Punctuated Similarity: Modeling Discontinuity in Representational Similarity Space

Pairwise similarity models describe the geometry of a population, but typically assume similarity changes smoothly with distance along a continuous dimension. This work introduces punctuated similarity, a model for when dissimilarity is instead concentrated at a specific, hypothesized point. Researchers specify a candidate point and evaluate the modeled structure against real similarity data. The model is demonstrated in two proof-of-concept analyses: puberty as a critical transition for child growth trajectories, and the COVID-19 pandemic as a transition point for stock market volatility. Both recovered the hypothesized transition as a point of localized dissimilarity. An open-source R package implementing the model is included as part of this work.