Representing asymmetric relationships by h-plots. Discovering the archetypal patterns of cross-journal citation relationships
Aleix Alcacer, Irene Epifanio
TL;DR
This paper tackles the challenge of representing asymmetric, non-metric proximity data by introducing the h-plot, which embeds proximity-defining variables rather than objects themselves. It couples the h-plot with archetypoid analysis (ADA) to identify archetypal journals and express other journals as convex combinations of these archetypoids, enabling interpretable, boundary-based summaries. On a dataset of 25 statistics journals, the authors achieve a 2D goodness-of-fit of 74.3% and reveal three archetypal journals that span theoretical/methodological, applied/computational, and specialized domains, with ADA mixtures providing nuanced journal profiles. The approach outperforms multidimensional unfolding and network representations in capturing asymmetric cross-journal relationships and offers reproducible code and data, supporting scalable, interpretable analysis with potential extensions to robustness and symbolic/ supervised settings.
Abstract
This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the method embeds the variables that define the proximity to or from each object. It is straightforward to implement, and the quality of the resulting representation can be easily evaluated. The methodology is illustrated by visualizing the asymmetric relationships between the citing and cited profiles of journals on a common map. Two profiles that are far apart (or close together) in the h-plot, as measured by Euclidean distance, are different (or similar), respectively. This representation allows archetypoid analysis (ADA) to be calculated. ADA is used to find archetypal journals (or extreme cases). We can represent the dataset as convex combinations of these archetypal journals, making the results easy to interpret, even for non-experts. Comparisons with other methodologies are carried out, showing the good performance of our proposal. Code and data are available for reproducibility.