The taxonomy of foot shapes or other parts of the body is important, especially for design purposes. We propose a methodology based on archetypoid analysis (ADA) that overcomes the weaknesses of previous methodologies used to establish typologies. ADA is an objective, data-driven methodology that seeks extreme patterns, the archetypal profiles in the data. ADA also explains the data as percentages of the archetypal patterns, which makes this technique understandable and accessible even for non-experts. Clustering techniques are usually considered for establishing taxonomies, but we will show that finding the purest or most extreme patterns is more appropriate than using the central points returned by clustering techniques. We apply the methodology to an anthropometric database of 775 3D right foot scans representing the Spanish adult female and male population for footwear design. Each foot is described by a 5626 × 3 configuration matrix of landmarks. No multivariate features are used for establishing the taxonomy, but all the information gathered from the 3D scanning is employed. We use ADA for shapes described by landmarks. Women’s and men’s feet are analyzed separately. We have analyzed 3 archetypal feet for both men and women. These archetypal feet could not have been recovered using multivariate techniques.

Size mismatch is a serious problem in online footwear purchase because size mismatch implies an almost sure return. Not only foot measurements are important in selecting a size, but also user preference. This is the reason we propose several methodologies that combine the information provided by a classifier with anthropometric measurements and user preference information through user-based collaborative filtering. As novelties: (1) the information sources are 3D foot measurements from a low-cost 3D foot digitizer, past purchases and self-reported size; (2) we propose to use an ordinal classifier after imputing missing data with different options based on the use of collaborative filtering; (3) we also propose an ensemble of ordinal classification and collaborative filtering results; and (4) several methodologies based on clustering and archetype analysis are introduced as user-based collaborative filtering for the first time. The hybrid methodologies were tested in a simulation study, and they were also applied to a dataset of Spanish footwear users. The results show that combining the information from both sources predicts the foot size better and the new proposals provide better accuracy than the classic alternatives considered.

We introduce a novel exploratory technique, termed biarchetype analysis, which extends archetype analysis to simultaneously identify archetypes of both observations and features. This innovative unsupervised machine learning tool aims to represent observations and features through instances of pure types, or biarchetypes, which are easily interpretable as they embody mixtures of observations and features. Furthermore, the observations and features are expressed as mixtures of the biarchetypes, which makes the structure of the data easier to understand. We propose an algorithm to solve biarchetype analysis. Although clustering is not the primary aim of this technique, biarchetype analysis is demonstrated to offer significant advantages over biclustering methods, particularly in terms of interpretability. This is attributed to biarchetypes being extreme instances, in contrast to the centroids produced by biclustering, which inherently enhances human comprehension. The application of biarchetype analysis across various machine learning challenges underscores its value.