Analysing the variation tendencies of the numbers of yearly citations for sleeping beauties in science by using derivative analysis

Abstract

To comprehensively characterize the citation histories of sleeping beauties (SBs), this paper presents a derivative analysis of SB citation curves. Derivative analysis can differentiate among periods with different variation tendencies (ascending, declining or unchanged) in the number of yearly citations; these variation tendencies can be identified from successive (positive, negative or zero) derivatives. To overcome the interference caused by fluctuations in the citation curves, a smoothing method is first applied. A sleeping period appears in a citation curve as a horizontal region with a low citation count. During an awakening period, the derivatives of the curve are positive and may include a few zeros. Some SBs experience a rapid increase in yearly citations once awakened and have a short awakening period, whereas for others, the number of yearly citations increases steadily over a long awakening period. Different SBs can also show different forms based on the change in the number of yearly citations after they reach their peak, and these forms can also be distinguished through derivative analysis. Derivative analysis can be used alone to identify SBs and determine their awakening times or in combination with other methods of identifying SBs to improve their performance by assisting in the identification of abnormal SBs. Derivative analysis enables the “beauty coefficient’’ method (Ke et al. in Proc Natl Acad Sci USA 112(24):7426–7431, 2015) to determine awakening times that do not vary over time, thereby making Ke et al.’s method immune to interference due to citation fluctuations. It also allows one to determine multiple awakening times for a single SB.