Kim H. Esbensen

Principal Component Analysis

Principal Component Analysis (PCA) is a multivariate exploratory analysis method, useful to separate systematic variation from noise. It allows to define a space of reduced dimensions that preserve ...

Multivariate Data Analysis in Chemistry

Any data table produced in a chemical investigation can be analysed by bilinear projection methods, i. e. principal components and factor analysis and their extensions. Representing the table rows (objects) as points in a p-dimensional space, these methods project the point swarm of the data set or parts of it down on a F-dimensional subspace (plane or hyperplane). Different questions put to the data table correspond to different projections.

Principal component analysis of multivariate images

Abstract Multivariate data analysis of 2-dimensional object arrays is explained and its application to images is demonstrated. The possibility of creating soft models in latent variables is a great aid in this process. The pattern classification, cognition and recognition processes as used in the SIMCA method can be translated to latent variables of the multivariate images. A small example of a satellite image is presented. The method aspires to make maximal use of the possibilities of standard image analysis equipment and to combine the results obtained with more traditional image analysis techniques. This article concentrates mainly on theoretical aspects.

Strategy of multivariate image analysis (MIA)

Abstract Bilinear decomposition (soft modelling using principal component analysis) of multivariate imagery results in: score and loading plots, score images, classification projections and residual images in the scene space. Feature space score plots are used as a starting point for pixel class delineations, followed by iterative scene space evaluation. This is a reversal of traditional image processing practice, which selects training samples in the scene space. The present feature space class definitions can be shown to have certain optimality characteristics with respect to traditional scene space delineations. After problem-dependent relevant pixel class delineations have been obtained, one can compute corresponding local class PC-models that serve as an alternative basis for problem-dependent classification and sequential segmentation. Multivariate image analysis (MIA) allows interactive exploration and classification of most types of technical multivariate imagery. We present a general strategy for multivariate image analysis, illustrated by a remote sensing showcase.

Systematic compositional variations in the Cape York iron meteorite

Concentrations of Re, Ir and Au are nearly constant within individual masses of the Cape York IIIAB iron meteorite, but differences between masses can be as large as a factor of 2, the extremes being Savik (5.1 μg/g Ir) and Agpalilik (2.7 μg/g Ir). The S concentration shows a still larger range from 13 mg/g in Agpalilik to 1.4 mg/g in Savik. A relatively large compositional hiatus between Dog and Agpalilik probably reflects inadequate sampling of the original material. Concentrations of Ir vary by ~10% and Au by ~3% between the ends of an 85-cm section from the Agpalilik mass of Cape York, but other sections through Agpalilik show smaller variations. These concentration ranges are much larger than expected from radial crystallization of a moderately large (radius 10 s of km) core. These variations in the Agpalilik mass may reflect dendritic crystallization, or they may have resulted from the process that produced the large concentration range among the Cape York masses. Large gradients in Re and Ir and small gradients in Ni and Au were also observed in samples within 2 cm of a large (100 cm3) troilite nodule. These gradients may reflect rapidly changing solid/liquid distribution coefficients during the final crystallization of S-rich liquid. The compositional trends among the various masses can either be explained by mixing of disparate end members followed by diffusive homogenization on a scale of m, or by dendritic crystallization on the ceiling of the IIIAB magma chamber. The mixing of a solid similar in composition to Savik with a liquid in equilibrium with this solid yields a good match to the observed trends, in which case Agpalilik consists of a mixture of 64% liquid and 36% solids. The bulk S content of the IIIAB core is calculated to be 14 mg/g on the basis of this model.

Fibrin clot structure in patients with end-stage renal disease

Fibrin clots with reduced permeability, increased clot stiffness and reduced fibrinolysis susceptibility may predispose to cardiovascular disease (CVD). Little is known, however, about the structure of fibrin clots in patients with end-stage renal disease (ESRD). These patients suffer from a high risk of CVD in addition to their chronic low-grade inflammation. Using permeability, compaction and turbidity studies in 22 ESRD patients and 24 healthy controls, fibrin clots made from patient plasma were found to be less permeable (p < 0.001), less compactable (p < 0.001), and less susceptible to fibrinolysis (p < 0.001) than clots from controls. The maximum rate of turbidity increase was also higher for the patients than controls (p < 0.001), and scanning electron microscopy revealed higher clot density of fibrin fibers in clots from patients than clots from controls (p < 0.001). Patients had higher plasma concentrations of fibrinogen, C-reactive protein and interleukin 6 than controls. These plasma markers of inflammation correlated significantly with most of the fibrin structure characteristics observed in the patients. In contrast, plasma markers of azothemia showed no such correlations. The results suggest that in ESRD patients fibrin clots are significantly different from healthy controls, and that the fibrin structure characteristics in the patients are associated primarily with the inflammatory plasma milieu rather than with level of azothemia.

Principal Component Analysis: Concept, Geometrical Interpretation, Mathematical Background, Algorithms, History, Practice

Principal Component Analysis : Concept, Geometrical Interpretation, Mathematical Background, Algorithms, History, Practice

Multi-way methods in image analysis—relationships and applications

This paper gives an overview of multi-way methods in image analysis, termed N-way image analysis. Both weak and strong multi-way methods are applied in order to decompose and characterize image data, and obtain insight into their abilities to capture and model the interpretable data structure. Multivariate Image Analysis (MIA) is a typical example based on weak multi-way methods like unfold-PCA/PLS. Strong multi-way methods such as PARAFAC, Tucker3, N-PLS are also introduced and applied to image analysis in this work. Which method to use is problem-dependent. Through macroscopic satellite images, virtual fluorescence images and microscopic functional property image examples, the performance of each alternative method is presented, as well as comparisons between weak and strong multi-way models. It is demonstrated that efficient handling of multiple images requires a clear a priori overview of the relationship between problem formulation and data array configuration. Appropriate preprocessing techniques, such as 2-D FFT and Wavelet transform, may also be needed in order to transform and configure some special types of image data to forms specifically suited for multi-way modeling. Application I shows the possibility for application of strong multi-way methods on multispectral images, otherwise conventionally analyzed by MIA. By contrast, application II attempts to investigate the feasibility of applying MIA models on typical three-way data, normally handled by the strong multi-way methods and provides a new perspective of dealing with fluorescence spectra as images. In application III, attempts have been made to predict rheological parameters from microscopic cheese images by multi-way methods. The present didactic exposition allows to draw some tentative first conclusions as to the dominant relationships between strong and weak multi-way data decompositions, their pros and cons and their relative merits.

Transflexive embedded near infrared monitoring for key process intermediates in anaerobic digestion/biogas production

This work reports an off-line method development simulating at-line anaerobic co-digestion process monitoring using a new transflexive embedded near infrared sensor (TENIRS) system as a process analytical chemistry (PAC) facility. The operative focus is on optimising anaerobic digestion biogas production with energy crops as the main feedstock. Results show that several key monitoring intermediates in the anaerobic fermentation process can be quantified directly using near infrared spectroscopy with good results, especially ammonium and total volatile fatty acids. Good feasibility study prediction validations have been obtained for total solids (TS), volatile solids (VS), ammonium, acetic acid and total volatile fatty acids. The TENIRS system is a new option for real-time, at-line/on-line monitoring of biogas fermentation operations, offering a robust, low-budget PAC approach to a rapidly growing bulk volume industry.

Multicomponent analysis of fermentation growth media using the electronic tongue (ET).

A potentiometric electronic tongue (ET) consisting of eight cross-sensitive chemical sensors and a standard pH electrode has been applied for analysis of simulated fermentation solutions typical for fermentation processes with Aspergillus niger. The electronic tongue has been found capable of simultaneous determination of ammonium, citrate and oxalate in complex media with good precision (typical error within 8%). The system preserved high sensitivity to the targeted substances also in the presence of sodium azide, which is commonly used for suppressing microbial activity in real-world fermentation samples. Sensor performance was fast and reproducible which promises well for routine application of the electronic tongue for fermentation process monitoring.