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REVIEW 4 major objections 6 minor 70 references

A bibliographic view on recurrence plots and recurrence quantification analyses

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that recurrence-plot research expanded exponentially for two decades, then slowed sharply after 2008 and nearly plateaued after 2019, with machine-learning applications the only fast-growing niche.

desk verdict A solid, honest bibliometric portrait of the recurrence-plot field built on a long-maintained curated database; the headline growth-rate change points are eyeballed rather than formally tested, but the paper ships its data and is worth a serious referee. read the letter →

arxiv 2508.20152 v1 pith:EFDZIYPV submitted 2025-08-27 physics.soc-ph nlin.CDphysics.data-an

Norbert Marwan This is my paper · ORCID
classification physics.soc-phnlin.CDphysics.data-an
keywords recurrenceplotsquantificationanalysisbibliometricspublicationgrowthco-authornetworkstopicclusteringcitationmachinelearning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to give a quantitative life history of the research field built around recurrence plots, a two-dimensional visual and numerical tool for detecting when a dynamical system returns to past states. It analyzes a bibliography of 4,563 relevant publications that the author has maintained for more than twenty years. The central result is that the field's annual output grew nearly exponentially from 1987 to 2008, then slowed markedly after 2008 and again after 2019, approaching saturation; meanwhile, a cluster of papers using recurrence plots as features for machine learning has been the only rapidly growing niche. The paper also maps the 21 topical subjects, the most-cited works, active institutions, and collaborative communities in the field.

What carries the argument

The load-bearing object is the author-maintained BibTeX bibliography (4,563 analysed entries, monthly updated for over two decades) and the analysis pipeline around it: exponential fits to yearly counts; lemmatization plus Gaussian-mixture clustering (a statistical grouping method) of titles, abstracts, and keywords, with the Davies-Bouldin index and silhouette score fixing the cluster number; in-community citation counts from two reference sources; and country-level and co-author networks partitioned by a community-detection algorithm. The recurrence plot itself—a binary matrix that marks when a trajectory returns close to an earlier state—is the shared object that all clusters and mileston

What would settle it

An independent comprehensive search of the published literature using a broad but literal query for 'recurrence plot' or equivalent method names in title and abstract, without relying on the author's curated bibliography, would produce annual publication counts for 2019-2024 much higher than the reported ~3% growth; if the independent growth is instead much steeper, the claimed saturation is an artifact of database curation.

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Extended reading notes

Core claim

The paper's central claim is that the recurrence-plot field has followed a specific life cycle visible in its own publication record. From a curated bibliography of 4,563 papers, the author finds annual output grew roughly exponentially from 1987 to 2008 at about e^{0.221t}, then slowed to e^{0.095t} (2008-2019), then e^{0.028t} (after 2019), approaching saturation. Gaussian-mixture clustering of titles, abstracts, and keywords yields 21 topical subjects; the one with rapid recent growth is cluster 4, where recurrence plots serve as image-like features for machine-learning classifiers. In-community citations are highly concentrated: 43% of papers are never cited by other database papers, whi

Load-bearing premise

The load-bearing premise is that the author-curated database is complete and accurate enough to represent the entire recurrence-plot literature; the paper itself acknowledges likely missing publications, 9% missing affiliations, and unresolved author-name ambiguity, especially among Chinese names.

Editorial extensions

If this is right

  • If the measured rates hold, the field is no longer in rapid self-driven expansion; further growth must largely come from new application communities.
  • Cluster 4's growth since 2014 signals that recurrence plots are now material for deep-learning pipelines, not only nonlinear-dynamics diagnostics.
  • The heavy citation concentration implies that a small set of canonical texts anchors the community and that most contributions integrate the method into applications rather than extend it.
  • The 2008 and 2019 rate breaks give future bibliometric updates clear tests: maintaining e^{0.028t} confirms a plateau; an upturn would indicate a new wave.
  • The database's in-community citation counts are only a lower bound on real influence, since external citations are not counted.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The post-2019 'saturation' may partly be an artifact of the curator's monthly update being unable to track an increasingly diffuse literature; an independent broad query on 'recurrence plot' in titles and abstracts would test whether true output has also plateaued.
  • Machine-learning papers that use recurrence plots as input images probably cite the broader ML literature more than the RP/RQA canon, so in-community citations understate their impact; full citation counts would likely show cluster 4 growing even faster than the curve here.
  • Author-name ambiguity (especially for Chinese names) is a measurable confound; re-running the author-level and co-author-network analysis on author-identifier-verified identities would quantify how much it shapes community sizes.
  • The same change-point-fitting recipe could be applied inside cluster 4 to see whether deep-learning-driven recurrence research is itself heading toward saturation or still in its exponential phase.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript analyzes a custom bibliographic database of 4,563 publications on recurrence plots, recurrence quantification analysis, recurrence networks, and related methods, curated by the author over more than 20 years. It reports: (i) an exponential growth in publications of about e^{0.221t} from 1987 to 2008, slowing to e^{0.095t} from 2008 to 2019 and e^{0.028t} from 2019 to 2024, with a corresponding saturation in the author community; (ii) journal-level publication patterns; (iii) a GMM-based clustering of papers into 21 topical subjects, with cluster 4 (recurrence plots as features for machine learning) identified as the fastest-growing recent topic; (iv) within-community citation statistics, including an approximate e^{-0.07t} decay in citations over time and a list of milestone papers; (v) institutional and author activity rankings; and (vi) country-level and co-author collaboration networks. The paper concludes that the field is lively but approaching saturation, with machine learning as a major future direction.

Significance. If the descriptive claims are robust, the paper provides a valuable quantitative portrait of nearly four decades of a specific methodological field. Its strengths include the long-term curated database, the explicit definition of the in-community citation measure, and the public availability of the data and scripts at Zenodo. The author is also commendably transparent about known gaps (missing publications, 9% missing affiliations, name ambiguity). However, the central quantitative claims about growth-rate change points, saturation, and the temporal evolution of clusters rest on informal fits and a database whose completeness may vary systematically over time. These concerns are not merely cosmetic: the saturation conclusion and the 'fast-growing cluster 4' narrative are load-bearing, and neither is currently supported with formal uncertainty or sensitivity analysis.

major comments (4)
  1. [§3.1, Figs. 3 and 5] The central claim of three growth regimes with breakpoints 'around 2008' and 'around 2019' is based on visual inspection of log-linear plots. No confidence intervals, formal change-point tests, or model-comparison statistics are given for the rates e^{0.221t}, e^{0.095t}, e^{0.028t} or for the community rates e^{0.316t}, e^{0.216t}, e^{0.134t}. Because the saturation conclusion depends entirely on these breakpoints, please fit a piecewise exponential (or Poisson/negative-binomial) model with estimated breakpoints and report parameter uncertainty and model selection. Also test sensitivity to the choice of endpoint years and to excluding 2025 (an incomplete year).
  2. [§2 and §3.1] The database is constructed by citation alerts from Web of Science and Scopus plus manual curation by the author, who is also one of the most cited authors within the database. Completeness may be time-dependent: recent papers that cite newer literature or appear in venues not covered by the alerts could be under-captured, which would make the post-2019 slowdown an artifact. The paper acknowledges missing publications but does not quantify their effect. Please add an independent validation, e.g., a Scopus/Web of Science keyword search for RP/RQA papers, and sensitivity analyses: with/without papers missing affiliations, with/without the author's own papers, and with/without self-citations. This is essential for the saturation claim and for institutional/author rankings.
  3. [§3.2, Table 3, Fig. 8] The choice of 21 clusters is only partially supported: the text says the Davies-Bouldin index has a local minimum at 22 but the selected number is 21, and the silhouette score shows a plateau. The temporal analysis applies 'the same clustering schema to a subset' but it is unclear whether this means re-clustering the subset or projecting onto the full-data clusters; if clusters are re-estimated, cluster labels may not be comparable across years. Since the claim that cluster 4 is rapidly growing since 2014 is a key result, please specify the exact clustering pipeline, report cluster stability (e.g., bootstrap or repeated runs), and clarify how cluster identity is maintained over time.
  4. [§3.3 and §3.5, Figs. 9, 10, 12] The fits e^{-0.07t} for citation decay, the N^{-1.1} citation distribution, and e^{-0.19t} for author activity are reported without fitting method, goodness-of-fit, or uncertainty. These are secondary descriptive claims, but they should be either given proper statistical support (e.g., least-squares or MLE fits with confidence intervals) or described as approximate visual guides.
minor comments (6)
  1. [§3.2] The text refers to 'clusters 18 and 119'; this should presumably be '18 and 19'.
  2. [§3.2, Fig. 7] Reconcile the caption and text: the caption says the dashed line indicates the local minimum and the selected cluster number 21, but the text states the local minimum is at 22.
  3. [§3.3] The sentence about papers 'frequently cited shortly after publication, typically within the same year or shortly thereafter' seems inconsistent with Fig. 9, which shows citations peaking 2–4 years after publication. Please clarify.
  4. [Table 4] The text says 'the top ten papers have more than 200 citations', but Table 4 lists 12 papers with more than 200 citations. Adjust the wording or the table.
  5. [§3.1] The sentence 'Including the current year, we have 38 years of publications (but last year not shown)' is unclear, since Fig. 2 stops at 2024. Please state explicitly which years are plotted and why 2025 is excluded.
  6. [Reference list] Reference [8] contains stray HTML anchor text; formatting, not content, appears corrupted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: descriptive bibliometric study; self-curation is a transparency/limitation issue, not a circular reduction.

full rationale

This paper is a descriptive bibliometric analysis of a self-curated database. The central claims—publication growth rates, cluster assignments, citation counts, community sizes, and institutional rankings—are summaries of the database contents themselves, not predictions derived from a model or from prior theoretical work. The exponential slopes in Fig. 3 (e^{0.221t}, e^{0.095t}, e^{0.028t}) are descriptive fits to the very publication counts they summarize; they are not fitted on one subset and then 'predicted' on a closely related quantity. The citation analysis is explicitly defined as in-community: 'This approach ensures that we only consider in-community citations and the influence of papers within the recurrence plot/ recurrence quantification field.' Thus the high citation counts of the author's own papers and the high publication counts of the author's institutions are measured facts about the curated database, not assumptions smuggled into the analysis. The author's role as database curator is a real potential source of selection bias—the paper acknowledges 'It is likely that it misses a few publications which are not easy to find' and 9% missing affiliations—but bias in data collection is not circularity unless the measured quantity is defined in terms of the selection procedure. No load-bearing result is justified solely by a citation to the author's own prior work; the self-citations that do appear (e.g., to the 2007 Physics Reports review) are themselves objects within the literature being measured. There is no uniqueness theorem imported from prior work, no ansatz smuggled in via citation, and no renaming of a known empirical pattern as an organizing principle. The growth-rate change points and possible time-dependent database completeness are legitimate robustness concerns, but they concern correctness and uncertainty, not circularity. No specific equation-level or definition-level reduction can be exhibited, so the circularity score is 0.

Assumptions & free parameters 10 free parameters · 5 assumptions · 0 invented entities

The analysis rests on the completeness and neutrality of the self-curated database, the chosen clustering granularity, and the use of in-community citations as a proxy for impact. These are reasonable but untested domain assumptions. The free parameters are the fitted growth and decay rates and the cluster-count choice.

free parameters (10)
  • publication growth rate 1987-2008 = 0.221 per year
    Exponential fit to publication counts in Fig. 3, read from log-linear plot.
  • publication growth rate 2008-2019 = 0.095 per year
    Second exponential growth phase in Fig. 3.
  • publication growth rate 2019-2024 = 0.028 per year
    Third exponential growth phase in Fig. 3.
  • community growth rate 1987-1997 = 0.316 per year
    Exponential fit to cumulative author count in Fig. 5.
  • community growth rate 1997-2009 = 0.216 per year
    Second phase in Fig. 5.
  • community growth rate 2009-2025 = 0.134 per year
    Third phase in Fig. 5.
  • citation decay rate = -0.07 per year
    Exponential decay fit in Fig. 9.
  • author activity decay rate = -0.19 per year
    Exponential decay fit in Fig. 12.
  • number of GMM clusters = 21
    Chosen as a trade-off between Davies-Bouldin index and silhouette score, plus subjective judgment in Sec. 3.2.
  • top features per cluster = 15
    Fixed number of top words used to label clusters in Table 3.
assumptions (5)
  • domain assumption The manually curated database is representative of the recurrence plot literature.
    Section 2 says the database is maintained with citation alerts and manual curation, but 'It is likely that it misses a few publications which are not easy to find.' The entire field-level analysis depends on this completeness assumption.
  • domain assumption The 21-cluster GMM solution is a meaningful and stable subject partition.
    Section 3.2 chooses 21 clusters using Davies-Bouldin and silhouette indices plus subjective judgment; the text acknowledges that some clusters contain multiple subjects and that labeling is imperfect.
  • domain assumption In-community citations, i.e., citations among papers within the database, are a valid measure of scholarly influence.
    Section 3.3 restricts citation analysis to papers in the database itself, ignoring citations from outside; this measures only intra-community influence, not overall impact.
  • domain assumption Affiliation retrieval from Scopus is sufficient despite known gaps.
    Section 2 reports 401 missing affiliation records (9%) and manual consolidation of institution names; the paper asserts that the retrieved affiliations are 'representative of the entire database.'
  • domain assumption Author name disambiguation does not materially corrupt the author-level and community analyses.
    Section 2 notes that surnames plus initials cause ambiguity, especially for Chinese names, and that these issues cannot be comprehensively resolved; the network and career-duration analyses rely on this assumption.

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Cite this review

Pith. "Pith review of A bibliographic view on recurrence plots and recurrence quantification analyses." pith.science (2026). https://pith.science/paper/EFDZIYPV

@misc{pith2026250820152,
  author       = {Pith},
  title        = {Pith review of: A bibliographic view on recurrence plots and recurrence quantification analyses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EFDZIYPV}},
  note         = {Machine review of arXiv:2508.20152}
}
read the original abstract

A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity, as well as the emergence, decline, and dynamics of topical subjects over time. Furthermore, the analysis unveils the activity and impact of the different groups, shedding light on their collaborative efforts and contributions to the field.

Figures

Figures reproduced from arXiv: 2508.20152 by the authors.

Figure 1
Figure 1. Monthly database updates in the last five years. The orange line indicates the median (34 papers per month) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Publications per year. 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 Publication year 100 101 102 103 Number of publications ~e0.221t ~e0.095t ~e0.028t [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Exponential growth of publications over the years (not a cumulative sum). The exponential growth between 1987 and 2008 was ∼ e 0.221t . Between 2008 and 2019 and between 2019 and 2024 the growth changed to ∼ e 0.095t and ∼ e 0.028t , respectively (orange lines). In the last two years the interest seems to decrease a bit and the fraction of new authors dropped to 60%. The cumulative sum of the new authors over the ye… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Number of authors and new authors per year, as well as the fraction of new authors. 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 …
Figure 5
Figure 5. Figure 5: Size of the community (total number of authors) on recurrence plot related methods, counted as the cumulative sum of the new authors. The exponential growth is changing around 1997 and 2009, with ∼ e 0.316t , ∼ e 0.216t , and ∼ e 0.134t (orange lines). comparing to the…
Figure 6
Figure 6. Figure 6: Evolution of the distribution of the top journals from 1987 to 2024 where the assorted colors are stacked upon one another with no hidden data and each year sums to 100%. larity dropped down to position 14 in the year 2025 (Tab. 2). For more than a decade, Physics Lett…
Figure 7
Figure 7. Figure 7: Davies-Bouldin and silhouette score for increasing number of clusters during GMM clustering of the papers. The dashed line indicates the local minimum in the Davies-Bouldin index and the selected cluster number of 21 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Subjects of papers evolving over the years (starting point of time interval is always 1987). The assorted colors are stacked upon one another with no hidden data and each year sums to 100%. Semanticscholar (see Sec. 2) and used to find the citations of papers. This ap￾…
Figure 9
Figure 9. Figure 9: Time between publication of a paper and its citations. The exponential decay is fitted as e −0.07t . Only citations within the RP/RQA community are considered [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Cumulative distribution function of citation numbers (papers not cited are not visible in this plot, because of the log-log axes). The scaling exponent of the fit is ∼ N −1.1 (with N the number of citations). Only citations within the RP/RQA community are considered. …
Figure 11
Figure 11. Figure 11: Maximum number of citations reached by a paper of a selected publication year, indicating milestone works. Only citations within the RP/RQA community are considered. based time series analysis [9], respectively. The small peak at 2018 indicates one of the first papers…
Figure 12
Figure 12. Figure 12: Time in years authors are publishing in the field. The exponential fit is e −0.19t [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]
Figure 13
Figure 13. Figure 13: Country-level collaboration network of co-authors. Link width indicate num￾ber of joint papers, node size correspond to number of publications assigned to the country (the larger the more publications). 123456789 10 11 12 13 14 Number co-authors per paper 0 200 (5%) 4…
Figure 14
Figure 14. Figure 14: Frequency distribution of the number of co-authors, with median = 4, and 1st and 3rd quartile as Q1 = 3 and Q3 = 5 co-authors [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: Co-author network, filtered to display only first-authors who have engaged in at least one collaboration (therefore, some communities appear to be splitted). Node size corresponds to the number of first-author papers, colour indicates different com￾munities (with only…

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