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The "Academic Trace" of the Performance Matrix: A Mathematical Synthesis of the h-Index and the Integrated Impact Indicator (I3)

The h-index provides us with nine natural classes which can be written as a matrix of three vectors. The three vectors are: X=(X1, X2, X3) indicate publication distribution in the h-core, the h-tail, and the uncited ones, respectively; Y=(Y1, Y2, Y3) denote 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 nine 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 two journal sets, two universities, and ourselves as two individual authors.