Archetypal analysis for interval data in marketing research

A typical problem in marketing research consists of segmenting and clustering products and/or consumers. However, classical cluster analysis and segmentation may fail in the interpretability as they tend to identify average consumers or products, sometimes not well-separated. In this framework, archetypal analysis has been introduced to find extreme segments and well separated typical consumers. On the other hand, we notice that often product attributes and consumer preferences could be more adequately expressed by a range of values in which attributes/preferences may vary. To face these two issues, in this work, we propose an extension of archetypal analysis to the case of interval data, providing a definition of archetypes using the Hausdorff distance, analizing their geometric properties, and offering some appropriate visualization tools. We present also an illustrative example on preference data.