New developments and applications of Archetypal Analysis

Abstract

This thesis advances data analysis through innovative methodologies centered on archetypal analysis (AA) and its extensions. It introduces archetypoid analysis for classifying foot shapes, improving footwear design by identifying archetypal profiles within a database of 3D foot scans. This approach, more effective than traditional clustering, is extended to integrate consumer preferences for better size prediction in online shoe shopping. Novel methods in data compression using AA with fuzzy clustering are introduced for efficient image data handling. Additionally, a new anomaly detection technique combines AA with k-nearest neighbors, enhancing performance in varied applications from computer vision to signal processing. The thesis also presents biarchetype analysis (BiAA) for concurrent analysis of observations and features, outperforming biclustering in interpretability. An open-source Python package, \texttt{archetypes}, is developed to facilitate the application of these analyses. Lastly, it improves ordinal classification by incorporating interval-valued data, providing robust solutions to practical and theoretical challenges.