Design Variety Measurement Using Sharma-Mittal Entropy

Design variety metrics measure how much a design space is explored. This article proposes that a generalized class of entropy metrics based on Sharma-Mittal entropy offers advantages over existing methods to measure design variety. We show that an exemplar metric from Sharma-Mittal entropy, namely, the Herfindahl-Hirschman index for design (HHID) has the following desirable advantages over existing metrics: (a) more accuracy: it better aligns with human ratings compared to existing and commonly used tree-based metrics for two new datasets; (b) higher sensitivity: it has higher sensitivity compared to existing methods when distinguishing between the variety of sets; (c) allows efficient optimization: it is a submodular function, which enables one to optimize design variety using a polynomial time greedy algorithm; and (d) generalizes to multiple metrics: many existing metrics can be derived by changing the parameters of this metric, which allows a researcher to fit the metric to better represent variety for new domains. This article also contributes a procedure for comparing metrics used to measure variety via constructing ground truth datasets from pairwise comparisons. Overall, our results shed light on some qualities that good design variety metrics should possess and the nontrivial challenges associated with collecting the data needed to measure those qualities.