Regularised nearest neighbour classification method for pattern recognition of near infrared spectra

When a data set contains a high number of variables compared to the number of objects, the k nearest neighbour classification method (kNN) cannot be applied with the Mahalanobis distance as similarity criterion. To solve this problem, kNN is modified to the regularised nearest neighbour classification method (RNN) by using the regularised covariance matrix in the Mahalanobis distance in the same way that LDA and/or QDA are modified to regularised discriminant analysis (RDA). Four simulated data sets and 14 real NIR data sets were studied to compare the new method with the classical kNN using Euclidean and Mahalanobis distances. Our results demonstrate that RNN improves the classification results by regularising the class covariance matrix in all kinds of data sets. When the ratio of variables to objects is very high, RNN cannot be directly applied. The data dimensionality must be reduced before using RNN. This is, for instance, the case when one wants to apply the method to classification of NIR spectra. Compared with RDA, RNN performs better than RDA when the normal distribution assumption is severely violated, and worse when the data are normally distributed, since it is a non-parametric version of RDA. However, it is more time consuming than RDA.