Abstract-HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the sense that a small change in mpts typically leads to only a small or no change in the clustering structure, choosing a "good" mpts value can be challenging: depending on the data distribution, a high or low value for mpts may be more appropriate, and certain data clusters may reveal themselves at different values of mpts.To explore results for a range of mpts values, however, one has to run HDBSCAN* for each value in the range independently, which is computationally inefficient. In this paper, we propose an efficient approach to compute all HDBSCAN* hierarchies for a range of mpts values by replacing the graph used by HDBSCAN* with a much smaller graph that is guaranteed to contain the required information. An extensive experimental evaluation shows that with our approach one can obtain over one hundred hierarchies for the computational cost equivalent to running HDBSCAN* about 2 times.

HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter mpts. While a small change in mpts typically leads to a small change in the clustering structure, choosing a "good" mpts value can be challenging: depending on the data distribution, a high or low mpts value may be more appropriate, and certain clusters may reveal themselves at different values. To explore results for a range of mpts values, one has to run HDBSCAN* for each value independently, which can be computationally impractical. In this paper, we propose an approach to efficiently compute all HDBSCAN* hierarchies for a range of mpts values by building upon results from computational geometry to replace HDBSCAN*'s complete graph with a smaller equivalent graph. An experimental evaluation shows that our approach can obtain over one hundred hierarchies for the computational cost equivalent to running HDBSCAN* about twice, which corresponds to a speedup of more than 60 times, compared to running HDBSCAN* independently that many times. We also propose a series of visualizations that allow users to analyze a collection of hierarchies for a range of mpts values, along with case studies that illustrate how these analyses are performed.

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Mobility data has been fostered by the widespread diffusion of wireless technologies. This data opens new opportunities for discovering the hidden patterns and models that characterise the human mobility behaviour. However, due to the huge size of generated mobility data and the complexity of mobility analysis, new scalable algorithms for efficiently processing such data are needed. In this paper we are particularly interested in using traffic data for finding congested areas within a city. To this end we developed a new distributed and efficient strategy of the DBScan algorithm that uses MapReduce to detect what are the density areas. We conducted experiments using real traffic data of a brazilian city (Fortaleza) and compare our approach with centralized and map-reduce based DBSCAN approaches. Our preliminaries results confirm that our approach is scalable and more efficient than others competitors.

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