Elastic Patterns: A Deformation-Based Approach to Interpretable Classification

Elastic Patterns are presented as a novel approach to prototype-based pattern classification that integrates concepts from cognitive psychology, fuzzy logic, and physics. Traditional prototypes are revisited through their different formulations: psychological prototypes as central category elements, Fuzzy Prototypes addressing vagueness, and Deformable Prototypes incorporating elasticity to adapt to data variability. Elastic Patterns extend these ideas by representing each parameter as an independent elastic component, conceptualized as springs, which deform to fit new cases while minimizing deformation energy. Elastic Patterns operate at two levels: parameter-level deformation, measured through axial strain, and pattern-level deformation, expressed as cumulative deformation energy. This structure enables a transparent and adaptive recognition process, where classification is achieved by selecting the pattern requiring the least energy to deform. A case study on the MNIST dataset validates the proposal, achieving approximately 80% accuracy and reducing the need for extensive preprocessing. These results indicate that Elastic Patterns offer a promising alternative to conventional methods, combining interpretability, adaptability, and physical grounding in pattern recognition tasks.