clumpformers

Clumpformers are a class of systems and algorithms designed to transform distributions of elements into localized aggregates called clumps. The term combines "clump," a localized group, with "form," indicating transformation. In data analysis and modeling, clumpformers seek representations that emphasize contiguity and local similarity, in contrast to global mixings.

Most clumpformers start from an initial partition of elements into tentative clumps. They assess proximities or affinities between elements, merge the closest members into existing clumps, and update clump prototypes. Convergence is declared when assignments stabilize or a pre-set number of iterations is reached. Some formulations allow splitting, pruning, or enforcing contiguity constraints to produce compact, interpretable clumps.

Variants include density-based clumpformers, which cluster based on local point density; hierarchical clumpformers, which produce multi-scale clump structures; and grid-based clumpformers, that discretize data space into cells and aggregate within cells.

Applications span data compression and visualization, image segmentation, geographic information systems, ecological modeling, and materials science for modeling particle aggregation. Like many clustering approaches, clumpformers can be sensitive to parameter choices and may struggle with non-contiguous or highly irregular cluster shapes. They typically require an appropriate distance or affinity measure and can be computationally intensive for large datasets.

See also: clustering, DBSCAN, k-means, watershed, regionalization.