Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x.

Using choquet integrals for evaluating citation indices in journal ranking

The use of citation-based indices to evaluate the quality of journals is becoming increasingly widespread. Recently, ISI Web of Knowledge has begun to include three new indices in their journal statistics, including a 5-year impact factor. Here, we continue our earlier research which modeled the behavior of journal assessors based on some of these indices and the Choquet integral. We interpret the obtained fuzzy measures of many new datasets toward understanding the importance of these newly published indices and how indicative they may be of a journal's quality. The problem is one of ordinal classification, and the values of the best-fitting fuzzy measures can be obtained using the FMtools software package.

Surface-sensitive method to determine calcium carbonate filler contents in cellulose matrices

This paper describes a method using attenuated total reflectance infra-red spectroscopy to determine the surface concentration of calcium carbonate in paper samples, by applying the linear relationship between the relative infra-red absorption integrals and the concentration. The method was able to detect micro-variations in the surface concentration and could also distinguish between different sheets as well as between the top and bottom side of one sheet. The samples were also split and the calcium carbonate concentration was determined within and compared to bulk calcium carbonate concentration determined from ash testing. The surface results were also compared with analysed scanning electron microscopy images generated from back-scattering electrons. The comparison shows that both sets of results are in excellent agreement. Depending on the sample, large errors (95% confidence) were observed. These, however, are caused by micro-variations of the surface concentration, rather than by inaccuracies of the technique, which is estimated to be less than 1%. Furthermore, measurements of various sample orientations suggest that anisotropic polarisation effects can be neglected. The method can be applied to paper and cellulose matrices having calcium carbonate filler contents of less than 50%. Due to spectral overlaps it is not suitable to determine kaolin filler contents.