Detecting bus delays and service anomalies in Niterói with autoencoder latent feature representations

Matheus Germano; Claudio E. C. Campelo

cs.LGOct 26, 2026

Detecting bus delays and service anomalies in Niterói with autoencoder latent feature representations

Authors: Matheus Germano, Claudio E. C. Campelo

Organizations: Systems and Computing Department, Federal University of Campina Grande (UFCG), Campina Grande, PB, Brazil

Abstract

Bus riders judge service by two failures: single trips that run late, and days on which the whole system misbehaves. We ask whether one unsupervised representation of raw GPS telemetry can serve both diagnoses on the NetMob 2026 Niterói bus dataset. An autoencoder compresses each trip into a 64-dimensional latent vector; the frozen encoder feeds supervised delay classifiers, and the reconstruction error serves as an anomaly score. Two findings are negative. First, the latent representation does not improve delay detection: gradient boosting on per-trip summary features reaches $0.846 \pm 0.013$ ROC-AUC against $0.838 \pm 0.016$ for the best latent setup, and the gap becomes significant once the preprocessing filters are relaxed. Second, two of the three external checks of the anomaly score were circular. Retraining without rainfall removes the rain association ( $5.4\%$ against $5.0\%$ flagged, $p = 0.84$ ) and an apparent citywide disruption on 23 March. What survives is a day-level signal stable across three autoencoders (Spearman $ρ\geq 0.96$ ), driven mostly by day type, with degraded-telemetry days still separable within weekday and weekend strata. The alarm threshold limits detection more than the score does: a pooled percentile cut flags $5.7\%$ of trips on the worst degraded day, while re-scaling within each bus line flags $29.3\%$ . The delay model rests almost entirely on one feature, no latent dimension is individually interpretable, and 22 chronic line-directions carry half of all delayed trips.

Figures & tables

Figure 1: How the delay label is made. Left, the distribution of median stop delay against the schedule over the $22{,}605$ retained trips, with the five-minute rule marked. The threshold falls on the shoulder of a broad unimodal distribution rather than at a natural gap, so the delayed share responds smoothly to where it is placed. The axis is clipped at $\pm 40$ minutes and the $5.6\%$ of trips beyond that are stacked into the end bins. Right, the delayed share of each of the 20 service dates against the overall rate of $20.9\%$ . The day-to-day spread is what makes service date the grouping variable for cross-validation (Section 4 . 4.3 ).

Gate	Threshold	Dropped	%
No GTFS match	no schedule join for trip id/direction	$0$	$0.00$
Too few points	$<10$ GPS points	$526$	$1.37$
Implausible duration	outside $8$ min– $3$ h	$1{,}186$	$3.09$
Off-route	$>40\%$ of points $>200$ m from shape	$2{,}112$	$5.50$
Low stop coverage	$<5$ matched stops or $<50\%$ coverage	$6{,}609$	$17.21$
Multi-vehicle trip id †	same trip id served by several vehicles	$4{,}267$	$11.11$

Table 1: Quality gates and how many trips each removes. Percentages are of the

38{,}411

candidate trip instances. Gates are applied in the order listed; each count is the number of instances that gate removed from what reached it. † The multi-vehicle row is a deduplication rather than a rejection, since the segment with the most points is kept and the others discarded, so the trip survives. See Section 3 . 3.5 . ‡ The midnight-flip row is a reassignment:

835

trips that crossed midnight were moved to the adjacent service day and kept.

Train / test split	ROC-AUC	PR-AUC
strict train, strict test	$0.850$	$0.648$
strict train, recovered test	$0.785$	$0.522$
relaxed train, strict test	$0.848$	$0.643$
relaxed train, all test	$0.853$	$0.641$

Table 2: RAW-STATS+XGBoost under the relaxed rule, mean over five folds. Training on the recovered trips is harmless; scoring on them is not.

Figure 2: Validation reconstruction MSE per fold, for the CNN-AE with rainfall in the input (solid) and without it (dashed). Fold 5 holds out 23 March, the 11.8 mm/h rain day. With rainfall as an input its error runs roughly four times higher than any other fold and never settles; drop the channel and the fold behaves like the rest. Error scales differ enough between folds that pooling raw MSE would confound fold identity with anomaly, which is why we standardise within each fold.

Representation	Classifier	ROC-AUC	PR-AUC	Precision	Recall	F1
CNN-AE	MLP	$0.824\pm 0.021$	$0.593\pm 0.054$	$0.437\pm 0.032$	$0.738\pm 0.072$	$0.548\pm 0.037$
CNN-AE	XGBoost	$0.838\pm 0.016$	$0.629\pm 0.051$	$0.539\pm 0.056$	$0.637\pm 0.054$	$0.581\pm 0.039$
CNN-AE	RF	$0.839\pm 0.015$	$0.621\pm 0.053$	$0.546\pm 0.057$	$0.612\pm 0.062$	$0.574\pm 0.039$
CNN-AE	LR	$0.811\pm 0.017$	$0.564\pm 0.054$	$0.446\pm 0.043$	$0.694\pm 0.057$	$0.541\pm 0.040$
CNN-AE	LSTM	$0.826\pm 0.020$	$0.601\pm 0.052$	$0.448\pm 0.040$	$0.738\pm 0.058$	$0.557\pm 0.041$
CNN-AE	GRU	$0.828\pm 0.023$	$0.607\pm 0.052$	$0.437\pm 0.050$	$\mathbf{0.752\pm 0.048}$	$0.552\pm 0.048$

Table 3: Delay detection on unseen days: mean

\pm

SD over the five day-grouped folds. Delayed-class prevalence is

0.209

. F1 is binary F1 on the delayed (positive) class. Best value per column in bold.

Comparison	Metric	Difference	$p_{t}$	$p_{W}$
CNN-AE+XGBoost vs RAW-STATS+XGBoost	ROC-AUC	$-0.0076$	$0.213$	$0.188$
CNN-AE+XGBoost vs RAW-STATS+XGBoost	PR-AUC	$-0.0082$	$0.087$	$0.062$
CNN-AE+XGBoost vs RAW-FLAT+XGBoost	ROC-AUC	$-0.0064$	$0.264$	$0.312$
CNN-AE+XGBoost vs RAW-FLAT+XGBoost	PR-AUC	$-0.0027$	$0.510$	$0.438$
CNN-AE+RF vs RAW-STATS+RF	ROC-AUC	$+0.0053$	$0.365$	$0.625$
CNN-AE+RF vs RAW-STATS+RF	PR-AUC	$+0.0108$	$0.262$	$0.312$

Table 4: Paired comparisons over the five folds. Positive difference favours the first model.

p_{t}

is the paired

t

-test,

p_{W}

the Wilcoxon signed-rank test.

Dataset	Trips	Delayed	RAW-STATS	CNN-AE	$\Delta$ ( $p_{t}$ )	RAW-STATS	CNN-AE	$\Delta$ ( $p_{t}$ )
			ROC-AUC			PR-AUC
strict (reported)	$22{,}605$	$20.92\%$	$0.846\pm 0.013$	$0.838\pm 0.016$	$-0.008$ ( $0.213$ )	$0.637\pm 0.053$	$0.629\pm 0.051$	$-0.008$ ( $0.087$ )
stop rule relaxed	$27{,}494$	$20.36\%$	$0.853\pm 0.011$	$0.839\pm 0.016$	$-0.014$ ( $\mathbf{0.028}$ )	$0.641\pm 0.025$	$0.623\pm 0.023$	$-0.017$ ( $\mathbf{0.033}$ )
multi-vehicle merged	$22{,}417$	$20.52\%$	$0.847\pm 0.015$	$0.837\pm 0.022$	$-0.010$ ( $0.155$ )	$0.639\pm 0.053$	$0.627\pm 0.064$	$-0.013$ ( $0.191$ )
all gates relaxed	$30{,}546$	$20.91\%$	$0.854\pm 0.023$	$0.830\pm 0.042$	$-0.024$ ( $0.067$ )	$0.652\pm 0.055$	$0.620\pm 0.074$	$-0.031$ ( $\mathbf{0.040}$ )

Table 5: Raw features against the latent representation across four versions of the dataset. Each row is a full rebuild of the preprocessing followed by a fresh autoencoder and a fresh baseline on the same day-grouped folds. Differences are CNN-AE minus RAW-STATS, so negative favours the raw features;

p_{t}

is a paired

t

-test over the five folds.

Latent dim	Conv blocks	ROC-AUC	PR-AUC
$128$	$3$	$0.8377$	$0.6326$
$64$	$4$	$0.8338$	$0.6198$
$64$	$3$	$0.8375$	$0.6292$
$64$	$2$	$0.8366$	$0.6298$
$32$	$3$	$0.8344$	$0.6237$
$16$	$3$	$0.8262$	$0.6078$

Table 6: Autoencoder architecture sweep, CNN-AE+XGBoost, mean over the five folds, ordered by descending latent dimension then depth. No configuration reaches the raw-feature baseline.

Figure 3: t-SNE of $5{,}000$ out-of-fold CNN-AE latents, coloured by anomaly score (left), delay label (centre) and service date (right). The five lobes correspond to the five fold-specific encoders.

Route seen	ROC-AUC	PR-AUC	Skill retained
$25\%$	$0.824\pm 0.011$	$0.581\pm 0.046$	$93.8\%$
$50\%$	$0.838\pm 0.012$	$0.620\pm 0.048$	$97.7\%$
$75\%$	$0.844\pm 0.012$	$0.635\pm 0.051$	$99.6\%$
$100\%$	$0.846\pm 0.013$	$0.637\pm 0.053$	$100\%$

Table 7: Delay detection from a prefix of the trip, RAW-STATS+XGBoost, mean

\pm

SD over the five folds. The last column is the share of the full-trip discriminative power retained, measured above the

0.5

chance baseline.

Figure 4: What the delay model uses. Left, the drop in ROC-AUC when each feature is permuted, averaged over the five folds with the cross-fold standard deviation as the error bar. Right, the logistic coefficient on standardised features, which gives the direction of each effect; a dot marks the features that reach $p<0.05$ in every fold.

Figure 5: CNN-AE versus LSTM-AE anomaly scores, standardised log reconstruction error, so zero is the average trip. Dashed lines mark each model’s 95th percentile flagging threshold ( $1.53$ for the CNN-AE, $1.61$ for the LSTM-AE). Trips in the upper-right quadrant are flagged by both models, those in the off-diagonal quadrants by only one.

Validation	With rainfall	Without rainfall	Verdict
Degraded days (20, 22 Mar), median score	$+0.37$ vs $-0.21$	$+0.50$ vs $-0.20$	survives
one-sided Mann–Whitney	$p=9\times 10^{-122}$	$p=6\times 10^{-118}$
Rain-hour flag rate vs dry	$12.2\%$ vs $4.4\%$	$5.4\%$ vs $5.0\%$	does not survive
significance	$p=2.8\times 10^{-23}$	$p=0.84$
23 Mar 15:30–17:00 window, median score	$+5.43$	$-0.22$	does not survive
trips in global top-20	$20/20$	$0/20$

Table 8: Weather-free ablation. Each validation is recomputed with the CNN-AE retrained without the rainfall channel. Two of the three original signals do not survive. The degraded-day row uses 20 and 22 March; see the text for 28 March.

Figure 6: Anomaly score by rain condition for the weather-inclusive models. The association shown here is the one the ablation in Table 8 removes; it is reproduced to document what the original validation looked like.

AE input	ROC-AUC	PR-AUC	recon. AUC
12 ch., no schedule	$0.838$	$0.629$	$0.505$
$+$ start deviation	$0.961$	$0.887$	$0.519$
$+$ median stop delay	$0.989$	$0.964$	$0.515$

Table 9: Adding a schedule channel to the AE input. Delay detection becomes close to trivial, while the reconstruction error stays uninformative about the label. Mean over the five folds.

Figure 7: Day-median anomaly score, sorted by the weather-free variant. Weekends (shaded) occupy five of the top seven positions.

Stratum	Degraded median	Normal median	one-sided $p$
Weekdays	$+0.002$ ( $n=612$ )	$-0.295$ ( $n=15{,}860$ )	$9.5\times 10^{-8}$
Weekends	$+0.418$ ( $n=1{,}494$ )	$+0.110$ ( $n=4{,}639$ )	$4.1\times 10^{-14}$
22 Mar vs other Sundays	$+0.740$ ( $n=1{,}045$ )	$+0.206$ ( $n=2{,}005$ )	$5.2\times 10^{-42}$

Table 10: Degraded versus normal days, stratified by day type (weather-free CNN-AE). The degraded-day effect holds within both strata, so it is not an artefact of 22 March being a Sunday.

Rule	Overall	22 Mar	Lift
global-p95	$5.0\%$	$5.7\%$	$1.1\times$
dynamic	$6.8\%$	$10.3\%$	$1.5\times$
per-line	$6.1\%$	$\mathbf{29.3\%}$	$\mathbf{4.8\times}$
per-hour	$6.6\%$	$10.3\%$	$1.6\times$

Table 11: Threshold rules evaluated on the weather-free CNN-AE scores. The diagnostic case is 22 March, the most severely degraded day.

Figure 8: Alarm rate per service date under the four threshold rules. Known degraded days shaded. Per-line calibration is the only rule that makes 22 March stand out.

Figure 9: Where the delay sits in the network. Left, the 14 worst of the 22 chronically late line-directions, with delay rate and its Wilson $95\%$ interval, coloured by direction of travel; the dashed line is the network rate of $20.9\%$ . The two directions of a line are ranked separately and often fall far apart. Right, delay rate against scheduled headway, with the number of trips in each band. The relation is U-shaped, so a single rank correlation describes it poorly.

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