The core problem, as the authors describe it, is that conventional recommendation systems treat a user’s trajectory as a simple sequence of visits and then model only the consecutive correlations between neighboring check-ins. That strategy is vulnerable to what the team calls time bias. Real people deviate from their routines: a commuter catches a later train, a lunch appointment shifts by forty minutes, an errand is skipped one week and doubled up the next. Sequence models that latch onto exact consecutive orderings are easily corrupted by these deviations and by random noise in the data. Worse, most methods ignore periodicity altogether or rely on pre-specified intervals and fixed ranges, hard-coded assumptions that prevent the model from learning the true rhythm of a user’s life adaptively. The researchers also identified a second blind spot: geography. Existing systems tend to reason about spatial proximity at a single, fine-grained scale, even though human mobility is organized hierarchically across neighborhoods, cities, and regions.

Before building their model, the team examined real-world data from Foursquare and found striking statistical evidence for both kinds of regularity. Users’ trajectories showed multi-span temporal patterns, meaning activity tendencies differ across periods such as weekdays versus rest days, and multi-interval patterns, in which a person returns to the same location after a roughly fixed gap, such as every day or every four hours. Spatially, different users roam across regions of very different extent, from a few city blocks to entire metropolitan areas. These observations framed the design brief for MultiPerG: the model needed to discover periodic patterns at multiple intervals and spans without being told what they are, tolerate the small biases that come with human behavior, and read geographic structure at multiple scales simultaneously.

Architecturally, MultiPerG is a hierarchical framework built on the foundations of temporal convolutional networks, or TCNs, a family of sequence models that use causal convolutions, which prevent information from the future leaking into the past, and dilated convolutions, which deliberately skip positions to widen the network’s receptive field. The researchers transform a user’s check-in history into a sequence feature map, a matrix analogous to an image in computer vision, by segmenting the week into equal one-hour gaps over seven days. Candidate locations are likewise converted into a geography feature map by gridding GPS coordinates into equal-area units, and this map is built hierarchically so that each level represents a coarser spatial granularity. A codebook stores the coordinates of every location across all scale levels, allowing the network to look up where any given POI sits within the multi-scale geographic structure.

The heart of the innovation lies in three novel kinds of deformable blocks. The first two handle time. A multi-interval deformable tree layer arranges dilated causal convolutions into a binary-tree structure, with left and right branches preserving the outermost elements of each segment. The convolutions carry learnable deformable offsets, a technique borrowed from deformable convolutional networks in computer vision, which let the sampling positions of each kernel float slightly rather than sitting at fixed intervals. In practice, these offsets absorb the consecutive time bias and accidental fluctuations produced by deviant visits, so the model can still detect that a user returns to a place roughly every day even when the actual visits drift by an hour or two. A second, segment-tree-structured layer works in the complementary direction, combining adjacent segments of the sequence into progressively larger spans so that patterns like day-long or month-long routines emerge adaptively. The outputs of the interval and span layers are then multiplied together to form a joint periodic representation of the user’s habits.

The third block addresses space. The geo-span learning layer stacks two-dimensional dilated causal convolutions across the hierarchical levels of the geography feature map, capturing spatial dependence at scales ranging from fine urban units up to broad regions. The authors note a subtle problem with this design: when locations are discretized onto maps, noise arises because two places that fall into the same unit at one scale may belong to distinct sections at a finer scale. To suppress this, they introduce a custom non-linear activation function called tan, described as the counterpart of tanh in the complex domain via Euler’s formula, whose steep gradient behavior approaching infinity amplifies large-scale influence while diminishing small-scale noise. After amplification and normalization, the outputs of all geographic levels are summed with adjusted weights, and the learned geographic patterns are combined with the periodic sequence patterns to produce, through a query embedding, a probability for every candidate location.

Training uses a cross-entropy loss summed over users, with randomly selected negative samples, and the network is optimized with Adam and mini-batch stochastic gradient descent. The team evaluated MultiPerG against eleven state-of-the-art baselines spanning four methodological families: CNN-based models such as Caser, CosRec, NextItNet and NASR; attention-based models including TiSASRec, STAN and ASPPA; the graph-neural-network-based CyGNet; and RNN-based models LSTPM and PLSPL. Experiments ran ten times on NVIDIA V100 GPUs with baselines fine-tuned for fairness, using four datasets: Foursquare check-ins from New York City and Tokyo, Yelp data from Tucson, and the full Gowalla dataset, filtered to remove inactive users and locations.

The results were decisive. MultiPerG outperformed every baseline on every recall metric at cutoffs of five, ten and twenty recommendations. On the New York and Tokyo datasets it improved Recall@5 by 5.5 and 6.4 percent respectively over the strongest competitor, the LSTM-based PLSPL, and on Gowalla the gains were larger still, at 10.5 percent for Recall@5 and 11.8 percent for Recall@10. The comparison also yielded interesting secondary findings: recurrent models excelled at personalized accuracy but lagged on generalized performance, while models built on temporal convolutional networks with large receptive fields, such as NASR and NextItNet, fared best among the CNN family. Ablation studies confirmed that every module earns its place. Removing the geo-span layer hurt most, underscoring how much geography contributes to next-POI prediction, while removing the interval layer cost slightly more than removing the span layer, suggesting interval periodicity is marginally more influential. Embedding dimensions of roughly 50 to 60 proved sufficient, and a modest geography map size of 128 units performed well.

Perhaps most compelling are the interpretability analyses. Heatmaps of the interval and span layer outputs for 32 New York users over 72 hours revealed a clear four-hour interval pattern during daytime hours, stronger relevance among midnight spans, and an overarching 24-hour daily repetition in both, matching the expected rhythm of human activity. The deformable offsets visibly corrected time bias in the trajectories. Geographic heatmaps, meanwhile, showed clustered high-relevance zones that align with users’ real activity centers: in the New York data the hot zones match the densest check-in areas, and in Gowalla they correspond to Texas and California, the two states contributing the most data. The authors conclude that MultiPerG’s advantage stems precisely from its ability to explore periodic patterns, and they point toward future work on more variations of the geography blocks and more generalized periodicity recovery. For now, the study offers a vivid demonstration that the key to predicting where someone will go next lies not just in where they have been, but in the nested rhythms of time and space that shape every journey.

Subject of Research: Next point-of-interest recommendation using periodic and geographic pattern learning in human trajectory data

Article Title: MultiPerG: Multiple Periodic Geography convolution for next POI recommendation

Article References: Wang, X., Wang, B., Wang, D., Wang, Z., Sun, G., Zhao, B., & Chen, M. (2025). MultiPerG: Multiple Periodic Geography convolution for next POI recommendation. Vicinagearth, 2(1), Article 3. https://doi.org/10.1007/s44336-025-00012-1

Image Credits: AI Generated

DOI: 10.1007/s44336-025-00012-1

Keywords: POI recommendation, human mobility, temporal convolutional network, periodic patterns, geographic patterns, deformable convolution, location-based social networks, sequence modeling, deep learning, trajectory mining, Foursquare, Gowalla