33: Statistical Inference for Fuzzy Clustering

Thomas M. Menino Convention & Exhibition Center 

Clustering is widely used in biomedical research to identify heterogeneous patient subpopulations with diffuse boundaries. While fuzzy c-means (FCM) allows mixed memberships, statistical inference for fuzzy clustering remains limited.

We propose weighted fuzzy c-means (WFCM) framework for settings with cluster-size imbalance. Cluster-specific weights prevent small clusters from being dominated and induce a likelihood-based model. Estimation is performed via a majorize–minimize algorithm, enabling likelihood-ratio tests and bootstrap confidence intervals. We establish consistency and asymptotic normality of the estimator. Simulation studies demonstrate improved accuracy and uncertainty quantification under imbalance. The method is robust to tuning choices and scales well to moderate dimensions. It provides interpretable soft memberships that reflect continuous disease or cellular states. Applications to RNA-seq and ADNI data show stable uncertainty quantification and biologically meaningful soft memberships, ranging from imbalanced cell populations to a graded Alzheimer's disease progression.

Clustering

Inference

FCM

weighted Fuzzy c-means 

Section on Statistical Learning and Data Science