Aproximace KNN problému

Abstract

Search for k nearest neighbors of an element in a space is ubiquitous problem in informatics. Exact solutions to the problem reach linear time complexity. Because of this, use cases requiring very efective search allow an approximation of the problem. Approximation returns a result where vectors that aren't truly nearest can be present. A value of an error is based on the number of such vectors. Performance of a solution of the approximation is computed from elapsed execution time, error and other metrics.

The thesis focuses on Hierarchical navigable small worlds technique (HNSW) which is a solution to the problem of approximation with one of the best ratios of speed and recall. HNSW builds from the elements of the space a series of directed graphs which are arranged into a stack of imaginary layers. Therefore the search is based on a graph traversal.

As a part of the thesis an implementation of the technique was developed. In the end, the original implementation and the new one are both benchmarked and compared against each other. The benchmarks show that the new implementation achieves similar query performance as the original one.