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

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

physics.soc-phOct 12, 2026

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

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

Organizations: Complex Connections Lab, Network Science Institute, Northeastern University, London, United Kingdom · Public Tech Media Lab, University of Wisconsin-Madison, Madison, WI, United States · Nokia Bell Labs, Cambridge, United Kingdom · Politecnico di Torino, Turin, Italy ·

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.

Figures & tables

Figure 1: Toy example of early classification of venue popularity trajectories. We test at which point of time $t$ (denoted as the percentage of data available to the model in the figure) the cost is minimized. Intuitively, for instance, trends are nearly indistinguishable when the data completeness is insufficient and if they are moving into the same direction (cluster 1 and cluster 3; cluster 2 and cluster 4 at 30%). It is only when more data are revealed (at 70%), we are able to distinguish the actual shapes of these paths. Notably, when the completeness is 100%, the task is the same as a detection task.

Figure 2: Typology of popularity trajectories of urban venues in London and Barcelona. Panel A : the general shapes of the six recurring trajectory types. Panel B : proportional count of each type in Barcelona and London. Both cities have a similar distribution, with Steady being the most common type and Underdogs the least common. Panel C : the empirical distribution of the two urban features, namely population density and scaled deprivation level, grouped by trajectory types.

Figure 3: Earliness-accuracy trade-off of early classification. Panel (A) shows the main result of XGBoost, the best performing model overall. Categories such as Fall and Steady do not gain much over

k

, meaning that most decisions can be made earlier given their values. However, other categories that are more difficult classify in the first place. Panel (B) - (D) are the learning curves with increasing

k

of different models.

$k$		Fall	Rise	Rise & Fall	Steady	Ephemeral	Underdogs	Overall
5	J	0.234	0.268	0.199	0.103	0.207	0.848	0.212
5	P	0.225	0.211	0.165	0.087	0.207	0.450	0.224
6	J	0.191	0.277	0.182	0.096	0.189	0.845	0.200
6	P	0.181	0.199	0.140	0.080	0.193	0.384	0.196
7	J	0.191	0.274	0.173	0.107	0.225	0.728	0.197
7	P	0.173	0.199	0.116	0.084	0.224	0.373	0.195

Table 1: Forecasting performance, measured as mean squared error (MSE).

k

indexes historical observations in decreasing recency, from

k=10

(6 months prior) to

k=5

(5 years prior), so a smaller

k

means an earlier and less informed forecast. Given the input length

k

, the model predicts the remaining values of a performance trajectory after time

k

the exact values from

k+1

until

k=T

. J = joint training, a single model trained on all venues; P = per-cluster training, a separate model trained for each trajectory shape. The six named columns shows the MSE of each trajectory type, and Overall gives the mean of all venues for a particular time

k

. Within each row, the lowest error is shaded green and the highest red . As hypothesized, the difficulty of trend forecasting grows as

k

decreases, meaning that long-term prediction is more challenging than short-term prediction. We also found that Underdogs are the most difficult to predict, meanwhile the Steady cluster is the easiest to predict across even all

k

Figure 4: Panel A: The mean chance-corrected assortativity coefficient $\hat{\alpha}$ is scale-variant in both London and Barcelona, with most venues experiencing stronger (dis)assortativity on the block-level, but decays toward zero due to the inclusion of more venues as $R$ increases. Panel B: Results of the spatial shuffle null model. The histograms show the distribution of the between-circle variance $\sigma_{\text{null}}^{2}$ generated from the null model with $R=300$ , and the gray vertical line is the observed between-circle $\sigma_{\text{obs}}^{2}$ . Panel C: For each pair of trajectory types, the heatmap shows how often venues of those two types are found within $R=300$ m of each other. This count is divided by the count expected under a random reassignment of labels to the same venue locations, and shown on a $\log_{2}$ scale. Values above zero mean the pair co-occurs more than chance would give, values below zero less. Note that this panel uses $R=300$ m for both cities, unlike the per-venue assortativity feature, which uses $300$ m in London and $500$ m in Barcelona.

Figure 5: Panel A: Street map of the focal areas investigated in London (left) and Barcelona (right). The size of the points indicates the assortativity (scaled for clarity) and the color indicates the trajectory types. Panel B: Upper panel shows the distribution of assortativity in both cities with the KDE plot (gray) showing the city average and the dotted vertical line indicates the mean assortativity of the focal zones. Lower panel shows the exact values of assortativity of each venue in the focal areas.

City	Venue Category	Trajectory	Status	Chain?
London	Premium hair salon	Rise	Open	✓
	Wine bar			X
	Vegan cafe			X
	French brasserie & cocktail bar	Steady		X
	Craft beer retailer			✓
	Hipster pizza			✓

Table 2: Comparative qualitative summary of the venue profiles in the focal areas in Hackney (London) and Ciutat Vella (Barcelona).

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1: Log-Log Rank-frequency distribution of like counts in London and Barcelona. The power law fit yielded $\alpha\approx 2.34$ and $\alpha\approx 2.50$ . However, we also note that, using the Vuong’s closeness test, the distribution is not distinguishable from a lognormal distribution ( $p>.05$ ) and thus we only describe this as a heavy-detailed distribution rather than a power law one.

Figure S2: Log frequency distribution of lifespan (in weeks) in London and Barcelona. We estimated the lifespan by taking the day difference between the earliest and the latest like made for the venue.

Figure S3: Frequency distribution of assortativity $\hat{a}$ in London and Barcelona. The distributions of assortativity coefficients for both cities are centred around zero.

Figure S4: Frequency distribution of categories in London and Barcelona. Due to some venues having multiple categories, we have displayed here the first appearing tag as the primary category. The data show a culturally aligned distribution of popular category types, for example pubs and Mediterranean food venues being the most popular primary categories in London and Barcelona respectively.

Figure S5: Normalized sentiment scores of venues in London (blue) and Barcelona (Orange) across 11 time points. Sentiment is first measured by DistilBERT-based multilingual sentiment model and rescaled to -2 to 2, aggregated on a six-monthly basis. Missing data are imputed by the mean of a given vector. Similar to the performance trajectory, we then length-normalized the sentiment time series to 11 points with a linear interpolation and extrapolation.

Trajectory type	Description
Rise	Popularity increases steadily over time.
Fall	Popularity decreases steadily over time.
Rise & Fall	Popularity rises at first, then declines in the later period.
Steady	Popularity is maintained over time without much fluctuation.
Ephemeral	Initially popular, but declines rapidly.
Underdogs	Initially unpopular, but gains popularity later on.

Appendix

Table 3: The six popularity-trajectory types recovered by DTW clustering, common to both London and Barcelona.

Figure S6: The standard deviation of the values in length-normalized trajectories for each shape. As Steady and Rise & Fall are visually similar, we also fitted the trajectories to the quadratic form $ax^{2}+bx+c$ and compared the average curvature of each group. A two-sided Mann-Whitney-U test shows significant differences betweeen the average curvature ( $U=3329523.0,p<.001$ ) with Rise & Fall (average $a=0.021$ ) trajectories being more curved than Steady ones (average $a=0.016$ ).

Model	Fall	Rise	Rise & Fall	Steady	Ephemeral	Underdogs	Macro F1
Logistic Regression	0.81	0.82	0.51	0.72	0.85	0.66	0.729
Random Forest	0.78	0.82	0.53	0.78	0.85	0.57	0.723
XGBoost	0.84	0.85	0.76	0.86	0.88	0.79	0.830
Class Average	0.79	0.82	0.54	0.77	0.86	0.56	—

Appendix

Table 4: Per-class F1-scores across all models. Easiest class to predict highlighted in green , hardest in red , and best results in bold .

City	Feature set	Model	Balanced Acc.	F1
London	Urban	Logistic Regression	0.514 $\pm$ 0.017	0.513 $\pm$ 0.018
		Random Forest	0.531 $\pm$ 0.009	0.529 $\pm$ 0.009
		XGBoost	0.534 $\pm$ 0.008	0.533 $\pm$ 0.009
	Venue	Logistic Regression	0.495 $\pm$ 0.012	0.491 $\pm$ 0.012
		Random Forest	0.814 $\pm$ 0.019	0.813 $\pm$ 0.019
		XGBoost	0.778 $\pm$ 0.018	0.778 $\pm$ 0.018

Appendix

Table 5: Binary classification performance (mean

\pm

std) with 5-fold cross-validation by city, feature set, and model. Best model per feature-set block shown in bold . Random seed is

98765

City	Feature set	Model	Balanced Acc.	F1
London	Urban	Logistic Regression	0.158 $\pm$ 0.017	0.100 $\pm$ 0.030
		Random Forest	0.175 $\pm$ 0.011	0.160 $\pm$ 0.006
		XGBoost	0.175 $\pm$ 0.013	0.166 $\pm$ 0.012
	Venue	Logistic Regression	0.191 $\pm$ 0.007	0.112 $\pm$ 0.016
		Random Forest	0.694 $\pm$ 0.031	0.686 $\pm$ 0.028
		XGBoost	0.620 $\pm$ 0.030	0.637 $\pm$ 0.030

Appendix

Table 6: Multiclass classification performance (mean

\pm

std) with 5-fold cross-validation by city, feature set, and model. Best model per feature-set block shown in bold . Random seed is

98765

Feature set	Model	F1 (London)	F1 (Barcelona)	$\Delta$ F1
Binary
Urban	Logistic Regression	0.513	0.538	$-$ 0.025
Urban	Random Forest	0.529	0.538	$-$ 0.009
Urban	XGBoost	0.533	0.559	$-$ 0.026
Venue	Logistic Regression	0.491	0.523	$-$ 0.031
Venue	Random Forest	0.813	0.688	$+$ 0.126

Appendix

Table 7: City comparison of F1 scores (averaged across folds) across feature sets and models, binary and multiclass tasks.

\Delta

F1 = F1(London)

-

F1(Barcelona). Random seed is

98765

City	Task	Deprivation	Pop. Density	Uniqueness	Assortativity
London	Binary	$.011\pm.004$	$.025\pm.008$	$.001\pm.003$	$.011\pm.005$
	Multiclass	$.010\pm.003$	$.010\pm.005$	$.006\pm.004$	$.014\pm.004$
Barcelona	Binary	$-.003\pm.002$	$\mathbf{.041\pm.014}$	$.007\pm.008$	$-.005\pm.006$
	Multiclass	$.003\pm.006$	$\mathbf{.021\pm.007}$	$.010\pm.005$	$.021\pm.005$

Appendix

Table 8: Permutation importance (mean

\pm

std) for predicting venue popularity trend using 5-fold cross-validation. Bolded cells indicate the most important feature for each model: (a) Logistic Regression, (b) Random Forest, (c) XGBoost. Random seed is

98765

Figure S7: Macro F1-score as a function of early-classification horizon $k$ , across feature ablations. Error bars denote $\pm$ std across 5 folds. Baseline_venue , Baseline_static (i.e., urban + venue), and All consistently outperform Baseline , Baseline_Sentiment , and Baseline_urban for $k\leq 9$ . All ablations exhibit a sharp increase in F1-score as $k$ approaches $10$ , consistent with the sequence itself becoming sufficiently informative once most of it has been observed.

City	$R$	Obs. variance	Null variance	$p$	# Circles
London	200	0.00805	0.00740	0.282	347
	250	0.00687	0.00597	0.218	384
	300	0.00664	0.00491	0.080	409
	500	0.00292	0.00271	0.317	468
Barcelona	200	0.01141	0.00666	0.022 ∗	327
	250	0.01025	0.00641	0.060	375

Appendix

Table 9: Spatial null model for

\hat{\alpha}

in London and Barcelona. * indicates a significant difference between the observed and null variance of

\hat{\alpha}

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