A research paper proposes Generalized Sparse Fuzzy Clustering (GSFC), a framework designed to address two limitations of conventional fuzzy clustering: its tendency to assign every data point to every cluster, and its reliance on knowing the number of clusters beforehand.
The method adds a continuous sparsity penalty to the fuzzy clustering objective. The researchers say this can drive negligible membership values to exactly zero, allowing the algorithm to prune redundant clusters. GSFC starts with more candidate clusters than the data is expected to contain, then estimates the cluster count as redundant candidates are removed.
To optimize the objective, the framework combines a primal-dual bisection search with analytic procedures that enforce the requirement that each point’s membership values sum to one. It also includes a virtual noise cluster intended to absorb outliers and reduce their influence on cluster representatives.
The paper describes two versions of the approach: one for compact clusters and another for elongated structures. The latter is applied to line-segment detection, where the authors report that sparse assignments help identify intersecting segments. Their evaluations cover synthetic data, high-noise geometric tests, the UCI wine dataset and hyperspectral images. The authors report that GSFC performed better than conventional fuzzy benchmarks and outperformed sparse possibilistic and probabilistic alternatives in line-detection tasks.
The work is presented in the paper “A Generalized Sparse Fuzzy Clustering Framework with Automated Cluster Cardinality Estimation Ability,” listed on arXiv as 2611.00159v1.
Sources: arXiv cs.AI.