EM and EM'-index sequence: Construction and application in scientific assessment of scholars

06/26/2018 ∙ by Anand Bihari, et al. ∙ NIT Patna 0

Most of the scientometric indicators use only the total number of citations of an article and produce a single number for scientific assessment of scholars. Although this concept is very simple to compute, it fails to show the scientific productivity and impact of scholars during a time-span or in a year. To overcome this, several time series indicators have been proposed that consider the citations from the entire research career of a scholar. However, these indicators fail to give a comparative assessment of two scholars having same or very similar index value. To overcome this shortcoming, h-index sequence was proposed to assess the impact of scholars during a particular time-span and to compare multiple scholars at a similar stage in their careers. The h-index sequence is based on the h-index formulation. One of the main issues related to the h-index is that it completely ignores the excess citation in scientific assessment; h-index sequence also exhibits a similar behaviour. To overcome these limitations, in this article, we have discussed the EM and EM^'-index sequence, and performed an empirical study based on yearly citation count earned from all publications of 89 scholars' publication data. The element of the EM and EM^'-index sequence for a given year shows the impact of a scholar for that year. We conclude that the EM and EM^'-index sequence could be used as an alternative metrics to asses the impact of scholars.

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1 Introduction

The scientometrics and bibliometrics indicators play a key role in the scientific assessment of scholars and are also used in faculty promotion in colleges/universities, scientific award distribution and project funding etc. King (1987). One of the most influential scientometrics/bibliometrics indicator h-index, proposed by Hirsch (2005), considers productivity as well as impact of scholars. However, this indicator suffers with several drawbacks that restrict its use in comparing scholars having similar index values computed based on their entire research careers. Several studies have been done to overcome this drawback and increase the acceptability in the scientific assessment (Rousseau (2006); Bornmann et al. (2008); Rousseau and Leuven (2008); Alonso et al. (2009); Rosenberg (2014); Wildgaard et al. (2014)). Generally, most of the indicators produced only a single number to asses the scientific impact of the entire career of the scholars. However, instead of a single number, a set of indicators seem to be more justified in this case. In this context, first Liang (2006) proposed the h-index sequence. The h-index sequence is the set of h-index values computed from yearly citation counts, where the sequence elements were computed in the reverse chronological order of the academic careers of the scholars, i.e., recent publications being considered first. However, Egghe (2009) mentioned that the calculation of sequence in the forward direction of time is more precise than the reverse direction, and it is easy to understand as well. Liu and Rousseau (2008) defined 10 different types of time series h-index sequences. Fred and Rousseau (2008) discussed the relationship between the power law model and the h-index sequence using values (discussed in Egghe’s sequences). Wu et al. (2011) performed an empirical study of real career h-index sequence based on values (discussed in Egghe’s sequences). Liu and Yang (2014) performed an empirical study of h-index sequence based on yearly citation performance of cumulative publications using values obtained from Egghe’s sequences. The authors proposed L-sequence obtained from . However, all of the above h-index based sequences consider only the citation and completely ignore the importance of excess citation. Another issue is that they do not consider all the items in the computation of sequences, whereas the articles that are cited even once have significance in scientific assessment. To overcome this, Bihari and Tripathi (2017) proposed a new measure called EM-index and -index. The EM-index gives full credit to highly influential articles, whereas the -index considers all articles that are cited even once.

This article proposes the EM and -index sequence as an effective way to evaluate the scientific impact of scholars. The EM and -index sequence is the sum of the elements calculated using EM and -index formula respectively. In this article, first we discuss EM-index, -index and L-sequence (Sec. 2). Then we discuss the comparative empirical analysis of EM and -index sequence done on yearly citation count earned from all the articles in the dataset of 89 scholars used in Bihari and Tripathi (2018). The experimental results highlight the properties of EM and -index sequence that reflect the overall impact of scholars. Used this way, we show that EM and -index sequence provide an alternative superior way to evaluate the scientific impact of scholars.

2 Background

The h-index, as proposed in Hirsch (2005), is described as: “The h-index of a scholar is if of his/her publications have at least citations each and the rest of the publications may have or less citations.”

This index attracted attention from the research community due to its characteristics, however, it has several limitations. In general, it seems that the most of the indicators give only a single number to show the scientific impact of scholars, but they do not differentiate between scholars having similar index values. Further, they do not take into account the career-duration of scholars. The primary limitation of h-index is that it completely ignores the excess citation (i.e., over and above ) of articles.

Example: Let 15 articles be published by scholar A with the following citation counts Cit={30, 30, 25, 22, 22, 21, 15, 15, 14, 10, 10, 10, 9, 8, 1 }. Let 15 articles be also published by scholar B with the following citation counts cit={10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 0}. In both the cases, the h-index value is 10, however, the scientific impact of scholar A is more than that of scholar B because scholar A has (i) more citation counts for each article and (ii) non-zero citation counts for h-tail articles when compared to scholar B who has zero citation count for h-tail articles. This shows that h-index may not be a good measure for comparative scientific assessment of scholars because it does not give any extra credit to excess citations and h-tail articles.

To overcome this shortcoming of h-index, the EM-index was proposed by Bihari and Tripathi (2017); and is defined as: “The EM-index of an author is the square root of the sum of the elements of the EM-index.” Here, the elements of the EM-index of an author are the h-index values computed from the h-core article citation count at multiple levels. The first element of the EM-index is the original h-index and the subsequent elements are the h-index values from the excess citation count of the h-core articles. In the previous example, if we consider the citation count of author A, the components of EM-index are {10, 6, 5, 3, 2, 2, 2} and the EM-index is 5.48. Author B has only one component of EM-index as {10} and the EM-index is 3.2. Clearly, the EM-index captures the significant difference in the scientific impact of these two authors.

The EM-index considers the impact of the excess citation count of the h-core articles, which is not considered in the h-index, but is helpful to differentiate between two different scholars having similar index values. However, the h-index and the EM-index do not consider the impact of all those articles that have been cited even once. If we look at the citation counts of author A, there are some articles having citation count equal to the h-index or less than that. However, both the h-index and the EM-index do not consider the impact of citation counts of such articles. To overcome this, a new indicator was proposed by Bihari and Tripathi (2017) named -index. This index is the multidimensional extension of the EM-index.

In spite of the progress so far, none of the above mentioned indices consider the career-duration of scholars, making it difficult to gauge the impact of a scholar at a particular stage of his/her career. Several articles have been published on this problem; Mahbuba and Rousseau (2013, 2016); Liu and Yang (2014) and Bihari and Tripathi (2018) are the recent ones among them. Mahbuba and Rousseau (2013, 2016) discussed the year based h-index that considers year wise impact of scholars based on (i) the total number of citations earned in a particular year, (ii) the total number of citations from all publications that are published in a particular year, and (iii) the total number of publications in a particular year. These year based indices still suffer with h-index limitations. To overcome the year based h-index excess citations problem, Bihari and Tripathi (2018) proposed year based EM and -index. The year based indicators cover the entire career of scholars, however they do not consider the year wise impact of scholars. To overcome this issue of year based indices, Liu and Yang (2014) studied the h-index sequence and proposed a new index called L-sequence. L-sequence considers the entire research career of a scholar to determine the scientific impact. To define L-sequence, consider a scholar who has published articles in his/her career. Let the first publication year be and the current year be . Then, the L-sequence of an author for year, denoted , is the h-index value computed on the basis of citation counts of all publications received in the year. Thus, the L-sequence of the author is .

The computation of L-sequence is based on h-index, but it does not account for the impact of excess citations and the h-tail items.

From the above discussion, it can be concluded that the scientific assessment of scholars is done with the help of citations earned by all articles, however, the career-duration of scholars is not considered, which is also significant in scientific assessment. To overcome this, we propose EM and -index sequence, which are described next

3 EM-index Sequence

As discussed in the previous section (sec: 2), the year based indices consider only the total number of citations earned by all publications in a particular year to produce a single number for scientific assessment. In this process, they ignore yearly impact of scholars. Instead of a single number, a set of numbers capturing the yearly impact of scholars will be more suited to evaluate and compare the performance of scholars. To this end, we introduce EM-index sequence based on yearly citations received by all publications.
Definition of EM-index Sequence
Let the research career of a scholar span years, publishing articles. Let be the year in which his/her first publication is published. Let the current year be . The EM-index sequence element for the year, denoted , is calculated from the citation count in year using the EM-index formula given in Bihari and Tripathi (2017). Then, the EM-index sequence value is computed as the sum of all such EM-index sequence elements. Formally,

(1)

For example, consider the scientific research history and impact of author Andrew D. Jackson (Source: Web of Science) as shown in Table 1. The corresponding EM-index sequence elements are 2.24, 2.65, 3.16, 2.83, 2.24, 3.16, 3.74, 3, 3.32, 2.45 & 1.73 and the EM-index sequence value is 29.17.

Publication Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
2006 11 9 11 15 12 11 20 14 16 11 5
2007 4 6 9 8 5 10 13 8 4 2 0
2007 0 0 0 0 0 0 0 0 0 0 0
2008 0 1 10 4 4 5 7 6 4 5 1
2008 0 0 0 0 0 1 0 0 0 0 0
2008 0 0 0 0 0 0 0 0 0 0 0
2009 0 0 0 3 5 9 4 6 10 6 2
2009 0 0 0 0 0 2 0 1 0 0 0
2010 0 0 0 0 1 0 0 0 0 0 0
2011 0 0 0 0 1 3 3 4 2 1 0
2013 0 0 0 0 0 0 0 1 1 1 1
2013 0 0 0 0 0 0 0 0 1 0 0
2013 0 0 0 0 0 0 0 0 0 0 0
2013 0 0 0 0 0 0 0 0 0 0 0
2014 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 1 1 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2016 0 0 0 0 0 0 0 0 0 1 0
2016 0 0 0 0 0 0 0 0 0 0 0
2016 0 0 0 0 0 0 0 0 0 0 0
2016 0 0 0 0 0 0 0 0 0 0 0
2017 0 0 0 0 0 0 0 0 0 0 0
EM-index 2.24 2.65 3.16 2.83 2.24 3.16 3.74 3 3.32 2.45 1.73
Table 1: Publication history and year wise impact of Author Andrew D. Jackson

4 Empirical Study of EM-index-sequence

In this section, we present an empirical study of EM-index sequence over the h-index sequence, h-index, EM-index, -index and year based EM-index by citations. The study illustrates the merit of EM-index sequence in comparison to others. To do this, we have used the publication-data of 89 scholars from reference Bihari and Tripathi (2018). Among the 89 scholars, most of them are working in scientometric and biblometrics fields of research. The h-index, EM-index, -index, year based EM-index by citations, h-index sequence and EM-index sequence for all 89 scholars is shown in Figure 1. As can be seen, there is significant variation in the indices values of all scholars. Table 2 shows the corresponding EM-index sequence value for each of the 89 scholars.

(a) The h-index of all Scholars
(b) The EM-index of all Scholars
(c) The -index of all Scholars
(d) The Year based EM-index by citations of all Scholars
(c) The h-index sequence of all Scholars
(d) The EM-index sequence of all Scholars
Figure 1: h-index, EM-index, -index, year based EM-index by citations, h-index sequence and EM-index sequence for the publication-data of 89 scholars from reference Bihari and Tripathi (2018)
ID Author EM-index Sequence ID Author EM-index Sequence
1 Adamantios Diamantopoulos 55.24 46 Lokman Meho 40.81
2 Albert Zomaya 39.06 47 Luca Mastrogiacomo 17.26
3 Alireza Abbasi 30.85 48 Ludo Waltman 44.00
4 Andrs Schubert 36.16 49 Lutz bornmann 47.42
5 Andrs Telcs 18.39 50 Maisano, DA 12.70
6 Andreas Thor 29.17 51 Marek Kosmulski 42.35
7 Andrew D. Jackson 30.51 52 Maria Bordons 28.49
8 Anne-Wil 36.07 53 Mark Fine 17.89
9 Aric Hagberg 35.29 54 Mark Newman 43.74
10 Barry Bozeman 37.23 55 Mathieu Ouimet 25.01
11 Ben R Martin 23.98 56 Matja Perc 73.17
12 Benny Lautrup 23.00 57 Matthew O. Jackson 41.33
13 Berwin Turlach 13.73 58 Mauno Vihinen 58.17
14 Birger Larsen 20.44 59 Michael Jennions 59.89
15 Blaise Cronin 36.21 60 Michael L. Nelson 10.00
16 C Lee Giles 25.17 61 Miguel A. 25.07
17 Carlos Pecharroman 35.97 62 Morten Schmidt 34.08
18 Caroline S. Wagner 25.53 63 Nees Jan van Eck 41.35
Table 2: The EM-index sequence of all 89 scholars
ID Author EM-index Sequence ID Author EM-index Sequence
19 Christoph Bartneck 25.64 64 Nils T. Hagen 17.99
20 Claes Wohlin 27.79 65 Olle Persson 18.39
21 Clint D. Kelly 28.62 66 Paul Wouters 25.96
22 Dimitrios Katsaros 32.75 67 Peter Jacso 30.36
23 Egghe Leo 68.69 68 Raf Guns 17.02
24 Elizabeth A. Corley 29.09 69 Raj Kumar Pan 27.83
25 Erhard Rahm 30.98 70 Richard S J Tol 50.67
26 Fiorenzo Franceschini 20.43 71 Roberto Todeschini 43.30
27 Fred Y. 20.50 72 Robin hankin 17.39
28 Gad Saad 25.56 73 Rodrigo Costas 31.87
29 Gangan Prathap 21.60 74 Ronald Rouseau 91.43
30 Gary M. Olson 5.00 75 Ruediger mutz 34.46
31 Gerhard Woeginger 26.38 76 Santo Fortunato 107.41
32 Guang-Hong Yang 41.37 77 Serge GALAM 34.26
33 Heidi Winklhofer 19.85 78 Sergio Alonso 49.48
34 Hendrik P. van Dalen 24.16 79 Steve Lawrence 20.16
35 Henk F. Moed 31.51 80 Sune Lehmann 33.80
36 Herbert Van de Sompel 14.20 81 Terttu Luukkonen 13.49
37 Hirsche 140.79 82 Vicen 47.50
38 James Moody 31.10 83 Walter W (Woody) Powell 37.21
39 Jayant Vaidya 42.25 84 Werner Marx 27.58
40 Jerome Vanclay 44.69 85 Wolfgang Glnzel 38.37
41 Johan Bollen 42.13 86 Yannis Manolopoulos 33.06
42 JOHN IRVINE 49.43 87 Ying Ding 42.58
43 Judit Bar-Ilan 37.21 88 Yu-Hsin Liu 18.65
44 Kne Henkens 28.71 89 Yvonne Rogers 29.57
45 Loet Leydesdorff 46.97
Table 2: The EM-index sequence of all 89 scholars continued……

The EM-index sequence provides a more balanced and efficient way to assess the scientific impact of scholars. The EM-index sequence elements provide year wise scientific impact of a scholar that helps to compare the performance of scholars at a particular year of their career. In order to validate this, a comparative analysis has been made with h-index sequence as shown in Table 3.

ID Author h-index Sequence Rank EM-index Sequence Rank
1 Adamantios Diamantopoulos 65 18 55.24 8
2 Albert Zomaya 64 19 39.06 27
3 Alireza Abbasi 47 37 30.85 47
4 Andrs Schubert 50 30 36.16 33
5 Andrs Telcs 22 76 18.39 77
6 Andreas Thor 42 48 29.17 51
7 Andrew D. Jackson 35 62 30.51 48
8 Anne-Wil Harzing 61 20 36.07 34
9 Aric Hagberg 43 44 35.29 36
10 Barry Bozeman 61 21 37.23 29
11 Ben R Martin 35 63 23.98 68
12 Benny Lautrup 20 81 23.00 69
Table 3: Comparison of h-index sequence with EM-index sequence
ID Author h-index Sequence Rank EM-index Sequence Rank
13 Berwin Turlach 17 84 13.73 85
14 Birger Larsen 24 72 20.44 72
15 Blaise Cronin 44 43 36.21 32
16 C Lee Giles 37 59 25.17 64
17 Carlos Pecharroman 49 31 35.97 35
18 Caroline S. Wagner 26 71 25.53 63
19 Christoph Bartneck 31 66 25.64 61
20 Claes Wohlin 41 49 27.79 57
21 Clint D. Kelly 40 52 28.62 54
22 Dimitrios Katsaros 40 53 32.75 42
23 Egghe Leo 88 8 68.69 5
24 Elizabeth A. Corley 48 35 29.09 52
25 Erhard Rahm 45 41 30.98 46
26 Fiorenzo Franceschini 29 68 20.43 73
27 Fred Y. Ye 28 70 20.50 71
28 Gad Saad 34 64 25.56 62
29 Gangan Prathap 30 67 21.60 70
30 Gary M. Olson 5 89 5.00 89
31 Gerhard Woeginger 39 56 26.38 59
32 Guang-Hong Yang 79 12 41.37 23
33 Heidi Winklhofer 24 73 19.85 75
34 Hendrik P. van Dalen 34 65 24.16 67
35 Henk F. Moed 47 38 31.51 44
36 Herbert Van de Sompel 15 86 14.20 84
37 Hirsch J.E. 105 5 140.79 1
38 James Moody 48 36 31.10 45
39 Jayant Vaidya 52 26 42.25 21
40 Jerome Vanclay 58 23 44.69 15
41 Johan Bollen 57 24 42.13 22
42 John Irvine 108 4 49.43 11
43 Judit Bar-Ilan 52 27 37.21 30
44 Kne Henkens 49 32 28.71 53
45 Loet Leydesdorff 98 6 46.97 14
46 Lokman Meho 52 28 40.81 26
47 Luca Mastrogiacomo 22 77 17.26 82
48 Ludo Waltman 71 15 44.00 16
49 Lutz Bornmann 90 7 47.42 13
50 Maisano, Domenico A. 15 87 12.70 87
51 Marek Kosmulski 41 50 42.35 20
52 Maria Bordons 37 60 28.49 55
53 Mark Fine 20 82 17.89 80
54 Mark Newman 76 13 43.74 17
55 Mathieu Ouimet 40 54 25.01 66
56 Matja Perc 157 2 73.17 4
57 Matthew O. Jackson 69 16 41.33 25
58 Mauno Vihinen 84 10 58.17 7
59 Michael Jennions 75 14 59.89 6
60 Michael L. Nelson 10 88 10.00 88
61 Miguel A. Garca-Prez 43 45 25.07 65
62 Morten Schmidt 38 57 34.08 39
63 Nees Jan van Eck 68 17 41.35 24
64 Nils T. Hagen 22 78 17.99 79
65 Olle Persson 19 83 18.39 78
Table 3: Comparison of h-index sequence with EM-index sequence continued….
ID Author h-index Sequence Rank EM-index Sequence Rank
66 Paul Wouters 29 69 25.96 60
67 Peter Jacso 49 33 30.36 49
68 Raf Guns 22 79 17.02 83
69 Raj Kumar Pan 40 55 27.83 56
70 Richard S. J. Tol 87 9 50.67 9
71 Roberto Todeschini 61 22 43.30 18
72 Robin Hankin 22 80 17.39 81
73 Rodrigo Costas 45 42 31.87 43
74 Ronald Rousseau 175 1 91.43 3
75 Ruediger mutz 52 29 34.46 37
76 Santo Fortunato 113 3 107.41 2
77 Serge Galam 36 61 34.26 38
78 Sergio Alonso 49 34 49.48 10
79 Steve Lawrence 23 75 20.16 74
80 Sune Lehmann 38 58 33.80 40
81 Terttu Luukkonen 17 85 13.49 86
82 Vicen 41 51 47.50 12
83 Walter W (Woody) Powell 43 46 37.21 31
84 Werner Marx 43 47 27.58 58
85 Wolfgang Glnzel 57 25 38.37 28
86 Yannis Manolopoulos 47 39 33.06 41
87 Ying Ding 81 11 42.58 19
88 Yu-Hsin Liu 24 74 18.65 76
89 Yvonne Rogers 46 40 29.57 50
Table 3: Comparison of h-index sequence with EM-index sequence continued….

The comparative result of h-index sequence and EM-index sequence values shows that the excess citation of articles can increase the impact of scholars, improving their rank in the group. For example:

  1. Author Hirsch J.E. (Author ID=37) is ranked 5 as per the corresponding h-index sequence value of 105. His rank improves to 1 when computed as per the corresponding EM-index sequence value of 140.79. This is because the h-index sequence did not account for 4122 excess citations that helped in improving the rank computed based on EM-index sequence.

  2. On the other hand, Author Ronald Rousseau (Author ID=74) is ranked 1 as per the corresponding h-index sequence value of 175. His rank reduces to 3 when computed as per the corresponding EM-index sequence value of 91.43. This is because the excess citation count of Author Ronald Rousseau, which is 1774, does not match up to the very high h-index sequence value of 175, resulting in a little bit lowering of rank computed based on EM-index sequence.

  3. As an extreme example, author Marek Kosmulski (Author ID=51) is ranked 50 based on h-index sequence value of 41, whereas his rank is 20 based on EM-index sequence value of 42.35. Here, a marginal difference in the two index values affects the corresponding ranks in a major way. Here, the author has 435 excess citations.

In general, the comparative analysis between scholars has been performed based on total index value. In this case, if two scholars get the same index value, then it is very difficult to discriminate the impact of scholars. Hence, instead of a single number, a set of numbers are more suited to compare the scientific impact of two scholars. Consider one such case: Figure 2 shows the EM-index sequence component analysis of scholars, where all have very similar EM-index sequence values. As shown in Figure 2(a), authors 78 and 42 have EM-index sequence values of 49.48 and 49.43 respectively; their career spans 12 and 18 years respectively. Even though both authors have similar EM-index sequence values, the scientific impact of author 78 is more than that of author 42 considering the latter’s career so far, i.e., the first 12 years only. Figure 2(b) compares scholars 82 (EM-index sequence value: 47.50, career span: 13 years) and 49 (EM-index sequence value: 47.42, career span: 12 years). Here both authors have similar career spans, however, as evident from the plot, author 49 has a greater scientific impact during the first half of his career, i.e., the first seven years, while scholar 82 has a greater scientific impact during the second half, i.e., the last four years. This is not evident by just looking at the EM-index sequence values of the two scholars. Figure 2(c) compares scholars 32 (EM-index sequence value: 41.37, career span: 12 years), 63 (EM-index sequence value: 41.35, career span: 12 years) and 57 (EM-index sequence value: 41.33, career span: 12 years). Here all scholars have similar career spans and their impacts are almost the same.

(a) The component analysis of EM-index sequence             of Author ID- 78 & 42 with corresponding index value 49.48 & 49.43
(b) The component analysis of EM-index sequence              of Author ID- 82 & 49 with corresponding index value 47.50 & 47.42
(c) The component analysis of EM-index sequence of Author ID- 32,63 & 57 with corresponding index value 41.37, 41.35 & 41.33
Figure 2: The component analysis of -index sequence

From the above discussion, it is clear that the elements of EM-index sequence helps in comparing the scientific impacts of scholars having equal or very similar EM-index sequence values.

While EM-index sequence values are better than h-index sequence values with respect to the excess citations of h-core articles, both can be limited due to complete ignorance of the citations of h-tail articles. This is not good because some of the h-tail articles have citation count similar to the h-core articles. Such h-tail articles are obviously important, however, even the h-tail articles with lesser citations can be significant in assessing the impact of a scholar, and hence, should not be ignored. Motivated by this, reference García-Pérez (2009) proposed multidimensional h-index and Bihari and Tripathi (2017) proposed -index. Both the proposed indices consider all publications with non-zero citations. Next, we introduce -index sequence and discuss how it can be used (i) to better assess the scientific impact of a scholar, and (ii) to compare scholars with similar career spans or having equal number of publications.

5 -index sequence

Let the research career of a scholar span years publishing articles. Let be the first year of publications and be the current year. The -index sequence element for the year, denoted , is computed from the citation count in the year using -index formula as given in Bihari and Tripathi (2017)). Then, the -index sequence is the sum of all such -index sequence elements. Formally, it is defined as:

(2)

To demonstrate the effectiveness of -index sequence, consider the data of author Andrew D. Jackson from Table 1. The corresponding -index sequence values are shown in Table 4.

Publication Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
2006 11 9 11 15 12 11 20 14 16 11 5
2007 4 6 9 8 5 10 13 8 4 2 0
2007 0 0 0 0 0 0 0 0 0 0 0
2008 0 1 10 4 4 5 7 6 4 5 1
2008 0 0 0 0 0 1 0 0 0 0 0
2008 0 0 0 0 0 0 0 0 0 0 0
2009 0 0 0 3 5 9 4 6 10 6 2
2009 0 0 0 0 0 2 0 1 0 0 0
2010 0 0 0 0 1 0 0 0 0 0 0
2011 0 0 0 0 1 3 3 4 2 1 0
2013 0 0 0 0 0 0 0 1 1 1 1
2013 0 0 0 0 0 0 0 0 1 0 0
2013 0 0 0 0 0 0 0 0 0 0 0
2013 0 0 0 0 0 0 0 0 0 0 0
2014 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 1 1 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2015 0 0 0 0 0 0 0 0 0 0 0
2016 0 0 0 0 0 0 0 0 0 1 0
2016 0 0 0 0 0 0 0 0 0 0 0
2016 0 0 0 0 0 0 0 0 0 0 0
2016 0 0 0 0 0 0 0 0 0 0 0
2017 0 0 0 0 0 0 0 0 0 0 0
2.24 3.0 3.32 3.87 3.46 3.74 4.47 3.74 4 3.32 2.24
Table 4: Publication history and year wise impact of Author Andrew D. Jackson for -index sequence

The elements of -index sequence are 2.24, 3.0, 3.32, 3.87, 3.46, 3.74, 4.47, 3.74, 4, 3.32 & 2.24 and the index sequence value is 37.40, whereas the EM-index sequence value is 29.17. Looking at these values, one can clearly see that -tail articles with at least one citation also have significance in assessing scientific impact of a scholar. Figure 3 shows the -index sequence values of all authors. Figure 4 compares -index sequence value, h-index sequence value and EM-index sequence value for all authors.




Figure 3: The -index sequence of all Scholars
Figure 4: Comparison of the h-index sequence, EM-index sequence and -index sequence of all Scholars

To demonstrate the impact of tail articles in the scientific assessment of scholars, we performed a component level analysis on top 4 authors based on -index sequence with reference of EM-index sequence as shown in Figure 5. Looking at Figure 5, it is clear that the -index sequence gives better result than the EM-index sequence by appropriately capturing the impact of citation counts of tail articles. For example, consider Author ID-37 (see Figure 5(a)). The author’s EM-index and index sequence values are very much the same for the first 10 years – the same is corroborated by a very low number of citations of tail articles during these years. However, after the year, the citation count of tail articles increases significantly – making sequence values significantly greater than EM-index sequence values.

(a)
(b)
(c)
(d)
Figure 5: Comparative result of EM-index sequences and -index sequence of top 4 authors with their tail articles citation distributions.

Another extreme analysis can be seen in Figure 6. In Figure 6, we performed a component level analysis of authors 78 and 42 with respect to EM and sequences. As can be seen in Figure 6, authors 78 & 42 have similar EM-index sequence value, however the -index sequence values exhibit significant difference. These two component level analyses show the impact of tail articles in scientific assessment of scholars and could be used as an effective alternative.

Figure 6: Component level comparison of EM-index sequence and -index sequence of Author ID- 78 & 42

Table 5 shows a rank-based comparison based on -index sequence value, h-index sequence value and EM-index sequence value. The comparative results show that the -index sequence gives better results than others and also one can clearly see that how the excess citation and tail articles citation count affect the scientific assessment of scholars. The result of the -index sequence shows the importance of tail publications’ citation count. If we consider the impact of author id: 76, whose total citation count is 19841, h-core citation count: 12769, excess citation: 6312 and the h-tail citation is 760. The h-index sequence used only the h-core citation count and left a huge amount of citation count (7072), the EM-index sequence considers the h-core citation and excess citation count and left only few amount of citations (760), whereas the -index sequence considers overall citation count in scientific assessment. Finally, we can conclude that the excess citation of h-core and tail articles citations gives a fair contribution in scientific assessment of scholars.




ID h-index Sequence Rank Excess Citations EM-index Sequence Rank Tail Citations -index Sequence Rank
1 65 18 897 55.24 8 606 69.47 17
2 64 19 401 39.06 27 1433 66.78 18
3 47 37 155 30.85 47 672 50.99 33
4 50 30 317 36.16 33 238 52.29 31
5 22 76 22 18.39 77 21 22.94 83
6 42 48 159 29.17 51 181 38.93 58
7 35 62 170 30.51 48 34 37.40 62
8 61 20 416 36.07 34 480 53.69 29
9 43 44 207 35.29 36 140 47.42 39
10 61 21 294 37.23 29 484 52.46 30
11 35 63 1 23.98 68 145 32.36 67
12 20 81 146 23.00 69 4 30.01 71
13 17 84 6 13.73 85 30 17.56 85
14 24 72 45 20.44 72 93 28.36 72
15 44 43 313 36.21 32 260 49.18 36
16 37 59 97 25.17 64 326 38.84 59
17 49 31 214 35.97 35 267 47.89 38
18 26 71 204 25.53 63 24 31.51 69
19 31 66 218 25.64 61 136 38.37 60
20 41 49 118 27.79 57 363 41.33 56
21 40 52 156 28.62 54 215 42.38 53
22 40 53 315 32.75 42 185 46.62 42
Table 5: Comparison of h-index, EM-index and -index sequence with corresponding rank
ID h-index Sequence Rank Excess Citations EM-index Sequence Rank Tail Citations -index Sequence Rank
23 88 8 962 68.69 5 1121 110.54 5
24 48 35 121 29.09 52 329 43.46 47
25 45 41 172 30.98 46 245 43.39 48
26 29 68 61 20.43 73 212 31.76 68
27 28 70 31 20.50 71 110 28.00 73
28 34 64 100 25.56 62 100 37.37 63
29 30 67 59 21.60 70 194 34.55 66
30 5 89 6 5.00 89 2 7.00 89
31 39 56 72 26.38 59 403 43.26 50
32 79 12 415 41.37 23 2694 85.50 10
33 24 73 41 19.85 75 37 25.16 79
34 34 65 67 24.16 67 133 31.46 70
35 47 38 274 31.51 44 275 47.37 40
36 15 86 11 14.20 84 13 18.63 84
37 105 5 4122 140.79 1 1342 225.12 1
38 48 36 205 31.10 45 235 43.33 49
39 52 26 564 42.25 21 201 64.69 21
40 58 23 442 44.69 15 393 58.34 24
41 57 24 943 42.13 22 155 81.70 12
42 108 4 584 49.43 11 2724 93.38 6
43 52 27 354 37.21 30 292 50.79 34
44 49 32 134 28.71 53 438 45.82 44
45 98 6 575 46.97 14 3037 91.10 7
46 52 28 535 40.81 26 114 65.38 20
47 22 77 49 17.26 82 127 26.34 76
48 71 15 591 44.00 16 699 58.04 25
49 90 7 508 47.42 13 2216 85.22 11
50 15 87 32 12.70 87 10 15.46 88
51 41 50 435 42.35 20 221 50.29 35
52 37 60 192 28.49 55 211 42.31 54
53 20 82 81 17.89 80 27 25.73 77
54 76 13 440 43.74 17 1491 77.54 13
55 40 54 98 25.01 66 177 35.08 65
56 157 2 1930 73.17 4 5242 111.18 4
57 69 16 466 41.33 25 586 57.22 26
58 84 10 947 58.17 7 1004 76.57 14
59 75 14 980 59.89 6 906 75.97 15
60 10 88 12 10.00 88 30 17.39 86
61 43 45 62 25.07 65 470 45.55 45
62 38 57 625 34.08 39 300 47.21 41
63 68 17 552 41.35 24 564 56.92 27
64 22 78 41 17.99 79 46 23.09 82
65 19 83 62 18.39 78 42 24.87 80
66 29 69 237 25.96 60 74 38.07 61
67 49 33 95 30.36 49 345 46.21 43
68 22 79 34 17.02 83 66 23.73 81
69 40 55 98 27.83 56 189 35.15 64
70 87 9 478 50.67 9 2152 87.09 9
71 61 22 633 43.30 18 343 56.56 28
72 22 80 53 17.39 81 38 26.44 75
73 45 42 226 31.87 43 250 44.36 46
74 175 1 1774 91.43 3 6215 181.65 2
75 52 29 340 34.46 37 316 51.30 32
Table 5: Comparison of h-index, EM-index and -index sequence with corresponding rank continued…
ID h-index Sequence Rank Excess Citations EM-index Sequence Rank Tail Citations -index Sequence Rank
76 113 3 6312 107.41 2 760 156.04 3
77 36 61 220 34.26 38 126 43.23 51
78 49 34 656 49.48 10 432 58.76 23
79 23 75 44 20.16 74 19 25.25 78
80 38 58 631 33.80 40 51 66.48 19
81 17 85 25 13.49 86 6 16.33 87
82 41 51 779 47.50 12 520 70.73 16
83 43 46 336 37.21 31 60 41.94 55
84 43 47 108 27.58 58 314 40.63 57
85 57 25 298 38.37 28 655 60.68 22
86 47 39 209 33.06 41 402 48.75 37
87 81 11 439 42.58 19 2819 88.33 8
88 24 74 29 18.65 76 70 26.50 74
89 46 40 94 29.57 50 237 42.65 52
Table 5: Comparison of h-index, EM-index and -index sequence with corresponding rank continued…

To find the correlation between indices, the Spearman Rank Correlation test has been performed on h-index sequence value, EM-index sequence value and -index sequence value. Table 6 shows the result of correlation test between indices. The result shows that all the indices are highly correlated mutually. Hence, it can be said that the proposed EM and index sequences are on the same path as the already established indicators.

h-index sequence EM-index sequence -index sequence
h-index sequence 1 0.93 0.94
EM-index sequence 0.93 1 0.96
-index sequence 0.94 0.96 1
Table 6: Result of Spearman rank correlation between h-index sequence, EM-index sequence and -index sequence

6 Conclusion

The h-index sequence uses the series of h-index based on individual year citation count along with the career-span of research for scientific assessment of scholars. A set of indices values helps users to discriminate between the performance of scholars at a particular stage of their careers or their whole careers. However, the h-index sequence completely ignored the importance of excess citations. In this article, the EM-index sequence and -index sequence has been discussed. The EM-index and -index sequence values can provide a superior alternative – when compared to -index sequence values – for assessing the scientific impact of scholars.

Acknowledgements.
The authors would like to acknowledge the help of Ministry of Electronics & Information Technology (MeitY),Government of India for supporting the financial assistance during research work through Visvesvaraya PhD Scheme for Electronics & IT.

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