, New Mexico. Permanent transects in desert shrub vegetation were sampled in 1972 and 1980. Emphasis was given to shrubs because of their importance to big game diets. Univariate paired t-tests and reciprocal averaging ordination were used to detect and display coordinated changes in species composition over time. Despite apparently less browsing pressure in desert shrub vegetation in 1980 there were few significant changes in species composition. In addition, preferred forage species showed reduced reproduction while species of intermediate and poor forage value dis-played increased reproduction during this time. These data do not support traditional rangeland succession theory which states that enhanced reproduction of preferred species should follow grazing or browsing pressure reduction.     

Probabilistic principal component analysis for metabolomic data

Background  

Data from metabolomic studies are typically complex and high-dimensional. Principal component analysis (PCA) is currently the most widely used statistical technique for analyzing metabolomic data. However, PCA is limited by the fact that it is not based on a statistical model.     

Pre-processing of chromatographic data for principal component analysis

This paper examines the selection of the appropriate representation of chromatogram data prior to using principal component analysis (PCA), a multivariate statistical technique, for the diagnosis of chromatogram data sets. The effects of four process variables were investigated; flow rate, temperature, loading concentration and loading volume, for a size exclusion chromatography system used to separate three components (monomer, dimer, trimer). The study showed that major positional shifts in the elution peaks that result when running the separation at different flow rates caused the effects of other variables to be masked if the PCA is performed using elapsed time as the comparative basis. Two alternative methods of representing the data in chromatograms are proposed. In the first data were converted to a volumetric basis prior to performing the PCA, while in the second, having made this transformation the data were adjusted to account for the total material loaded during each separation. Two datasets were analysed to demonstrate the approaches. The results show that by appropriate selection of the basis prior to the analysis, significantly greater process insight can be gained from the PCA and demonstrates the importance of pre-processing prior to such analysis.     

Global mapping analysis: stochastic approximation for multidimensional scaling.

In this paper, we propose global mapping analysis (GMA) as a new method to solve multidimensional scaling (MDS). By GMA, MDS is done by an online learning rule based on stochastic approximation. GMA need not directly calculate the disparity matrix for carrying out MDS, as Oja's PCA network do not calculate the correlation matrix. So, GMA is expected to be useful for multivariate data analysis on a large scale. Actually, it was verified by numerical experiments based on artificial data that GMA can work well even if the number of the attribute N is quite large (N=10,000.)     

Analyses of multivariately determined community matrices using cluster analysis and multidimensional scaling

Linear discriminant analysis was used to compute the p-variate MACARTHUR-LEVINS and Density Overlap measures of niche overlap between all pairs of 24 passerine bird species. The overlap values for the species pairs were then organized into a community matrix for each approach. The relationships inherent in the community matrices were structured by cluster analysis and non-metric multidimensional scaling. Cluster analysis identified the highly related species groups whereas multidimensional scaling demonstrated community wide relationships. In particular, the scaling approach clearly delineated shrub density and ground cover gradients.     

Identification of movement-related cortical potentials with optimized spatial filtering and principal component analysis

We present a method for detecting movement intention from multichannel electroencephalographic (EEG) recordings. Movement intention is expressed as a slow negative deflection in amplitude of the EEG signal recorded above the motor cortex. This deflection is known as a movement-related cortical potential (MRCP). Detection of movement intention implies discrimination between MRCPs and noise. The signal-to-noise ratio of MRCPs was improved by an optimized spatial filter. Features were extracted with principal component analysis or locality preserving projections from the spatially filtered signals and classification between MRCPs and noise was performed with a k-nearest neighbors algorithm, modified by adjusting the decision rule to improve specificity, and a support vector machine approach. In one representative subject the sensitivity and specificity in detection were in the range 80–90% and 98–99.5%, respectively. The method seems promising for the development of asynchronous brain–computer interfaces (BCIs) based on MRCPs.     

A robust subspace algorithm for principal component analysis

We present a noise robust PCA algorithm which is an extension of the Oja subspace algorithm and allows tuning the noise sensitivity. We derive a loss function which is minimized by this algorithm and interpret it in a noisy PCA setting. Results on the local stability analysis of this algorithm are given and it is shown that the locally stable equilibria are those which minimize the loss function.     

Trajectory analysis of Chinese vegetation types in a multidimensional climatic space

Abstract. The concept of trajectory of a vegetation type is used as a tool to study the position of vegetation types in a multidimensional climatic space. This space was obtained by Principal Component Analysis based on climatic data - based on monthly means. The positions of the main vegetation types distinguished in China were plotted in the climatic space and trajectory lengths and shapes of the types were compared. Three main groups were found, which correspond to: (1) cold and temperate, (2) alpine and mountain, and (3) subtropical and tropical conditions. Within each main category sub-categories were distinguished on the basis of trajectory length and direction. In total, seven trajectory shapes were defined. Based on the correlation between climatic variables and PCA-axes temperature is suggested to be the overriding factor in determining the trajectory shape. But, trajectories can also be affected by the combination of other climatic variables.     

Component retention in principal component analysis with application to cDNA microarray data

Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given.     

Analysis of breast cancer progression using principal component analysis and clustering

We develop a new technique to analyse microarray data which uses a combination of principal components analysis and consensus ensemble k-clustering to find robust clusters and gene markers in the data. We apply our method to a public microarray breast cancer dataset which has expression levels of genes in normal samples as well as in three pathological stages of disease; namely, atypical ductal hyperplasia or ADH, ductal carcinoma in situ or DCIS and invasive ductal carcinoma or IDC. Our method averages over clustering techniques and data perturbation to find stable, robust clusters and gene markers. We identify the clusters and their pathways with distinct subtypes of breast cancer (Luminal,Basal and Her2+). We confirm that the cancer phenotype develops early (in early hyperplasia or ADH stage) and find from our analysis that each subtype progresses from ADH to DCIS to IDC along its own specific pathway, as if each was a distinct disease.     

Decomposing complex reaction networks using random sampling,principal component analysis and basis rotation

Background  

Metabolism and its regulation constitute a large fraction of the molecular activity within cells. The control of cellular metabolic state is mediated by numerous molecular mechanisms, which in effect position the metabolic network flux state at specific locations within a mathematically-definable steady-state flux space. Post-translational regulation constitutes a large class of these mechanisms, and decades of research indicate that achieving a network flux state through post-translational metabolic regulation is both a complex and complicated regulatory problem. No analysis method for the objective, top-down assessment of such regulation problems in large biochemical networks has been presented and demonstrated.     

Quantitative gait evaluation of hip diseases using principal component analysis

The measurement of five gait parameters, namely, joint angular displacement of lower extremities, floor reaction forces, trajectory for a point of force application, temporal factor and distance factor has been performed with ease and high speed using mini-computer on-line real-time processing. Gait data of 211 patients with hip diseases was normalized, quantified and summarized by the principal component analysis. A 'gait evaluation plane' was formed according to the results obtained by the principal component analysis. The gait evaluation using the plane was compared with clinical conditions of patients, and it was evident that this system can evaluate the recovery of the gait by treatment.