Efficient Neighbor Searching in Nonlinear Time Series Analysis

We want to encourage the use of fast algorithms to find nearest neighbors in k-dimensional space. We review methods which are particularly useful for the study of time-series data from chaotic systems. As an example, a simple box-assisted method and possible refinements are described in some detail. The efficiency of the method is compared to the naive approach and to a multidimensional tree for some exemplary data sets.