B. Treiger

IDAS : a Windows based software package for cluster analysis

Abstract This article is an electronic publication in Spectrochimica Acta Electronica (SAE), the electronic section of Spectrochimica Acta Part B (SAB). The hardcopy text, comprising the main article and one appendix, is accompanied by two installation diskettes with the software package and data files. The main article discusses the chemometric aspects of the package and explains its purpose. The IDAS software package combines three cluster analysis methods (hierarchical, non-hierarchical and fuzzy) and runs under MS Windows. Modified algorithms for non-hierarchical and fuzzy clusterings are described. The interpretation of the clustering results is facilitated by the extensive use of different types of graph. New approaches to the graphical representation of the results of fuzzy clustering are proposed. Two data sets, the Iris data by Fisher and a data set on the chemical composition of tea, are used to demonstrate the capabilities of the software.

Fractal dimensional classification of aerosol particles by computer-controlled scanning electron microscopy

~~ ~~ A method for the classification of individual aerosol particles into one of two main groups, namely, fly ash and soil dust, is presented. It is based on the calculation of the fractal dimensions of the images of the particles obtained with the computer-controlled scanning electron microscopy. The risk of an improper determination of the fractal dimension is pointed out. It is shown that spherically shaped particles that normally compose the majority of the fly ash particles do not possess fractality. The rarely met fly ash particles with very irregular shape possess two types of the fractal dimensions, namely, textural and structural. On the other hand, it is found that the soil dust particles have only a textural fractal dimension. The obtained results allow the unequivocal identification of the particle source, which is especially important when the chemical compositions of the particles are nearly the same.

Hierarchical cluster analysis with stopping rules built on Akaike's information criterion for aerosol particle classification based on electron probe X-ray microanalysis

Abstract The interpretation of the results of hierarchical cluster analysis depends very much on the correct choice of the number of clusters. An approach based on the application of the Akaike information criterion is proposed. Examples of the classification of Lake Baikal aerosol particles based on the clustering of electron probe X-ray microanalysis data are given. Bondarenko, I., Van Malderen, H, Treiger, B., Van Espen, P. and Van Gricken, R., 1994. Hierarchical cluster analysis with stopping rules built on Akaikes information criterion for aerosol particle classification based on electron probe X-ray microanalysis. Chemometrics and Intelligent Laboratory Systems , 22: 87–95.

Elucidating the composition of atmospheric aerosols through the combined hierarchical, non-hierarchical and fuzzy clustering of large electron probe microanalysis data sets

Abstract Combined utilization of hierarchical, non-hierarchical and fuzzy clustering is introduced to find the intrinsic Structure of large analytical data sets. Modified algorithms for nonhierarchical and fuzzy clustering are used. The interpretation of the results of clustering is based on the extensive use of different types of graphs. New approaches to the graphical representation of the results of fuzzy clustering are proposed. The method is applied to data of electron probe X-ray microanalysis of individual aerosol particles. The advantages of the method are shown.

Quantitative characterization of individual particle surfaces by fractal analysis of scanning electron microscope images

Morphological characterization of individual particle surfaces was explored by off-line image processing of data obtained by scanning electron microscope — microanalyzer. The fractal geometry was studied by two methods, the power spectrum and the variogram approach. Both methods were evaluated, theoretically by a series of numerically simulated surface profiles and experimentally on a set of pre-recorded secondary electron images of particle surfaces exposing characteristic textures. It was shown that the fractal approach could stand as a base of the methods enlarging the application of electron probe X-ray microanalyzers for individual particle characterization.

Extraction of environmental information from large aerosol data sets through combined application of cluster and factor analyses

To reveal useful environmental information which is contained in large analytical data sets, an approach, based on the successive application of hierarchical cluster analysis and factor analysis, is proposed. Estimation criteria to determine the most suitable number of clusters and/or factors, are discussed and the interpretation of the cluster and factor analyses results is performed using visual techniques. The data sets were obtained by scanning electron microscope-energy-dispersive X-ray analysis of individual North Sea aerosol particles.

Characterisation of the Shape of Microparticles via Fractal and Fourier Analyses of Scanning Electron Microscope Images

Two different approaches based on Fourier and fractal analyses, are applied for particle shape characterisation. The advantages and limitations of both approaches as well as their fields of application are discussed. Examples of the application of these approaches for particles of various types are given.

Chemometrical approach to the determination of the fractal dimension(s) of real objects

Abstract Fractal dimension has been recognized for a long time as a useful parameter for shape characterisation. However, the use of the fractals concept requires the visual inspection of the Richardson plot which hampers the practical applications. In this paper a fully automatical method for the analysis of the Richardson plot is described. A clustering approach is adopted instead of the visual inspection of Richardson plot. Cases which explain the application of the method are examined.

X-ray spectral microanalysis of the phase composition of high temperature superconductor bismuth–lead–strontium–calcium–copper–oxygen ceramics using chemometric approaches

The work described in this paper deals with the investigation of the phase composition of high temperature (Tc) superconductor (HTSC) ceramic samples with the help of cluster and principal component analyses (CA and PCA) of the electron microprobe data. The peculiarities of the joint application of CA and PCA are shown. The phase composition of eight specially fabricated Bi—Pb—Sr—Cu—O samples is determined. The results of the investigation are compared with those obtained by X-ray diffraction (XRD), differential thermal (DTA) and differential dissolution (DDA) analyses. The correlations between the Bi, Sr and Cu contents are revealed and their nature is discussed. Finally, it is concluded that the valence of Bi is +2.

Electron probe X-ray microanalysis for the assessment of homogeneity of candidate reference materials at the nanogram level

A new approach to the assessment of homogeneity for powder samples of candidate reference materials with the help of electron probeX-ray micro-analysis (EPMA) is proposed. It is based on the utilisation of the Kolmogorov—Smirnov statistics coupled with the Akaike Information Criterion in the processing of the quantitative EPMA data. The evaluation of three IAEA candidate reference materials with the described approach is discussed.