New Algorithms for Efficient High-Dimensional Nonparametric Classification

This paper is about non-approximate acceleration of high dimensional non-parametric operations such as k-nearest neighbor classifiers and the prediction phase of Support Vector Machine classifiers. We attempt to exploit the fact that even if we want exact answers to non-parametric queries, we usually do not need to explicitly find the datapoints close to the query, but merely need to ask questions about the properties about that set of datapoints. This offers a small amount of computational leeway, and we investigate how much that leeway can be exploited. For clarity, this paper concentrates on pure KNN-classification and the prediction phase of SVMs. We introduce new ball tree algorithms that on real-world datasets give accelerations of 2-fold up to 100-fold compared against highly optimized traditional ball-tree-based KNN. These results include datasets with up to 106 dimensions and 105 records, and show non-trivial speedups while giving exact answers.