• Classifying NIR spectra of textile products with kernel methods

      Langeron, Yves; Doussot, Michel; Hewson, David; Duchêne, Jacques; Université de technologie de Troyes (Elsevier, 2007-04-30)
      This paper describes the use of kernel methods to classify tissue samples using near-infrared spectra in order to discriminate between samples, either with or without elastane. The aim of this real-world study is to identify an alternative method to classify textile products using near-infrared (NIR) spectroscopy in order to improve quality control, and to aid in the detection of counterfeit garments. The principles behind support vector machines (SVMs), of which the main idea is to linearly separate data, are recalled progressively in order to demonstrate that the decision function obtained is a global optimal solution of a quadratic programming problem. Generally, this solution is found after embedding data in another space F with a higher dimension by the means of a specific non-linear function, the kernel. For a selected kernel, one of the most important and difficult subjects concerning SVM is the determination of tuning parameters. Generally, different combinations of these parameters are tested in order to obtain a machine with adequate classification ability. With the kernel alignment method used in this paper, the most appropriate kernel parameters are identified rapidly. Since in many cases, data are embedded in F, a linear principal component (PC) analysis (PCA) can be considered and studied. The main properties and the algorithm of k-PCA are described here. This paper compares the results obtained in prediction for a linear classifier built in the initial space with the PCs from a PCA and those obtained in F with non-linear PCs from a k-PCA. In the present study, even if there are potentially discriminating wavelengths seen on the NIR spectra, linear discriminant analysis and soft independent modelling of class analogy results show that these wavelengths are not sufficient to build a machine with correct generalisation ability. The use of a non-linear method, such as SVM and its corollary methods, kernel alignment and k-PCA, is then justified.