Clustering moving entities in euclidean space
| dc.contributor.author | Hassan, Md Yeakub | |
| dc.contributor.examiningcommittee | Kamali, Shahin (Computer Science) Mohammed, Noman (Computer Science) | en_US |
| dc.contributor.supervisor | Durocher, Stephane (Computer Science) | en_US |
| dc.date.accessioned | 2020-08-24T18:30:24Z | |
| dc.date.available | 2020-08-24T18:30:24Z | |
| dc.date.copyright | 2020-08-10 | |
| dc.date.issued | 2020-08 | en_US |
| dc.date.submitted | 2020-08-10T16:19:42Z | en_US |
| dc.degree.discipline | Computer Science | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.abstract | Clustering is a fundamental problem of spatio-temporal data analysis. Given a set X of n moving entities, each of which corresponds to a sequence of tau time-stamped points in R^d, a k-clustering of X is a partition of X into k disjoint subsets that optimizes a given objective function. In this thesis, we consider two clustering problems, k-Center and k-MM, where the goal is to minimize the maximum value of the objective function over the duration of motion for the worst-case input X. We show that both problems are NP-hard when k is an arbitrary input parameter, even when the motion is restricted to R. We provide an exact algorithm for the 2-MM clustering problem in R^d that runs in O(tau dn^2) time. The running time can be improved to O(tau n log n) when the motion is restricted to R. We show that the 2-Center clustering problem is NP-hard in R^2. Our 2-MM clustering algorithm provides a 1.15-approximate solution to the 2-Center clustering problem in R2. Moreover, finding a (1.15 - epsilon)-approximate solution remains NP-hard for any epsilon > 0. For both the k-MM and k-Center clustering problems in R^d, we provide a 2-approximation algorithm that runs in O(tau dnk) time. We show that the worst case of the k-MM clustering over a continuous time interval is realized at the interval's endpoints. Furthermore, we apply our k-MM algorithm for clustering sets of trajectories to real-world data recorded from motion capture on humans, GPS cycling trajectories, and GPS trajectories from a fleet of taxis. We examine what the resulting clusters “look like” when the algorithm is applied to various common real-word scenarios for different values of k. | en_US |
| dc.description.note | October 2020 | en_US |
| dc.identifier.citation | Durocher, S., & Hassan, M. Y. (2020). Clustering Moving Entities in Euclidean Space. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/34885 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | Trajectories, Clustering, Moving entities, K-Center, Algorithms | en_US |
| dc.title | Clustering moving entities in euclidean space | en_US |
| dc.type | master thesis | en_US |