Evolutionary Biological Data Science Laboratory

academic trace

The Academic Trace (Ye and Leydesdorff 2014; Ye et al. 2017) starts by taking the concept of the citation curve and describing it as three vectors of information. The first vector (X) separates publications into those in the core (X₁), those in the tail with at least one citation (X₂), and those with zero citations (X₃). These three values are each calculated as the square of the count of publications in each category, divided by the total number of publications. The second vector (Y) separates citations into those in the core block (Y₁), those in the tail (Y₂), and the excess citations in the core above the core block (Y₃). These values are calculated as the square of the count of citations within each category, divided by the total citation. The third vector (Z) contrasts particularly highly cited publications and those with zero citations, and is simply the difference of the corresponding values of the first two vectors, X₁ - Y₁, X₂ - Y₂, and X₃ - Y₃. These vectors form a 3D matrix, the trace of which is a measure of academic performance. The trace can be determined as X₁ + Y₂ + Z₃; a "shortcut" formula (Ding et al. 2020) is as follows:

$$tr\left(V\right)=\frac{h^4+\left(C^h-h^2\right)^2}{C^P} + \frac{\left( P-h-P_z\right)^2-P_z^2}{P}.$$

where P_z is the number of publications with zero citations and the rest of the values have been defined earlier.

Example

Publications are ordered by number of citations, from highest to lowest.

Citations (Ci)	57	26	16	12	11	10	4	3	2	1	1	1	1	0	0	0	0	0
Rank (i)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
						h = 6

The h-index is 6; the total number of citations (C^P) is 145; the number of citations in the top h publications (C^h) is 132; the total number of publications (P) is 18; and the number of publications with zero citations (P_z) is 5. Entered in the above formula, the academic trace is 73.8299.

History