Soft Learning Vector Quantization and Clustering Algorithms Based on Mean-type Aggregation Operators

This paper presents a framework for developing soft learning vector quantization (LVQ) and clustering algorithms by minimizing reformulation functions based on aggregation operators. An axiomatic approach provides conditions for selecting the subset of all aggregation operators that lead to admissible reformulation functions. For mean-type aggregation operators, the construction of admissible reformulation functions reduces to the selection of admissible generator functions. Nonlinear generator functions result in a broad family of soft LVQ and clustering algorithms, which include fuzzy LVQ and clustering algorithms as special cases. The formulation considered in this paper also provides the basis for exploring the structure of the feature set by identifying outliers in the data. The procedure described in this paper for identifying outliers in the feature set is tested on a set of vowel data.