Multiple-resolution classification with combination of density estimators

We introduce a classification algorithm based on an idea of ‘multiple-resolution’ (or ‘multiscale’) approach to analysis of the data. In practice, the method uses an average of kernel density estimators where each estimator corresponds to a different data ‘resolution’. First, we examine theoretical properties of this method; next, we propose a practical implementation of such an algorithm with parameters of density estimators adjusted to minimise the misclassification probability. Subsequently, we test the algorithm on artificial data sets characterised by a ‘multiple-resolution’ property. The tests show that the introduced algorithm is superior to the basic version based on one estimator per class. We also test the algorithm on benchmark data sets and compare the results obtained with the results of other classification algorithms.