Heuristics for Computing k-Nearest Neighbors Graphs

The k-Nearest Neighbors Graph (kNNG) consists of links from an object to its k-Nearest Neighbors. This graph is of interest in diverse applications ranging from statistics, machine learning, clustering and outlier detection, computational biology, and even indexing. Obtaining the kNNG is challenging because intrinsically high dimensional spaces are known to be unindexable, even in the approximate case. The cost of building an index is not well amortized over just all the objects in the database. In this paper, we introduce a method to compute the kNNG without building an index. While our approach is sequential, we show experimental evidence that the number of distance computations is a fraction of the \(n^2/2\) used in the naive solution. We make heavy use of the notion of pivot, that is, database objects with full distance knowledge to all other database objects. From a group of pivots, it is possible to infer upper bounds of distance to other objects.