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The widespread use of GPS-enabled devices generates voluminous and continuousamounts of traffic data but analyzing such data for interpretable andactionable insights poses challenges. A hierarchical clustering of the tripshas many uses such as discovering shortest paths, common routes and oftentraversed areas. However, hierarchical clustering typically has time complexityof $O(n^2 \log n)$ where $n$ is the number of instances, and is difficult toscale to large data sets associated with GPS data. Furthermore, incrementalhierarchical clustering is still a developing area. Prefix trees (also calledtries) can be efficiently constructed and updated in linear time (in $n$). Weshow how a specially constructed trie can compactly store the trips and furthershow this trie is equivalent to a dendrogram that would have been built byclassic agglomerative hierarchical algorithms using a specific distance metric.This allows creating hierarchical clusterings of GPS trip data and updatingthis hierarchy in linear time. %we can extract a meaningful kernel and can alsointerpret the structure as clusterings of differing granularity as oneprogresses down the tree. We demonstrate the usefulness of our proposedapproach on a real world data set of half a million taxis' GPS traces, wellbeyond the capabilities of agglomerative clustering methods. Our work is notlimited to trip data and can be used with other data with a stringrepresentation.

On The Equivalence of Tries and Dendrograms - Efficient Hierarchical Clustering of Traffic Data