Mathematical Geosciences

, Volume 43, Issue 2, pp 165–181 | Cite as

Functional Methods for Classification of Different Petrographic Varieties by Means of Reflectance Spectra

  • Vera Hofer


The need for improved product quality in the aggregates industry is driving the search for greater automation in rock type identification. In practice, reflectance spectra in visible and near-infrared light may reliably be used for the classification of rock classes and their variants. Previous studies introduced statistical classification of six rock variants by means of infrared spectra. The present investigation extends these studies to cover twelve rock types and variants of worldwide economic importance. These were measured by visible and near-infrared light. Statistical classification of these spectra is highly challenging due to the high number of groups and the high dimensionality of the data. In functional data analysis, spectra are regarded as curves instead of vectors of characteristics. To obtain a compact form that is more susceptible to further analysis, the spectra are represented by a B-spline basis. Two functional versions of linear support vector machines and penalized functional discriminant analysis are considered for classification. The multiclass problem is addressed by margin trees and by considering all one-against-one classifications combined with a voting strategy for testing. Since classification error estimated by 5-fold cross-validation is very low, in particular for penalized discriminant analysis, we conclude that the rock types can be classified reliably.


Aggregates Geoengineering Functional discrimination Functional data analysis Functional support vector machines Margin trees Penalized functional discriminant analysis 


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© International Association for Mathematical Geosciences 2011

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchKarl-Franzens UniversityGrazAustria

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