Consistency constraints for overlapping data clustering
This work addresses theoretical limitations in clustering methods for overlapping data, which is incremental as it builds on existing functorial frameworks.
The paper tackles the problem of overlapping data clustering by introducing functorial constraints to avoid chaining issues in partition-based methods, showing that any clustering functor must refine single-linkage clusters and be refined by maximal-linkage clusters.
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.