Abstract
The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate clustering results. A very popular measure is the Silhouette. We discuss the efficient medoid-based variant of the Silhouette, perform a theoretical analysis of its properties, and provide two fast versions for the direct optimization. We combine ideas from the original Silhouette with the well-known PAM algorithm and its latest improvements FasterPAM. One of the versions guarantees equal results to the original variant and provides a run speedup of \(O(k^2)\). In experiments on real data with 30000 samples and k = 100, we observed a 10464\(\times \) speedup compared to the original PAMMEDSIL algorithm.
Part of the work on this paper has been supported by Deutsche Forschungsgemeinschaft (DFG) – project number 124020371 – within the Collaborative Research Center SFB 876 “Providing Information by Resource-Constrained Analysis” project A2.
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Lenssen, L., Schubert, E. (2022). Clustering by Direct Optimization of the Medoid Silhouette. In: Skopal, T., Falchi, F., Lokoč, J., Sapino, M.L., Bartolini, I., Patella, M. (eds) Similarity Search and Applications. SISAP 2022. Lecture Notes in Computer Science, vol 13590. Springer, Cham. https://doi.org/10.1007/978-3-031-17849-8_15
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