New approach based on fuzzy logic and principal component analysis for the classification of two-dimensional maps in health and disease: Application to lymphomas

Two-dimensional (2D) electrophoresis is the most wide spread technique for the separation of proteins in biological systems. This technique produces 2D maps of high complexity, which creates difficulties in the comparison of different samples. The method proposed in this paper for the comparison of different 2D maps can be summarised in four steps: (a) digitalisation of the image; (b) fuzzyfication of the digitalised map in order to consider the variability of the two-dimensional electrophoretic separation; (c) decoding by principal component analysis of the previously obtained fuzzy maps, in order to reduce the system dimensionality; (d) classification analysis (linear discriminant analysis), in order to separate the samples contained in the dataset according to the classes present in said dataset. This method was applied to a dataset constituted by eight samples: four belonging to healthy human lymph-nodes and four deriving from non-Hodgkin lymphomas. The amount of fuzzyfication of the original map is governed by the σ parameter. The larger the value, the more fuzzy the resulting transformed map. The effect of the fuzzyfication parameter was investigated, the optimal results being obtained for σ=1.75 and 2.25. Principal component analysis and linear discriminant analysis allowed the separation of the two classes of samples without any misclassification.