**6. Conclusions**

Detecting urban hotspots in smart cities is a challenging task, due to the fact that geo-spatial urban data, e.g., traffic, crimes, mobility, and events, are generally characterized by multiple densities that can differ widely from one area to another. This paper discussed research issues, challenges and approaches to discover multi-density hotspots in urban areas. Then, it compared the performance of four approaches (i.e., DBSCAN, OPTICSxi, HDBSCAN, and CHD) available in the literature, and analyzed their performance on synthetic and real-world data. The evaluation on synthetic datasets was performed considering the best parameter setting for each algorithm, selected by a parameter sweeping methodology taking into account several quantitative clustering indexes. Similarly, a qualitative comparison of the different algorithms was performed on real urban data. Overall, the results showed that multi-density clustering algorithms (CHD and HDBSCAN) outperform classic density-based algorithms (DBSCAN and OPTICS-xi) when analyzing data characterized by multiple densities. Therefore, multi-density approaches are more appropriate for urban hotspot detection.

**Author Contributions:** Conceptualization, E.C. and A.V.; methodology, E.C. and A.V.; software, P.L. and A.V.; validation, E.C. and P.L.; formal analysis, E.C., P.L. and A.V.; investigation, P.L. and A.V.; resources, E.C. and P.L.; data curation, E.C., P.L. and A.V.; writing—original draft preparation, E.C. and A.V.; writing—review and editing, E.C., P.L. and A.V.; visualization, E.C., P.L. and A.V.; supervision, E.C. and A.V.; funding acquisition, E.C. and A.V.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been partially supported by the "ICSC National Centre for HPC, Big Data and Quantum Computing" (CN00000013) within the NextGenerationEU program, and by European Union—NextGenerationEU—National Recovery and Resilience Plan (Piano Nazionale di Ripresa e Resilienza, PNRR)—Project: "SoBigData.it—Strengthening the Italian RI for Social Mining and Big Data Analytics"—Prot. IR0000013—Avviso n. 3264 del 28/12/2021.

**Data Availability Statement:** The analyzed datasets are available as follows. The chess dataset is available at https://gitlab.com/chd3/datasets, accessed on 28 December 2022. The compound dataset is available at http://cs.joensuu.fi/sipu/datasets/, accessed on 18 December 2022. The Chicago "Crimes—2001 to present" dataset is available at https://data.cityofchicago.org/Public-Safety/Crimes-2001-to-Present/ijzp-q8t2, accessed on 18 December 2022.

**Conflicts of Interest:** The authors declare no conflict of interest.
