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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 Pz 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)592616111110433211100000
Rank (i)123456789101112131415161718
h = 6

The h-index is 6; the total number of citations (CP) is 148; the number of citations in the top h publications (Ch) is 133; the total number of publications (P) is 18; and the number of publications with zero citations (Pz) is 5. Entered in the above formula, the academic trace is 73.6644.

History

Yeartr(V)
1997-2.0000
19985.4375
199920.9924
200034.8361
200173.6644
2002116.4538
2003175.5319
2004303.4853
2005472.9897
2006734.8057
2007994.6057
20081306.5250
20091618.5271
20102010.5558
20112447.9727
20122890.4928
20133482.6885
20144058.6488
20154592.1852
20165200.4650
20175659.2860
20186200.0213
20196741.9163
20207207.5655
20217709.2457
20228206.1775
20238718.4258
20249177.3679
20259296.9721

References