SVD-based principal component analysis of geochemical data

• Authors: Petr Praus
• Languages of publication: EN

Abstracts

EN

Principal Component Analysis (PCA) was used for the mapping of geochemical data. A testing data matrix was prepared from the chemical and physical analyses of the coals altered by thermal and oxidation effects. PCA based on Singular Value Decomposition (SVD) of the standardized (centered and scaled by the standard deviation) data matrix revealed three principal components explaining 85.2% of the variance. Combining the scatter and components weights plots with knowledge of the composition of tested samples, the coal samples were divided into seven groups depending on the degree of their oxidation and thermal alteration.The PCA findings were verified by other multivariate methods. The relationships among geochemical variables were successfully confirmed by Factor Analysis (FA). The data structure was also described by the Average Group dendrogram using Euclidean distance. The found sample clusters were not defined so clearly as in the case of PCA. It can be explained by the PCA filtration of the data noise.

Keywords

EN

Principal component analysis; singular value decomposition; factor analysis; hierarchical cluster analysis; altered coals; geochemistry

• Publisher: De Gruyter Open
• Journal: Open Chemistry
• Year: 2005
• Volume: 3
• Issue: 4
• Pages: 731-741

Dates

published

1 - 12 - 2005

online

1 - 12 - 2005

Contributors

author

Petr Praus

• Department of Analytical Chemistry and Material Testing, VSB-Technical University Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic

References

• [1] P. Comon: “Independent Component Analysis, a new concept?”, Signal Process., Vol. 36, (1994), pp. 287–314. http://dx.doi.org/10.1016/0165-1684(94)90029-9[Crossref]
• [2] H. Attias: “Independent factor analysis”, Neural Comput., Vol. 11, (1998), pp. 803–851. http://dx.doi.org/10.1162/089976699300016458[Crossref]
• [3] C.M. Bishop, M. Svensén and C.K.I. Williams: GTM: “The generative topographic mapping”, Neural Comput., Vol. 10, (1998), pp. 215–234. http://dx.doi.org/10.1162/089976698300017953[Crossref]
• [4] P. Geladi and B.R. Kowalski: “Partial least square regression: A tutorial”, Anal. Chim. Acta, Vol. 185, (1986), pp. 1–17. http://dx.doi.org/10.1016/0003-2670(86)80028-9[Crossref]
• [5] P. Geladi: “Chemometrics in spectroscopy. Part 1. Classical chemometrics”, Spectrochim. Acta Part B, Vol. 58, (2003), pp. 767–782. http://dx.doi.org/10.1016/S0584-8547(03)00037-5[Crossref]
• [6] E.R. Malinowski: Factor Analysis in Chemistry, 2nd ed., John Wiley & Sons, New York, 1991.
• [7] M.E. Wall, A. Rechtsteiner and L.M.M. Rocha: “Singular value decomposition and principal component analysis”, In: D.P. Berrar, W. Dubitzky and M. Granzow (Eds): A Practical Approach to Microarray Data Analysis, Kluwer, Norwell, MA, 2003.
• [8] M.W. Berry, Z. Drmač and E.R. Jessup: “Matrices, Vector Spaces, and Information Retrieval”, Siam. Rev., Vol. 41, (1995), pp. 335–362. http://dx.doi.org/10.1137/S0036144598347035[Crossref]
• [9] P. Praks P., J. Dvorský and V. Snášel: Latent Semantic Indexing for Image Retrieval Systems. SIAM Conference on Applied Algebra, July 15–19, Williamsburg, 2003, http://www.siam.org/meetings/la03/proceedings/Dvorsky.pdf
• [10] Safavi and H. Abdollahi: “Thermodynamic characterization of weak association equilibria accompanied with spectral overlapping by a SVD-based chemometric method”, Talanta, Vol. 53, (2001), pp. 1001–1007. http://dx.doi.org/10.1016/S0039-9140(00)00591-9[Crossref]
• [11] Z. Klika and J. Kraussová: “Properties or Altered Coals Associated with Carboniferous Red Beds in the Upper Silesian Coal Basin and their Tentative Classification”, Int. J. Coal. Geology, Vol. 22, (1993), pp. 217–235. http://dx.doi.org/10.1016/0166-5162(93)90027-8[Crossref]
• [12] B.K. Lavine: “Clustering and Classification of Analytical Data”, In: R.A. Meyers (Ed.): Encyclopedia of Analytical Chemistry, John Wiley & Sons, Chichester, 2000.
• [13] P. Mather: Computational Methods of Multivariate Analysis in Physical Geography, John Wiley & Sons, New York, 1976.
• [14] M. Kurková, Z. Klika, Ch. Kliková and J. Havel: “Humic acids from oxidized coals. I. Elemental composition, titration curves, heavy metals in HA samples, nuclear magnetic resonance spectra of HA and infrared spectroscopy”, Chemosphere, Vol. 54, (2004), pp. 1237–1245. http://dx.doi.org/10.1016/j.chemosphere.2003.10.020[Crossref]

Identifiers

DOI

10.2478/BF02475200