A parameter-free index for identifying under-cited sleeping beauties in science

We developed a systematic methodology for identifying the under-cited (or not-so-highly cited) Sleeping Beauty (SB) publications and tried to figure out their key characteristics. Based on the identification framework of "beauty coefficient" (B) introduced by Ke et al. (Proc Natl Acad Sci USA 112:7426-7431, 2015), taking into account the whole citation history of the publications concerned, we substituted yearly citations in "beauty coefficient" with yearly cumulative percentage of citations, and eliminated the denominator in "beauty coefficient" since the curve of a given document's cumulative citations is always monotonically increasing if only the document is cited. The value of the modified beauty coefficient is denoted as Bcp. We also redefined the awakening year, sleeping length and sleeping depth within the Bcp framework with the intention of avoiding arbitrary thresholds as much as possible. We tested the new index using the data of SB articles identified from Science and Nature. The results showed that Bcp is more sensitive in identifying the "lower level SBs", which refers to the case when the total citations and the maximum annual citations of SBs are not so high in comparison with other typical SBs. Bcp works better than B in at least two aspects: (1) it "punishes" the situations when the SBs experienced early citations instead of continuous sleeping; (2) it allows for comparing the extent of delayed citation impact of publications in different fields with different citation patterns. We also figured out some key characteristics of such SB publications and pondered some policy implications about the associations of SB publications with transformative research, research front and research evaluation.