Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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discounted cumulated impact (mild decay)

The discounted cumulated impact index (Järvelin and Pearson 2008; Ahlfren and Järvelin 2010) is designed to reduce the role of older citations, but still reward researchers for older publications receiving new citations. To begin, let cx represet the total number of citations received by a researcher to all of their publications in year x. Over a citation interval of Y years, the cumulated impact vector is simply the sum of these values from the first year to be considered (Y years ago) up through the current year. If the citation interval is the entire career of a researcher, this would be a vector of CP calculated each year. This raw vector incorporates citation counts without decay over time, i.e., old and new citations are treated equally. To incorporate a time decay, one divides the count of new citations each year by the logarithm of the number of years elapsed. The discounted cumulative impact vector is thus:

$$\text{DCI}_Y\left(i\right)=\left|\begin{matrix} \frac{c^i}{\max\left[1, \log_b\left(Y-1\right)\right]} & \text{if }i=1 \\ \text{DCI}_Y\left(i-1\right)+\frac{c^i}{\max\left[1, \log_b\left(Y-i\right)\right]} & \text{otherwise} \end{matrix} \right. ,$$

where b is the base of the logarithm used for scaling. Larger values of b discount older citations less than smaller values.

In this version we use a mild decay with b = 10.

History

YearDCI (b = 10)
1997[2.0000]
1998[2.0000, 13.0000]
1999[2.0000, 13.0000, 36.0000]
2000[2.0000, 13.0000, 36.0000, 67.0000]
2001[2.0000, 13.0000, 36.0000, 67.0000, 133.0000]
2002[2.0000, 13.0000, 36.0000, 67.0000, 133.0000, 240.0000]
2003[2.0000, 13.0000, 36.0000, 67.0000, 133.0000, 240.0000, 367.0000]
2004[2.0000, 13.0000, 36.0000, 67.0000, 133.0000, 240.0000, 367.0000, 585.0000]
2005[2.0000, 13.0000, 36.0000, 67.0000, 133.0000, 240.0000, 367.0000, 585.0000, 845.0000]
2006[2.0000, 13.0000, 36.0000, 67.0000, 133.0000, 240.0000, 367.0000, 585.0000, 845.0000, 1176.0000]
2007[2.0000, 13.0000, 36.0000, 67.0000, 133.0000, 240.0000, 367.0000, 585.0000, 845.0000, 1176.0000, 1509.0000]
2008[1.9205, 12.9205, 35.9205, 66.9205, 132.9205, 239.9205, 366.9205, 584.9205, 844.9205, 1175.9205, 1508.9205, 1889.9205]
2009[1.8533, 12.4160, 35.4160, 66.4160, 132.4160, 239.4160, 366.4160, 584.4160, 844.4160, 1175.4160, 1508.4160, 1889.4160, 2315.4160]
2010[1.7954, 11.9883, 34.0741, 65.0741, 131.0741, 238.0741, 365.0741, 583.0741, 843.0741, 1174.0741, 1507.0741, 1888.0741, 2314.0741, 2785.0741]
2011[1.7450, 11.6198, 32.9323, 62.7001, 128.7001, 235.7001, 362.7001, 580.7001, 840.7001, 1171.7001, 1504.7001, 1885.7001, 2311.7001, 2782.7001, 3212.7001]
2012[1.7005, 11.2981, 31.9454, 60.6709, 124.0476, 231.0476, 358.0476, 576.0476, 836.0476, 1167.0476, 1500.0476, 1881.0476, 2307.0476, 2778.0476, 3208.0476, 3594.0476]
2013[1.6610, 11.0140, 31.0815, 58.9106, 120.0681, 222.8151, 349.8151, 567.8151, 827.8151, 1158.8151, 1491.8151, 1872.8151, 2298.8151, 2769.8151, 3199.8151, 3585.8151, 4028.8151]
2014[1.6254, 10.7607, 30.3170, 57.3646, 116.6136, 215.7628, 337.7149, 555.7149, 815.7149, 1146.7149, 1479.7149, 1860.7149, 2286.7149, 2757.7149, 3187.7149, 3573.7149, 4016.7149, 4459.7149]
2015[1.5933, 10.5331, 29.6342, 55.9927, 113.5779, 209.6330, 327.3148, 536.6499, 796.6499, 1127.6499, 1460.6499, 1841.6499, 2267.6499, 2738.6499, 3168.6499, 3554.6499, 3997.6499, 4440.6499, 4863.6499]
2016[1.5640, 10.3271, 29.0194, 54.7644, 110.8825, 204.2403, 318.2497, 520.2547, 769.9203, 1100.9203, 1433.9203, 1814.9203, 2240.9203, 2711.9203, 3141.9203, 3527.9203, 3970.9203, 4413.9203, 4836.9203, 5250.9203]
2017[1.5372, 10.1394, 28.4621, 53.6561, 108.4680, 199.4473, 310.2552, 505.9563, 746.8797, 1064.7233, 1397.7233, 1778.7233, 2204.7233, 2675.7233, 3105.7233, 3491.7233, 3934.7233, 4377.7233, 4800.7233, 5214.7233, 5524.7233]

References