Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators

This paper presents the development and investigates the properties of ordered weighted learning vector quantization (LVQ) and clustering algorithms. These algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators. An axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions. Minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft LVQ and clustering algorithms, which includes fuzzy LVQ and clustering algorithms as special cases. The proposed LVQ and clustering algorithms are used to perform segmentation of magnetic resonance (MR) images of the brain. The diagnostic value of the segmented MR images provides the basis for evaluating a variety of ordered weighted LVQ and clustering algorithms.