=Paper=
{{Paper
|id=Vol-3745/paper20
|storemode=property
|title=Understanding Citation Mobility in the Knowledge Space
|pdfUrl=https://ceur-ws.org/Vol-3745/paper20.pdf
|volume=Vol-3745
|authors=Shuang Zhang,Feifan Liu,Haoxiang Xia
|dblpUrl=https://dblp.org/rec/conf/eeke/ZhangLX24
}}
==Understanding Citation Mobility in the Knowledge Space==
https://ceur-ws.org/Vol-3745/paper20.pdf
Understanding Citation Mobility in the Knowledge Space⋆
Shuang Zhang1, Feifan Liu1,2 and Haoxiang Xia1,2,∗
1 Institute of Systems Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian, 116024, P.R.
China
2 Institute for Advanced Intelligence, Dalian University of Technology, No. 2 Linggong Road, Dalian, 116024, P.R.
China
Abstract
Despite persistent efforts to reveal the temporal patterns of citation dynamics, little is known
about its spatial patterns in knowledge space, owing to the unquantifiability of citation diffusion
in the virtual high-dimensional space. Here, drawing on millions of papers in the Physics field, we
consider individual papers’ citation sequences as a mobility process and track trajectories with
embedding methods learning the semantic proximity. We first quantify the spatial scale of
citation mobility and find Gaussian-distributed citation scope and exponentially-distributed
citing embedding distance, indicating the constrained mobility of citations. Simulations with the
Gravity model and Radiation model further confirm that epistemic distance and popularity are
key push-and-pull factors, respectively, in citation mobility. It is then found that compared with
high-cited papers, disruptive papers are more likely to receive distant recognition. As science
evolves, papers nowadays make narrower citation mobility than those in earlier decades. These
findings provide insights into understanding the diversified knowledge diffusion and scientific
innovation efficiency.
Keywords
citation dynamics, spatial patterns, knowledge diffusion, disruptive innovation
1. Introduction quantitatively revealed. Moreover, “sleeping beauties”
whose atypical citation dynamics have been explored
Citations encapsulate the dynamics of ideas in terms of identification and awakening
circulation, unfolding both in temporal and spatial mechanism[13]. However, despite the fruitful efforts
dimensions in the abstract knowledge space[1]. on the temporal aspects of the citation dynamics, our
Extensive research has delved into citation patterns at understanding of the spatial dimension remains
levels from the paper[2], author[3], discipline[4], to limited.
nation[5]. For individual papers, despite the diversity On collective level, citations signify collective
of citation profiles[6], researchers attempt to attention. Albeit with the explosion of papers and
quantify[2], model[7], and predict[8] citation citation inflation[14], we find that citations are
dynamics. Key drivers of citation dynamics, including increasingly concentrated on elite scientists[15] and
preferential attachment, aging, and fitness[2] have top papers[16], leaving new publications less likely to
been identified. Universal patterns, such as scale laws be recognized[17]. Growing citation inequality
in citation distributions[9], first mover effect[10], indicates a narrowing and decaying scientific
citation probability decreasing with papers’ age[11], attention, exacerbating the stratification of the
and “jump-decay” patterns[12] have been scientific system and entrenching science trapped in
Joint Workshop of the 5th Extraction and Evaluation of Knowledge
Entities from Scientific Documents and the 4th AI + Informetrics
(EEKE-AII2024), April 23~24, 2024, Changchun, China and Online
∗ Corresponding author.
hxxia@dlut.edu.cn (H. Xia)
shuang94@mail.dlut.edu.cn (S. Zhang)
liufeifan@dlut.edu.cn (F. Liu)
© Copyright 2024 for this paper by its authors. Use permitted under
Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
128
existing norms[12,18]. This narrowing attention 2.2. Construction of citation trajectories on
phenomenon warrants detailed investigation through the epistemic landscape
the lens of a holistic knowledge landscape.
Papers receive citations spanning different We develop a framework, which combines
epistemic distances. On citation dynamics of representative learning algorithms and manifold
individual papers in the knowledge space, similar learning algorithms, for the construction of the
studies focus on mapping structure and evolution of quantifiable disciplinary knowledge landscape based
disciplines with citation flows[19], associations on semantics association. Unlike citation networks
between interdisciplinary citations and novelty[20], merely representing the topological connections of
and measuring the breadth and depth of impact by elements, this landscape provides a continuous
examining textual proximity between citing distance scale, allowing for the tracking and
papers[21]. However, exsiting studies remains quantifying of citation trajectories of individual
inadequate for quantifying the knowledge aspect of papers.
citation trajectories due to their abstract nature and Here, we employ the Doc2Vec algorithm[24],
high dimensionality. capturing the semantics of content, and the popular
Major obstacles in large-scale quantitative UMAP algorithm[25] preserving the global and local
investigations on individual papers’ citation dynamics topology in dimension reduction. The majority of
in knowledge space are the inability to track architectures and hyperparameters we utilized were
trajectories and the lack of an appropriate set to their default values throughout the model
quantitative metric for this dynamical progress. It is training process.
unclear how papers diffuse impact and ideas in the Figure 1 illustrates the proposed framework for
knowledge space over lifecycles. constructing the knowledge landscape. After building
Here, we regard the sequential citation process of the corpus with the title and abstract, we train the
papers as mobility on a quantifiable epistemic Doc2vec model to obtain semantic vectors of papers.
landscape and use machine-learning techniques to The UMAP algorithm is subsequently applied to
trace the trajectories. In this manner, we introduce the project the semantic vectors into a two-dimensional
theoretical and methodological framework of space based on their cosine distance. Finally, we
geospatial human mobility to characterize citation obtain the coordinates of each paper and the
mobility. Some key research questions are epistemic landscape. Thus, the citation trajectories of
quantitatively analyzed. First, we explore the spatial individual papers are traced by mapping their citation
scale characteristics and collective-level mechanisms sequences onto this landscape.
of citation mobility. Second, we probe whether
different types of novel papers exhibit diversified
spatial patterns. Third, evolutionary patterns of
citation mobility over decades are checked.
2. Data and methods
2.1. Data
This study focuses on the discipline of Physics. The
dataset used is SciSciNet[22], a large-scale scientific Figure 1: Illustration for constructing the epistemic
dataset built on MAG[23], covering over 134 million landscape and citation trajectories based on the
scientific publications up to the year 2021. semantic proximity embedded in the textual content
Using the “fields of study” classification, we of papers
extract 3,263,546 papers labeled "Physics". Then we
select focal papers satisfying: (i) number of citations 2.3. Radius of gyration and jump lengths
no less than 10, to ensure sufficient trajectory points Two indicators are applied to characterize the spatial
for quantification; (ii) citation history spanning at scale of citation mobility[26,27]. The radius of
least 10 years, to ensure sufficient timespans to gyration (rg) refers to the typical distance from
capture spatiotemporal patterns; (iii) receiving at individual trajectories from their centroid of mass.
least one citation every five years, to exclude noisy The jump length (∆r) measures the epistemic distance
data. Finally, we obtain 214,867 focal papers. between a citing-cited pair.
129
In the context of citation mobility, rg is applied to 2d intuitively shows one’s trajectory is locally
measure the degree to which one’s citations are distributed.
concentrated or dispersed. ∆r quantifies the research
proximity of the focal paper to its citing papers.
1 𝑁
𝑖=1(𝒓𝑖 − 𝒓𝑐𝑚 ) , 𝑟𝑐𝑚 = ∑𝑖=1 𝒓𝑖 /𝑁
𝑟𝑔 = √ ∑𝑁 (1)
2
𝑁
∆𝑟 = 𝒓𝑖 − 𝒓0 (2)
In formulas (1-2), r0 is the coordinates of the focal
paper; ri and ri-1 are the coordinates of its ith and (i-
1)th citing paper; rcm is the centroid of the N citing
papers.
2.4. Gravity model and Radiation model
The distance-based Gravity model, and the
opportunity-based Radiation model, are introduced to
characterize aggregated citation flows on the
epistemic landscape. These two classical population-
level models depict distinct flow generation
mechanisms and could reveal key drivers of citation
flows in terms of research popularity, knowledge
distance, and opportunities.
In citation scenarios, Gravity models assume flows
Figure 2: Visualization of individual papers’ citation
between two locations are proportional to research
mobility on the epistemic landscape
hotness and decay with knowledge distance[28].
Radiation models assume movement probability of We quantify spatiotemporal characteristics with
citations is proportional to destination opportunities two indicators. The citing epistemic distance ∆r is
and inversely proportional to intervening more approximated by an exponential function, than
opportunities[29]. power-law (Fig. 3a). It indicates that papers are likely
𝑇ⅈ𝑗 ∝ 𝑚ⅈ 𝑚𝑗 𝑓(𝑟ⅈ𝑗 ) (3) to receive massive short-distanced citations and a few
𝑚ⅈ 𝑚𝑗 longer-distanced ones. Then, the radius of gyration rg
𝑇ⅈ𝑗 = 𝑂ⅈ (4)
(𝑚ⅈ +𝑠ⅈ𝑗 )(𝑚ⅈ +𝑚𝑗 +𝑠 )
ⅈ𝑗
approximates lognormal distribution, suggesting the
where Tⅈj is citation flows from tile i of the citing paper narrower impact of most papers and the broader
to tile j of the focal paper. mi and mj are the paper impact of a few papers (Fig. 3b). These findings
density in tile i and j; f(rij) is the distance function indicate that both citing distance and overall impact
modeled with power-law form. Oi represents flows scope follow the typical scale variation in citation
from tile i; sij is the number of intervening mobility, in contrast to the fat-tailed spatial scale
opportunities (paper density) between tile i to j. displayed by human mobility in the biological
Model performance is assessed with metrics: R2, world[26,27,30].
RMSE, Spearman, and Pearson correlations. Furthermore, we note the more citations papers
receive, the wider their impact scope (Fig. 3d).
However, exponentially distributed citing distance
3. Results
and lognormal-distributed citation concentration are
3.1. The spatial characteristics of independent of the number of citations (Fig. 3c&d). In
trajectories of citation mobility a word, we observe constrained mobility of citations
in the knowledge space.
We start by visualizing the individual papers’ citation
trajectories on the epistemic landscape. In Fig. 2c,
paper points are clustered and semantically
distributed, depicting the knowledge structure. After
mapping citation dynamics (Fig. 2a) of papers onto
the epistemic landscape, we find citations are not
homogeneous, as they span different knowledge
distances (Fig. 2b). However, the visualization in Fig.
130
recognition, and disruptiveness, and measure them
with the number of citations, sleeping beauty
coefficient[13], and disruption index[31], respectively.
The top 10% of papers by each metric are identified
as highly cited, sleeping beauties, and disruptive
papers (Fig. 5a).
Figure 3: Empirical distribution of spatiotemporal
characteristics of citation trajectories
3.2. The Gravity and Radiation modeling in
citation mobility
To further delineate the observed narrow movements,
we use the classic Gravity model and Radiation model
to fit the aggregated flow of citation mobility. After Figure 5: The rg and ∆r of citation trajectories of high-
discretizing the Physics epistemic landscape to a cited papers, sleeping beauties, and disruptive papers.
spatial tessellation, we aggregate individual ****p≤.0001, ***: p≤ .001, ns: p ≥ 0.05
trajectories into origin-destination citation flows.
Most citation flows are intra-flows and only inter- We observe that these three representative novel
flows between two different grids are used to employ papers with a low degree of overlap (Fig. 5a), have
parameter fitting and flow generation. above-average impact scopes, with disruptive papers
standing out in particular (Fig. 5b). The finding that
sleeping beauties with a broader impact is in line with
their interdisciplinary nature [13].
We further examine the citing distance in the first
year post-publication. The consistent patterns
observed in Fig. 5c reinforce our previous findings. It
suggests that compared with the influential high-cited
papers, sleeping beauties and high-disruptive papers
Figure 4: Actual and simulated citation flows promptly attract attention from more distant
generated by Gravity and Radiation models knowledge communities once published.
Fig. 4 shows the simulated results. It could be seen 3.4. Evolution of citation mobility
that the gravity model outperforms the radiation
model, especially for long-distance flows. This Finally, we group focal papers into different decades
suggests that epistemic distance and popularity are according to their publication year to investigate how
key factors in citation behavior, whereas the research citation mobility evolved over decades.
gap representing potential research intersection area, The first finding is that papers nowadays make
is not significant in attracting citations. more restricted mobility than those in the early years,
as shown in Fig. 6a. To rule out the possibility that this
3.3. Comparisons of high-cited, sleeping result is due to semantic differences between papers
beauties, and disruptive papers from different decades, we analyze the citing distance
of citing pairs with one year gap. In Fig. 6b, the
The further question is how citation mobility differs observed decrease in the trend of citing distance over
across papers with various types of novelty. We focus publication years indicates the narrowing of literature
on three attributes of papers: popularity, delayed use. These two results suggest a possible shorter-
131
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