Assessing the Scientific Impact of Individual Scholars With Multi-Scale H-Index

Quantitative evaluation on the individual’s scientific impact is an important research topic in the academic evaluation fields. Following the pioneering milestone of h-index, many variants have been proposed and but still suffer some limitations. In this paper, we propose a novel multi-scale h-index (MH-index, or Ma-Huang index) to comprehensively measure the scientific impact of scholars based on the publication record. We investigate the index from the mathematical perspective of correlation function between citation count and paper number. We reveal that different definitions of the correlation function lead to different index schemes. By defining the correlation functions with gradually varied slope, we can obtain a series of index elements, each of which captures the citation record in different granularities. Our approach can be essentially interpreted as a generalized h-index in multiple scales, which is obtained by first generating a multi-scale representation of a scholar’s paper citation record and then calculating the h-index score for each scale. Our approach can be extended to consider all publication citations and subtly emphasizes those highly cited publications. To validate the proposed indicators, an experimental study is conducted on 82 scholars in the scientometrics field and comparison is made with several existing indices. Our proposed MH-index is demonstrated to be more balanced and fine-grained for evaluating and comparing the scientific impact of individual scientists.