Advanced Deformation Models and Adaptive Mechanisms in Elastic Patterns

The concept of Elastic Patterns was originally proposed as a prototype-based classification approach that unifies perspectives from cognitive psychology, fuzzy logic, and physics. At their core, Elastic Patterns operate across two levels of deformation: a parameter-level deformation, quantified in terms of axial strain, and a pattern-level deformation, understood as the accumulation of deformation energy to perfectly fit the sample to be classified. This dual representation supports an interpretable and adaptive recognition mechanism, where classification emerges from selecting the Elastic Pattern that requires the minimal deformation energy to align with a real case to classify. This paper extends the theoretical and practical foundations of the proposed Elastic Patterns approach for adaptive pattern classification by introducing several deformation models, Spring Hardening, Weighted Spring Deformation, or Group Parameter Deformation to improve the capacity of Elastic Patterns to adapt to different contexts. These deformation models allow the proposal to adapt to different semantic contexts by controlling how parameter contraction and elongation are penalised. Additionally, novel adaptive mechanisms are introduced, which enable Elastic Patterns to dynamically adjust parameter relevance, capture inter-parameter dependencies, and better reflect contextual knowledge. Furthermore, the framework offers inherently interpretable classification via explicit parameter deformations and energies, avoiding post hoc explanations.