forked from D-Net/openaire-graph-docs
73 lines
4.3 KiB
Markdown
73 lines
4.3 KiB
Markdown
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---
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sidebar_position: 2
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---
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# Impact scores
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<span className="todo">TODO - add intro</span>
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## Citation Count (CC)
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This is the most widely used scientific impact indicator, which sums all citations received by each article. The citation count of a
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publication $i$ corresponds to the in-degree of the corresponding node in the underlying citation network: $s_i = \sum_{j} A_{i,j}$,
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where $A$ is the adjacency matrix of the network (i.e., $A_{i,j}=1$ when paper $j$ cites paper $i$, while $A_{i,j}=0$ otherwise).
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Citation count can be viewed as a measure of a publication's overall impact, since it conveys the number of other works that directly
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drew on it.
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## "Incubation" Citation Count (iCC)
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This measure is essentially a time-restricted version of the citation count, where the time window is distinct for each paper, i.e.,
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only citations $y$ years after its publication are counted (usually, $y=3$). The "incubation" citation count of a paper $i$ is
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calculated as: $s_i = \sum_{j,t_j \leq t_i+3} A_{i,j}$, where $A$ is the adjacency matrix and $t_j, t_i$ are the citing and cited paper's
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publication years, respectively. $t_i$ is cited paper $i$'s publication year. iCC can be seen as an indicator of a paper's initial momentum
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(impulse) directly after its publication.
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## PageRank (PR)
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Originally developed to rank Web pages, PageRank has been also widely used to rank publications in citation
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networks. In this latter context, a publication's PageRank
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score also serves as a measure of its influence. In particular, the PageRank score of a publication is calculated
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as its probability of being read by a researcher that either randomly selects publications to read or selects
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publications based on the references of her latest read. Formally, the score of a publication $i$ is given by:
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$$
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s_i = \alpha \cdot \sum_{j} P_{i,j} \cdot s_j + (1-\alpha) \cdot \frac{1}{N}
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$$
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where $P$ is the stochastic transition matrix, which corresponds to the column normalised version of adjacency
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matrix $A$, $\alpha \in [0,1]$, and $N$ is the number of publications in the citation network. The first addend
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of the equation corresponds to the selection (with probability $\alpha$) of following a reference, while the
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second one to the selection of randomly choosing any publication in the network. It should be noted that the
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score of each publication relies of the score of publications citing it (the algorithm is executed iteratively
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until all scores converge). As a result, PageRank differentiates citations based on the importance of citing
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articles, thus alleviating the corresponding issue of the Citation Count.
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## RAM
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RAM is essentially a modified Citation Count, where recent citations are considered of higher importance compared
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to older ones. Hence, it better captures the popularity of publications. This "time-awareness" of citations
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alleviates the bias of methods like Citation Count and PageRank against recently published articles, which have
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not had "enough" time to gather as many citations. The RAM score of each paper $i$ is calculated as follows:
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$$
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s_i = \sum_j{R_{i,j}}
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$$
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where $R$ is the so-called Retained Adjacency Matrix (RAM) and $R_{i,j}=\gamma^{t_c-t_j}$ when publication $j$ cites publication
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$i$, and $R_{i,j}=0$ otherwise. Parameter $\gamma \in (0,1)$, $t_c$ corresponds to the current year and $t_j$ corresponds to the
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publication year of citing article $j$.
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## AttRank
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AttRank is a PageRank variant that alleviates its bias against recent publications (i.e., it is tailored to capture popularity).
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AttRank achieves this by modifying PageRank's probability of randomly selecting a publication. Instead of using a uniform probability,
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AttRank defines it based on a combination of the publication's age and the citations it received in recent years. The AttRank score
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of each publication $i$ is calculated based on:
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$$
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s_i = \alpha \cdot \sum_{j} P_{i,j} \cdot s_j
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+ \beta \cdot Att(i)+ \gamma \cdot c \cdot e^{-\rho \cdot (t_c-t_i)}
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$$
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where $\alpha + \beta + \gamma =1$ and $\alpha,\beta,\gamma \in [0,1]$. $Att(i)$ denotes a recent attention-based score for publication $i$,
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which reflects its share of citations in the $y$ most recent years, $t_i$ is the publication year of article $i$, $t_c$ denotes the current
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year, and $c$ is a normalisation constant. Finally, $P$ is the stochastic transition matrix.
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