The "academic trace" of the performance matrix: A mathematical synthesis of the h-index and the integrated impact indicator (I3)

• Published in: Journal of the Association for Information Science and Technology Vol. 65; no. 4; pp. 742 - 750
• Main Authors: Ye, Fred Y., Leydesdorff, Loet
• Format: Journal Article
• Language: English
• Published: Malden, MA Blackwell Publishing Ltd 01-04-2014; Wiley
• Subjects: Bibliometrics; Bibliometrics. Scientometrics; Bibliometrics. Scientometrics. Evaluation; Construction; Dimensional measurements; Documents; Exact sciences and technology; Hirsch index; Indicators; Information and communication sciences; Information science. Documentation; informetrics; Library and information science. General aspects; Mathematical analysis; Sciences and techniques of general use; Scientific papers; Synthesis; Vectors (mathematics); Weighting; Hirsch index; Citation; Periodical; Indicator
• ISSN: 2330-1635; 2330-1643
• DOI: 10.1002/asi.23075

The h‐index provides us with 9 natural classes which can be written as a matrix of 3 vectors. The 3 vectors are: X = (X1, X2, X3) and indicates publication distribution in the h‐core, the h‐tail, and the uncited ones, respectively; Y = (Y1, Y2, Y3) denotes the citation distribution of the h‐core, the h‐tail and the so‐called “excess” citations (above the h‐threshold), respectively; and Z = (Z1, Z2, Z3) = (Y1‐X1, Y2‐X2, Y3‐X3). The matrix V = (X,Y,Z)T constructs a measure of academic performance, in which the 9 numbers can all be provided with meanings in different dimensions. The “academic trace” tr(V) of this matrix follows naturally, and contributes a unique indicator for total academic achievements by summarizing and weighting the accumulation of publications and citations. This measure can also be used to combine the advantages of the h‐index and the integrated impact indicator (I3) into a single number with a meaningful interpretation of the values. We illustrate the use of tr(V) for the cases of 2 journal sets, 2 universities, and ourselves as 2 individual authors.