DBSCAN Revisited

Abstract

DBSCAN is a popular method for clustering multi-dimensional objects. Just as notable as the method's vast success is the research community's quest for its efficient computation. The original KDD'96 paper claimed an algorithm with O(n log n) running time, where n is the number of objects. Unfortunately, this is a mis-claim; and that algorithm actually requires O(n 2 ) time. There has been a fix in 2D space, where a genuine O(n log n)-time algorithm has been found. Looking for a fix for dimensionality d ≥ 3 is currently an important open problem.In this paper, we prove that for d ≥ 3, the DBSCAN problem requires Ω(n 4/3 ) time to solve, unless very significant breakthroughs-ones widely believed to be impossible-could be made in theoretical computer science. This (i) explains why the community's search for fixing the aforementioned mis-claim has been futile for d ≥ 3, and (ii) indicates (sadly) that all DBSCAN algorithms must be intolerably slow even on moderately large n in practice. Surprisingly, we show that the running time can be dramatically brought down to O(n) in expectation regardless of the dimensionality d, as soon as slight inaccuracy in the clustering results is permitted. We formalize our findings into the new notion of ρ-approximate DBSCAN, which we believe should replace DBSCAN on big data due to the latter's computational intractability.

Fast Data Sorting with Modified Principal Component Analysis to Distinguish Unique Single Molecular Break Junction Trajectories

“…See the Supplemental Material [14] (which includes Refs. [17][18][19]), where we demonstrate that when the number of measurements is larger than about 1000, PCA is computationally faster than another recent method [2] introduced to categorize SMBJ traces.…”

Real Time Density-Based Clustering (RTDBC) Algorithm for Big Data

“…RTDBC performance on different synthetic datasets created by DBSCANR (DBSCAN variant) (Gan and Tao, 2015) shown in Fig. 13 with synthetic 1 (9 with 2000000 points) and synthetic 2 (11 with 2000000 points) dimensions on different values of є with µ = 5.…”

“…During execution in existing approaches works on batch scheme, does not permit the user communication (Brecheisen et al, 2004;Gan and Tao, 2015). In other side, during the run time anytime algorithm (Zhou et al, 2000) rapidly generate approximate result and refine continuously and permit the users to suspend for verifying the result, resume to finding satisfactory result is obtained.…”

“…A set of Dense objects connected and separated by a new created cluster with low density region clusters while density object more than p objects inside ε radius of neighborhood. DBSCAN is mainly considerable clustering algorithm with various applications and extension (Brecheisen et al, 2004;Gan and Tao, 2015) like satellite images, x-ray crystallography, anomaly detection in temperature data, astronomy (Settles, 2009) and neuroscience (Mai et al, 2012). Bur its real weakness complex data sets if they located too close with each other even if they are different densities.…”

Accurate Sybil Attack Detection Based on Fine-Grained Physical Channel Information

“…Secondly, on the dynamic side, it is well known that an attack may move its position within a detection threshold to avoid static detection. Therefore, we use the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering method [15] for all attack nodes constructed by Sybil clients that fall within the detection threshold and within the RSSI threshold. The clustering method distinguishes the attacking nodes from the normal nodes simultaneously.…”