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The p-index: Ranking Scientists Using Network Dynamics

Profile image of Mahendra PiraveenanMahendra Piraveenan

2014, Procedia Computer Science

https://doi.org/10.1016/J.PROCS.2014.05.042
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11 pages

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Abstract

The indices currently used by scholarly databases, such as Google scholar, to rank scientists, do not attach weights to the citations. Neither is the underlying network structure of citations considered in computing these metrics. This results in scientists cited by well-recognized journals not being rewarded, and may lead to potential misuse if documents are created purely to cite others. In this paper we introduce a new ranking metric, the p-index (pagerank-index), which is computed from the underlying citation network of papers, and uses the pagerank algorithm in its computation. The index is a percentile score, and can potentially be implemented in public databases such as Google scholar, and can be applied at many levels of abstraction. We demonstrate that the metric aids in fairer ranking of scientists compared to h-index and its variants. We do this by simulating a realistic model of the evolution of citation and collaboration networks in a particular field, and comparing h-index and p-index of scientists under a number of scenarios. Our results show that the p-index is immune to author behaviors that can result in artificially bloated h-index values.

Figures (11)
oo ee he le It could be asked, whether we could not have simply weighed citations by using the impact factor of journals in whic the citing documents are published. However, careful analysis reveals this method has many pitfalls. There is considerab debate about the dependability of the impact factors of journals (van Nierop, 2009), and we cannot therefore consider that imp factors are sacrosanct. In any case, conference papers and relatively new journals do not have impact factors. There is 1 guarantee either, that a paper which is published in a journal with high impact factor will itself have high impact. Our intention to reward the quality of the citing document, not the quality of journal in which it is published. Even if we count the number. citations received by the citing document, and weight the citation accordingly in a dynamic manner, it is possible that the weights could be manipulated again by less impactful documents: thus the influence of such documents only becomes indirec and does not go away. Our intention therefore, is to introduce an index which has ‘infinite’ levels of feedback, and the impact citing documents is factored in as much as possible. This is portrayed in Fig. 1. From the figure it could be seen that the numb of citations a document receives could be not always proportional to its impact factor, and we must reward actual numbers | citations at all levels, and not the impact factors. This could only be done by fully utilizing the overall dynamic citatic network, and by an elegant algorithm such as pagerank, which has had proven success in measuring the impact of suc feedback loops in the Google search engine. Figure 1: Multiple levels of citations; IF stands for the impact factor of each node (paper) and an arrow represents a citation from he node at the tail end to the node at the head of the arrow.
oo ee he le It could be asked, whether we could not have simply weighed citations by using the impact factor of journals in whic the citing documents are published. However, careful analysis reveals this method has many pitfalls. There is considerab debate about the dependability of the impact factors of journals (van Nierop, 2009), and we cannot therefore consider that imp factors are sacrosanct. In any case, conference papers and relatively new journals do not have impact factors. There is 1 guarantee either, that a paper which is published in a journal with high impact factor will itself have high impact. Our intention to reward the quality of the citing document, not the quality of journal in which it is published. Even if we count the number. citations received by the citing document, and weight the citation accordingly in a dynamic manner, it is possible that the weights could be manipulated again by less impactful documents: thus the influence of such documents only becomes indirec and does not go away. Our intention therefore, is to introduce an index which has ‘infinite’ levels of feedback, and the impact citing documents is factored in as much as possible. This is portrayed in Fig. 1. From the figure it could be seen that the numb of citations a document receives could be not always proportional to its impact factor, and we must reward actual numbers | citations at all levels, and not the impact factors. This could only be done by fully utilizing the overall dynamic citatic network, and by an elegant algorithm such as pagerank, which has had proven success in measuring the impact of suc feedback loops in the Google search engine. Figure 1: Multiple levels of citations; IF stands for the impact factor of each node (paper) and an arrow represents a citation from he node at the tail end to the node at the head of the arrow.
Figure 4: Variation of average h-index and p-index for non- nanipulative and manipulative authors at each timestep. Variation of the average h-index and p-index for non-manipulative and manipulative authors at each iteration is shown in Fig. 4. It can be inferred from Fig. 4 that p-index is a fairer metric to rank scientists when everyone is not non- manipulative. The difference between the average h-index of non-manipulative authors and manipulative authors is far greater than the difference between the average p-index of non-manipulative authors and manipulative authors. Quantitatively, the difference of h-index is 110.93% whereas the difference of p-index is only 10.58% which is ten times smaller. The implication is that using h-index, a non-manipulative author will be penalized in average ten times more compared to a manipulative author. We also tested whether the percentile ranking of p-index causes this difference. Thus, we next used the percentile rank of authors with respect to their h-index against the p-index as shown in Fig. 5. Even here, p-index still emerges as the fairer index but the advantage of using p-index diminishes slightly when a percentile h-index is used. The difference of h-index percentile is 53.03% while the difference of p-index is 10.68%. Therefore, the p-index is indeed a fairer measure in comparison to h-index in reducing manipulation by authors. Figure 5: Variation of average h-index percentile and p-index for non-manipulative and manipulative authors at each timestep.
Figure 4: Variation of average h-index and p-index for non- nanipulative and manipulative authors at each timestep. Variation of the average h-index and p-index for non-manipulative and manipulative authors at each iteration is shown in Fig. 4. It can be inferred from Fig. 4 that p-index is a fairer metric to rank scientists when everyone is not non- manipulative. The difference between the average h-index of non-manipulative authors and manipulative authors is far greater than the difference between the average p-index of non-manipulative authors and manipulative authors. Quantitatively, the difference of h-index is 110.93% whereas the difference of p-index is only 10.58% which is ten times smaller. The implication is that using h-index, a non-manipulative author will be penalized in average ten times more compared to a manipulative author. We also tested whether the percentile ranking of p-index causes this difference. Thus, we next used the percentile rank of authors with respect to their h-index against the p-index as shown in Fig. 5. Even here, p-index still emerges as the fairer index but the advantage of using p-index diminishes slightly when a percentile h-index is used. The difference of h-index percentile is 53.03% while the difference of p-index is 10.68%. Therefore, the p-index is indeed a fairer measure in comparison to h-index in reducing manipulation by authors. Figure 5: Variation of average h-index percentile and p-index for non-manipulative and manipulative authors at each timestep.
Figure 2: Spread of the h-index for each manipulative and non-manipulative author (as absolute values) ch manipulative Figure 3: Spread of p-index for each manipulative a ues) non-manipulative author (as percentiles) As portrayed in Fig. 2, the spread of the h-index for non-manipulative authors and manipulative authors provide evidence to the fact that manipulative authors can indeed massage their h-index by publishing low impact papers with the sole purpose of referencing their previous work. On the contrary, we can detect a mixed distribution for the p-index of manipulative and non-manipulative authors as seen in Fig. 3. Whereas in Fig. 2 there is clear separation between, in Fig. 3 the two categories are overlapping. It should be noted that the IDs of the authors signify their duration as a researcher, thus author ID 0 is bound to get more citations than author ID 1300. This explains the lower values obtained by the authors at the right end of the Fig. 2 and Fig. 3. This effect has been discussed in the context of h-index and can be addressed by using a time dependent version of the same index.
Figure 2: Spread of the h-index for each manipulative and non-manipulative author (as absolute values) ch manipulative Figure 3: Spread of p-index for each manipulative a ues) non-manipulative author (as percentiles) As portrayed in Fig. 2, the spread of the h-index for non-manipulative authors and manipulative authors provide evidence to the fact that manipulative authors can indeed massage their h-index by publishing low impact papers with the sole purpose of referencing their previous work. On the contrary, we can detect a mixed distribution for the p-index of manipulative and non-manipulative authors as seen in Fig. 3. Whereas in Fig. 2 there is clear separation between, in Fig. 3 the two categories are overlapping. It should be noted that the IDs of the authors signify their duration as a researcher, thus author ID 0 is bound to get more citations than author ID 1300. This explains the lower values obtained by the authors at the right end of the Fig. 2 and Fig. 3. This effect has been discussed in the context of h-index and can be addressed by using a time dependent version of the same index.
Figure 6: Variation of h-index and p-index for highest ranking non-manipulative and manipulative authors at each timestep.
Figure 6: Variation of h-index and p-index for highest ranking non-manipulative and manipulative authors at each timestep.
Figure 7: Variation of multiplier at each timestep.
Figure 7: Variation of multiplier at each timestep.
Fig. 8 shows the spread of h-index for collaborative and non-collaborative authors, while Fig. 9 shows the spread of p-index for collaborative and non-collaborative authors, over author-ID. We can see that most non-collaborative authors have relatively low h-indices, whereas in terms of p-indices the distribution is more evenly spread. As shown in Fig. 8 and Fig. 9, it is visible that collaborative authors usually have higher h-indices whereas both classes of authors have similar p-indices. Figure 9: The spread of p-index for collaborative and non- collaborative authors (as percentile). Figure 8: The spread of h-index for collaborative and non- collaborative authors (as absolute values).
Fig. 8 shows the spread of h-index for collaborative and non-collaborative authors, while Fig. 9 shows the spread of p-index for collaborative and non-collaborative authors, over author-ID. We can see that most non-collaborative authors have relatively low h-indices, whereas in terms of p-indices the distribution is more evenly spread. As shown in Fig. 8 and Fig. 9, it is visible that collaborative authors usually have higher h-indices whereas both classes of authors have similar p-indices. Figure 9: The spread of p-index for collaborative and non- collaborative authors (as percentile). Figure 8: The spread of h-index for collaborative and non- collaborative authors (as absolute values).
Figure 10: Variation of average h-index and p-index for collaborative and non-collaborative authors. Figure 11: Variation of h-index and p-index for highest ranking collaborative and non-collaborative authors. that the p-index, at steady state, is roughly about twenty times ‘fairer’ than the h-index when collaborative tendencies are considered.
Figure 10: Variation of average h-index and p-index for collaborative and non-collaborative authors. Figure 11: Variation of h-index and p-index for highest ranking collaborative and non-collaborative authors. that the p-index, at steady state, is roughly about twenty times ‘fairer’ than the h-index when collaborative tendencies are considered.
Figure 12: Variation of multiplier over each iteration for | Figure 13: The spread of h-index for quantity oriented collaborative and non-collaborative authors over each timestep. authors and quality oriented authors.
Figure 12: Variation of multiplier over each iteration for | Figure 13: The spread of h-index for quantity oriented collaborative and non-collaborative authors over each timestep. authors and quality oriented authors.
Figure 15: Variation of average h-index and p-index for quantity oriented authors and quality oriented authors. Figure 14: The spread of p-index for quantity oriented authors Fi nd quality oriented authors. quantit
Figure 15: Variation of average h-index and p-index for quantity oriented authors and quality oriented authors. Figure 14: The spread of p-index for quantity oriented authors Fi nd quality oriented authors. quantit
st Figure 17: Variation of multiplier of the quantity oriented authors and quality oriented authors over each timestep. Figure 16: Variation of h-index and p-index for highest Figure 17: ranking quality oriented authors and quantity oriented authors. authors and qu a ee ay he - Fig. 16, on the other hand, shows the h-index and p-index variation of the highest ranked quality oriented authors and quantity oriented authors where we can infer that the percentage difference of h-index maybe as much as 104% while the difference of p-index is as low as 2% showing that the differences can be amplified more than 50x times when h-index is used and this can have a dire effect on the quality oriented authors. Fig. 17 plots the multiplier for the average quality vs quantity oriented authors, in this scenario. It can be observed that the multiplier fluctuates around 15 in steady state, meaning that the advantage a quantity oriented author gains over a quality oriented author is fifteen times less when p-index is used.
st Figure 17: Variation of multiplier of the quantity oriented authors and quality oriented authors over each timestep. Figure 16: Variation of h-index and p-index for highest Figure 17: ranking quality oriented authors and quantity oriented authors. authors and qu a ee ay he - Fig. 16, on the other hand, shows the h-index and p-index variation of the highest ranked quality oriented authors and quantity oriented authors where we can infer that the percentage difference of h-index maybe as much as 104% while the difference of p-index is as low as 2% showing that the differences can be amplified more than 50x times when h-index is used and this can have a dire effect on the quality oriented authors. Fig. 17 plots the multiplier for the average quality vs quantity oriented authors, in this scenario. It can be observed that the multiplier fluctuates around 15 in steady state, meaning that the advantage a quantity oriented author gains over a quality oriented author is fifteen times less when p-index is used.

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