Popularity Trajectories and Mixing Patterns of Urban Venues in Two European Cities

arXiv:2610.18917 · physics.soc-ph, cs.LG, cs.SI · Submitted 2026-10-12 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "Popularity Trajectories and Mixing Patterns of Urban Venues in Two European Cities".

Jane: The gist Urban venues such as restaurants, shops, bars and parks host the daily life of a city,

Tom: First, who's behind it and why it matters.

Title and authors: Tom: So, to summarize what they found about these trajectory shapes, the study looked at whether a neighborhood’s socioeconomic status or density could actually predict a venue’s trajectory <ref:2610.18917#pg5>.

Jane: And their finding was that those external factors don't have that predictive power, which is something most people might assume they should <ref:2610.18917#pg5>.

Lu: Instead of focusing on neighborhood features, the authors propose looking at the venues in the vicinities of each other to see if their trajectories are mirrored by those nearby venues <ref:2610.18917#pg5>.

Meng: They suggest this is consistent with a local performance spillover effect, and they found that most venues with the same trajectory shape are neighbours far more often than chance within a two hundred to six hundred meter radius <ref:2610.18917#pg5>.

Lalam: This spatial mixing pattern of trajectory types is scale-variant and type-specific, meaning how these shapes mix changes depending on the size of the area you look at <ref:2610.18917#pg5>.

Jane: They point out that assortativity, which is when venues cluster with their own kind, is the strongest predictor of a venue’s trajectory type <ref:2610.18917#pg5>.

Tom: That's a big shift because it moves the focus away from external neighborhood factors and towards internal spatial relationships between venues themselves <ref:2610.18917#pg5>.

Lu: The paper also mentioned that this pattern isn't spatially concentrated; it’s more of a generalizable phenomenon across neighborhoods in both cities <ref:2610.18917#pg6>.

Jane: So they are suggesting that the vibrancy you see is really happening at the block- and street-level, driven by local conditions and histories, not just big city metrics.

The paper's summary: Tom: So what they suggest to improve this research is that we should focus on those spatial relationships between venues instead of neighborhood stats <ref:2610.18917#pg5>.

Jane: They also explored how early a specific shape can be recognized, finding that "how early a shape can be recognized depends on when its distinctive segment occurs, not a shape’s complexity" <ref:2610.18917#pg5>.

Lu: The classification experiments tested the trade-off between earliness and accuracy using four classical machine learning models <ref:2610.18917#pg5>.

Meng: For forecasting, they trained a Seq2Seq model using a GRU-based Encoder-Decoder architecture to predict actual normalized popularity values <ref:2610.18917#pg5>.

Lalam: The results of that forecasting showed something specific about the "Underdog" shape: it depends on a late reversal that the model cannot anticipate, so the capacity to turn a declining venue around is largely unpredictable from past popularity alone <ref:2610.18917#pg5>.

Jane: They also mentioned that when completeness is one hundred percent, classifying the shapes becomes exactly like a detection task, and they found that Ephemeral cluster are the easiest to classify across all models with a mean F1 of zero point eight six <ref:2610.18917#pg5>.

Tom: That’s an interesting result because it suggests that when we have complete data, the task becomes much simpler, and Ephemeral venues are pretty easy to spot <ref:2610.18917#pg5>.

The paper's improvements: Jane: So to wrap up this paper on "Popularity Trajectories and Mixing Patterns of Urban Venues in Two European Cities," the main idea is that urban vibrancy emerges at the block- and street-level, meaning local conditions and histories really matter for these patterns.

Tom: So what they're saying is that understanding a city's vibrancy requires looking at the specific characteristics of those local conditions and histories rather than just broad socioeconomic metrics <ref:2610.18917#pg5>.

Lu: The work unveils a lot about the complexity behind venue performance, showing how neighborhood vibrancy comes from particular local conditions and histories <ref:2610.18917#pg5>.

Meng: It’s about moving past the idea that big-picture things dictate small-scale performance, proving that the block level is where most of this happens <ref:2610.18917#pg5>.

Lalam: And they found that social and historical contexts matter in terms of the characteristics of these patterns, which is a key piece for understanding this data <ref:2610.18917#pg5>.

Jane: So we've seen how those six shapes repeat in London and Barcelona, what they found about their predictive factors, and where they suggest we should look next <ref:2610.18917#pg5>.

Tom: Exactly. They showed that you can't predict popularity just by looking at socioeconomic status or density; the local performance spillover is the real driver here <ref:2610.18917#pg5>.

Meng: It’s about moving past the idea that big-picture things dictate small-scale performance, showing that the block level is where most of this happens <ref:2610.18917#pg5>.

Jane: That’s it for "Popularity Trajectories and Mixing Patterns of Urban Venues in Two European Cities." It shows the complexity of urban venue performance is deeply rooted in local conditions and histories.

Tom: Yeah, next time we'll look at some models that try to predict those trajectories using early data signatures.

Conclusion: Jane: So we’ve seen how this study on "Popularity Trajectories and Mixing Patterns of Urban Venues in Two European Cities" shows that urban vibrancy isn't just about big neighborhood stats or socioeconomic status.

Tom: Exactly, it comes down to the specific historical path of a venue itself, which is what this study is really showing us.

Lu: It unveils a lot about the complexity behind venue performance, showing how neighborhood vibrancy comes from particular local conditions and histories.

Meng: It’s about moving past the idea that big-picture things dictate small-scale performance, proving that the block level is where most of this happens.

Lalam: And they found that social and historical contexts matter in terms of the characteristics of these patterns, which is a key piece for understanding this data.

Jane: So we’ve seen how those six shapes repeat in London and Barcelona, what they found about their predictive factors, and where they suggest we should look next.

Tom: Exactly. They showed that you can't predict popularity just by looking at socioeconomic status or density; the local performance spillover is the real driver here.

Lu: The work unveils a lot about the complexity behind venue performance, showing how neighborhood vibrancy comes from particular local conditions and histories.

Meng: It’s about moving past the idea that big-picture things dictate small-scale performance, proving that the block level is where most of this happens.

Lalam: And they found that social and historical contexts matter in terms of the characteristics of these patterns, which is a key piece for understanding this data.

Tom: Yeah, next time we'll look at some models that try to predict those trajectories using early data signatures.

Wang Ngai Yeung, Lakmal Meegahapola, Daniele Quercia, Riccardo Di Clemente

Complex Connections Lab, Network Science Institute, Northeastern University · Nokia Bell Labs · Public Tech Media Lab, University of Wisconsin-Madison · Politecnico di Torino · ISI Foundation

physics.soc-ph, cs.LG, cs.SI

Submitted: 2026-10-12

Updated: 2026-10-12

Comments: 18 pages for main body, 8 pages for supplementary materials; 5 figures and 2 tables in main body, 7 figures and 9 tables in supplementary materials

Code: https://github.com/ComplexConnectionsLab/urban_

License: http://creativecommons.org/licenses/by/4.0/

The gist: The gist Urban venues such as restaurants, shops, bars and parks host the daily life of a city, and their collective rise and fall signals how vibrant a neighbourhood is <ref:2610.18917#pg6>.

Key concepts

Trajectory Shapes: These are six distinct patterns (Fall, Rise, etc.) that venue popularity follows over time. The researchers found these shapes recur in both cities, showing different ways venues can gain or lose popularity.
Assortativity: This describes the tendency for venues of the same popularity shape to locate near each other. This clustering is a strong predictor of a venue's trajectory type, especially within 200 to 600 meters.
Block-Level Phenomenon: The study concludes that urban vibrancy is not just about large neighborhoods but happens at the block and street level. Local conditions and specific historical contexts significantly shape these patterns.

Summary

The gist Urban venues such as restaurants, shops, bars and parks host the daily life of a city, and their collective rise and fall signals how vibrant a neighbourhood is <ref:2610.18917#pg6>. This study found six distinguishable shapes recur in both cities that are (1) Fall, (2) Rise, (3) Rise & Fall, (4) Steady, (5) Ephemeral and (6) Underdogs <ref:2610.18917#pg7>.

How it works

The researchers used 5.5 years of Foursquare data for about 104 venues in London and Barcelona to analyze popularity trajectories <ref:2610.18917#pg4>. They treated each venue’s popularity as a time series, segmented into several six-month periods, and compared pairs of series using Dynamic Time Warping (DTW) to account for unequal time series lengths <ref:2610.18917#pg5>. Grouping venues by this similarity yields six distinct trajectory shapes common to both cities <ref:2610.18917#pg5>.

Key Findings on Trajectory Shapes

The six recurring shapes are (a) Fall, (b) Rise, (c) Rise & Fall, (d) Steady, (e) Ephemeral and (f) Underdogs <ref:2610.18917#pg4>. The near-linear shapes include the Fall, Rise and Steady clusters which are generally expected patterns <ref:2610.18917#pg5>. The non-linear ones capture more complex shifts in venue popularity <ref:2610.18917#pg5>. Notably, no U-shaped Fall & Rise cluster emerged in either city, meaning recovery after a sustained decline is not one of the recurring shapes <ref:2610.18917#pg6>.

Predictors of Trajectory Type

The study investigated whether a neighbourhood’s socioeconomic status and density predict a venue’s trajectory <ref:2610.18917#pg5>. The results show that a neighbourhood’s socioeconomic status and density do not predict a venue’s trajectory <ref:2610.18917#pg5>. Instead, a venue’s trajectory is mirrored by those of the venues that are in their vicinities, which is consistent with a local performance spillover <ref:2610.18917#pg5>. Most venues with the same trajectory shape turn out to be neighbours far more often than chance within roughly 200–600 m <ref:2610.18917#pg5>. Cluster assortativity is the strongest predictor of a venue’s trajectory type <ref:2610.18917#pg5>.

Early Classification and Forecasting

The research explored how early a shape can be recognized, finding that how early a shape can be recognized depends on when its distinctive segment occurs, not a shape’s complexity <ref:2610.18917#pg5>. The classification experiments tested the trade-off between earliness and accuracy with four classical machine learning models <ref:2610.18917#pg5>. For forecasting, a Seq2Seq model using a GRU-based Encoder-Decoder architecture was trained to predict actual normalized popularity values <ref:2610.18917#pg5>. The results reflect an uncomfortable reality of business decision-making, as the earlier an answer is sought, the less trustworthy that answer is <ref:2610.18917#pg5>.

Spatial Mixing Patterns

The mixing pattern of trajectory types is scale-variant and type-specific <ref:2610.18917#pg5>. Assortativity is a block-level phenomenon that vanishes with scale, being most distinguishable at radii of roughly 200–600 m <ref:2610.18917#pg6>. The pattern is not spatially concentrated, and instead it is a generalizable phenomenon across neighbourhoods in both cities <ref:2610.18917#pg6>. The type that most strongly clusters with its own kind differs, being Rise & Fall in London and Fall in Barcelona <ref:2610.18917#pg6>.

Case Study Insights

A qualitative close reading of two contrasting districts showed that comparable socioeconomic conditions but divergent gentrification histories can generate vastly different popularity trajectories <ref:2610.18917#pg5>. In Hackney, Rise venues co-located with established venues born out of gentrification, exemplifying 'hipster urbanism' <ref:2610.18917#pg6>. In Ciutat Vella, Fall venues were strongly over-represented both among themselves and alongside Fall venues <ref:2610.18917#pg6>. These findings suggest that the neighbourhood effect is not organized entirely in the same way in the two cities <ref:2610.18917#pg6>.

The study concludes that urban vibrancy emerges at the block- and street- level, and social and historical contexts matter in terms of the characteristics of such patterns <ref:2610.18917#pg5>. This work unveils the complexity behind urban venue performance, showing how neighbourhood vibrancy emerges from particular local conditions and histories >.

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Spatial Mixing Patterns

Improvements for AI systems

The system can perform Early Time Series Classification (ETSC) by training models to predict trajectory shapes based on partial data, achieving a sharp increase in F1-score as k approaches 10 when more data is revealed. This allows for a better decision-making process for business owners by inferring what they should and should not do from partial information about their past and current performance.
The system can predict the actual popularity values of a given trajectory using per-cluster training, which showed that Underdogs depend on a late reversal that the model cannot anticipate, so the capacity to turn a declining venue around is largely unpredictable from past popularity alone. This informs strategic planning by providing forecasts with varying levels of predictability based on the forecast horizon (k).
The system can distinguish between trajectory shapes with high accuracy when sufficient data is available, as when completeness is 100%, the task is the same as a detection task, and it identifies Ephemeral cluster are the easiest to classify (mean F1 = 0.86) across all models.
The system can assess spatial spillover effects on a block- or street-level scale by leveraging assortativity, as this feature is the strongest predictor of a venue’s trajectory type and that most venues with the same trajectory shape turn out to be neighbours far more often than chance within roughly 200–600 m.
The system can perform context-aware classification by integrating urban and venue features, as this combination yielded improved performance in both binary and multiclass settings, demonstrating that Venue Random Forest 0.814 ± 0.688 +0.126 in the binary task for London shows how these features contribute to prediction accuracy over shape-only models.

Abstract

Urban venues such as restaurants, shops, bars and parks host the daily life of a city, and their collective rise and fall signals how vibrant a neighbourhood is. The usual assumption is that a venue's fortunes follow its neighbourhood's, so that how wealthy an area is and how many people live there will decide a venue's performance. Yet whether there is a common performance trajectory shared by venues over time is underexplored. In this study, we use 5.5 years of Foursquare data for about 10 4 venues in London and Barcelona. We found six distinguishable shapes recur in both cities, that are (1) Fall, (2) Rise, (3) Rise & Fall, (4) Steady, (5) Ephemeral (an early hit that loses popularity fast) and (6) Underdogs (a slow starter that gains popularity late). However, no recovery shape appears, that is neither city yields a U-shaped fall-and-rise group. Additionally, we found that deprivation and population density are not indicative which shape a venue follows. We also discovered that how early a shape can be recognized depends on when its distinctive segment occurs, not a shape's complexity. Proximity between venues, however, does predict how well-performing a venue is. We uncovered a mixing pattern where venues of the same shape tend to locate together more often than chance within roughly 200 to 600 metres. Finally, our qualitative reading of two contrasting districts, one rising in London and one falling in Barcelona, show that comparable socioeconomic conditions but divergent gentrification histories can generate vastly different popularity trajectories. All in all, our results altogether point at that urban vibrancy emerges at the block- and street- level, and social and historical contexts matter in terms of the characteristics of such patterns.

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Key concepts

Summary

Improvements for AI systems

Abstract

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