2016/08/15 by Jared Culbertson, Culbertson, Jared, Dan P. Guralnik +5 · 1 citation
Computer Science · Mathematics · #51K05 #68P01 #Advanced Clustering Algorithms Research #Data Management and Algorithms #FOS: Computer and information sciences #H.3.3 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis #acm:51K05 #acm:68P01 #cs.LG #msc:51K05 #msc:68P01 #stat.ML
paper · pdf · doi:10.48550/arxiv.1608.04331
12 pages
arxiv created 2016/08/15 · openalex publication_date 2016/08/15 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information content.