Multivariate mixed kernel density estimators and their application in machine learning for classification of biological objects based on spectral measurements

A problem of non-parametric multivariate density estimation for machine learning and data augmentation is considered. A new mixed density estimation method based on calculating the convolution of independently obtained kernel density estimates for unknown distributions of informative features and a known (or independently estimated) density for non-informative interference occurring during measurements is proposed. Properties of the mixed density estimates obtained using this method are analyzed. The method is compared with a conventional Parzen-Rosenblatt window method applied directly to the training data. The equivalence of the mixed kernel density estimator and the data augmentation procedure based on the known (or estimated) statistical model of interference is theoretically and experimentally proven. The applicability of the mixed density estimators for training of machine learning algorithms for the classification of biological objects (elements of grain mixtures) based on spectral measurements in the visible and near-infrared regions is evaluated.