Rime samples characterization and comparison using classical and fuzzy principal components analysis

摘要

The main objective of this paper is to introduce principal component analysis and two robust fuzzy principal component algorithms as useful tools in characterizing and comparing rime samples collected in different locations in Poland (2004-2007). The efficiency of the applied procedures was illustrated on a data set containing 108 rime samples and concentration of anions, cations, HCHO, as well as pH and conductivity. The fuzzy principal component algorithms achieved better results mainly because they are more compressible than classical PCA and very robust to outliers. For example, a three component model, fuzzy principal component analysis-first component (FPCA-1) accounts for 62.37% of the total variance and fuzzy principal component analysis-orthogonal (FPCA-o) 90.11%; PCA accounts only for 58.30%. The first two principal components explain 51.41% of the total variance in the case of FPCA-1 and 79.59% in the case of FPCA-o as compared to only 47.55% for PCA. As a direct consequence, PCA showed only a partial differentiation of rime samples onto the plane or in the space described by different combination of two or three principal components, whereas a much sharper differentiation of the samples, regarding their origin and location, is observed when FPCAs are applied.