A Gaussian-based kernel Fisher discriminant analysis for electronic nose data and applications in spirit and vinegar classification

Fisher discriminant analysis (FDA) is a very useful pattern recognition technique widely used in electronic nose system (e-nose). However, due to its linear characteristic, the classification problems of multi-class and high-dimensional e-nose data cannot be handled effectively. Therefore, a Gaussian-based kernel FDA (KFDA) method is proposed to solve multi-class and high-dimensional classification problems of complex samples such as food classification using e-nose. The key point of the method is how to determine the Gaussian kernel parameter. Firstly, according to distance discriminant analysis viewpoint, a desired kernel matrix adapted to Gaussian kernel function can be given successfully. Secondly, an evaluation function based on Euclidean distance is established for measuring the degree of approximation between actual kernel matrix containing an unknown Gaussian kernel parameter and the desired kernel matrix so as to get an optimal solution of the parameter, and then the actual kernel matrix can be definitely determined. Finally, the principal component analysis (PCA) for the actual kernel matrix is carried out. Meanwhile, FDA for the principal component matrix generated by PCA is also implemented in succession, and the KFDA is completed. Six kinds of Chinese spirit and six kinds of Chinese vinegar samples as two classification applications were respectively carried out accurately with the KFDA method; and the KFDA method is tested to be very simple and effective. The KFDA method may be promising for complex samples classification dataset of e-nose.