Fast Euclidean OPTICS with Bounded Precision in Low Dimensional Space.

OPTICS is a popular method for visualizing multidimensional clusters. All the existing implementations of this method have a time complexity of $O(n^2)$ --- where n is the size of the input dataset --- and thus, may not be suitable for datasets of large volumes. This paper alleviates the problem by resorting to approximation with guarantees. The main result is a new algorithm that runs in $O(n łog n)$ time under any fixed dimensionality, and computes a visualization that has provably small discrepancies from that of OPTICS. As a side product, our algorithm gives an index structure that occupies linear space, and supports the cluster group-by query with near-optimal cost. The quality of the cluster visualizations produced by our techniques and the efficiency of the proposed algorithms are demonstrated with an empirical evaluation on real data.