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

Social influence estimation is a cornerstone problem for platforms that rely on word-of-mouth dynamics. Identifying influential users underpins targeted advertising, viral marketing campaigns, and behavior prediction models. Prior work has long suggested that similarity between users is a significant driver of influence: people tend to trust, imitate, and adopt behaviors from those who resemble them. Traditional approaches measured that resemblance through structural metrics such as common neighbors, Jaccard coefficients, or path-based distances within the social graph. More recent methods turned to representation learning, embedding users into continuous vector spaces where proximity reflects similarity. Yet, as the authors point out, these techniques capture only limited facets of user characteristics, typically ignoring the rich geographic dimension that location-based social networks uniquely provide.

The study addresses this gap with two progressive contributions. The first, called NSH, short for Node Embedding and Spatial Homophily, is a hybrid, unsupervised method that linearly combines embedding-based structural similarity with spatial homophily, the well-documented tendency of geographically close users to be socially connected and behaviorally alike. NSH is deliberately simple and interpretable: it takes a user similarity score derived from network embeddings and blends it with a spatial homophily score computed from check-in co-location patterns. The result is a transparent similarity measure that serves as a strong baseline for analyzing the relationship between similarity and influence, and one that practitioners can compute without heavy machinery.

The second and central innovation is GeoSocial2Vec, an end-to-end unified embedding model designed to learn a single representation for each user by intrinsically merging social ties and spatial co-visitation patterns. Rather than computing two separate similarity scores and averaging them, GeoSocial2Vec constructs a heterogeneous graph in which users, social links, and locations coexist as nodes of different types. An adaptive random walk mechanism then traverses this combined graph, generating sequences of nodes that alternate between social hops and spatial transitions. These walks are fed into a skip-gram style embedding procedure, so that the resulting vectors encode both who a user knows and where a user goes within one coherent geometric space. The adaptive component weights different transition types dynamically, allowing the model to balance social and spatial evidence according to the structure of the data rather than a fixed heuristic.

This design reflects a broader shift in representation learning toward heterogeneous graph embeddings, where multiple node and edge types are embedded jointly instead of being projected into separate spaces. In the context of location-based social networks, the payoff is substantial. Two users who never interact directly but repeatedly visit the same neighborhoods at similar times will land close together in the GeoSocial2Vec embedding, capturing a latent affinity that pure network metrics would miss. Conversely, two friends who live in different cities and never share locations will still be pulled together by their social tie, something a purely geographic model would overlook. The embedding, in effect, learns the full socio-spatial signature of each user.

To test whether these richer similarity measures actually track influence, the researchers evaluated the relationship between user similarity and social influence through Pearson correlation and regression analysis on geographically filtered segments of three real-world location-based social networks: Gowalla, Brightkite, and Foursquare. These datasets, drawn from check-in services that were popular in the early 2010s, remain standard benchmarks in this field because they pair explicit friendship graphs with millions of timestamped location records. Filtering the data geographically ensured that the spatial component of the analysis was meaningful, focusing on regions dense enough for co-visitation patterns to be statistically robust.

The results were striking. Both proposed methods, in which spatial homophily is integrated with embedding-based similarity, produced a significantly stronger correlation with observed influence patterns than classical approaches that rely on structure alone. The GeoSocial2Vec framework achieved the highest accuracy across the benchmarks, demonstrating that intrinsically coupled socio-spatial learning outperforms post-hoc fusion of separate signals. In other words, it matters not just that social and geographic information are both considered, but that they are woven together during representation learning itself, allowing the model to capture interactions between the two dimensions that a linear combination cannot express.

At the same time, the authors are careful not to declare NSH obsolete. While GeoSocial2Vec offers the best predictive performance, the NSH framework retains clear advantages in interpretability and computational simplicity. Because NSH is a linear fusion of two comprehensible scores, an analyst can inspect exactly how much of a predicted influence relationship stems from network proximity versus geographic overlap. This transparency matters in business applications where stakeholders must justify targeting decisions, and in settings where training a deep heterogeneous embedding model is impractical due to limited compute or data volume. The two frameworks thus occupy complementary niches: GeoSocial2Vec as the accuracy-oriented state of the art, and NSH as a practical, explainable tool for everyday analysis.

The implications extend well beyond academic benchmarking. For advertisers on check-in-driven platforms, influence estimation that accounts for where people go, not just who they know, could sharpen the selection of seed users in viral campaigns, ensuring that promotional content spreads through communities that are both socially and geographically primed to receive it. For behavior prediction, the fused embeddings offer a way to anticipate adoption of products, venues, or even public health behaviors by modeling the twin channels of social contagion and spatial co-presence. Urban planners and mobility researchers may also find the technique useful, since the same embeddings encode movement regularities that correlate with social structure.

The study also contributes to a long-running scientific conversation about homophily, the principle that similar individuals connect and influence one another. Spatial homophily has been documented repeatedly in location-based social networks, where the probability of friendship decays with physical distance and shared places act as meeting grounds for ties. By demonstrating that this geographic dimension measurably strengthens the link between similarity and influence, the research quantifies how much predictive power has been left on the table by purely structural methods. It suggests that future influence models, and by extension the recommendation and marketing systems built on them, should treat location not as metadata but as a first-class signal in the learning process.

Technically, the work sits at the intersection of network embedding, heterogeneous graph learning, and random-walk-based representation methods. The adaptive random walk at the heart of GeoSocial2Vec echoes the logic of metapath-guided walks in heterogeneous graphs, but with a twist: transition probabilities are tuned to the data, letting the model decide how often to follow social edges versus spatial co-visit links. This adaptivity is what allows a single embedding space to serve both dimensions faithfully, and it is likely the key reason the framework outperformed the linear NSH fusion. The evaluation methodology, combining Pearson correlation with regression analysis across three independent platforms, adds confidence that the findings are not an artifact of one dataset’s quirks.

Limitations and open questions remain, as they do in any study of this kind. The benchmark datasets are aging, and modern platforms may exhibit different spatial dynamics, particularly as privacy changes and check-in behavior declines in some services. Influence itself is a latent quantity, inferred from observed diffusion patterns rather than measured directly, so all correlation results inherit the assumptions of the influence estimation pipeline. The authors also note that the published version is an early-access, peer-reviewed accepted manuscript carrying a permanent DOI, subject to final editorial edits. Still, the core message is robust: when it comes to understanding who moves whom in location-based social networks, knowing both the social graph and the map beats knowing either alone.

As location-aware platforms continue to blend commerce, mobility, and social connection, methods like GeoSocial2Vec point toward a future in which influence is predicted not from a single flattened network, but from the rich, coupled reality of how people relate and where they roam. The research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors, and the authors declare no competing interests.

Subject of Research: Estimating social influence in location-based social networks using embedding-based similarity and spatial homophily

Article Title: Investigating social influence using embedding-based similarity and spatial homophily on the location based social networks

Article References: Akhavan-Hejazi, Z. S., Ghobaei-Arani, M., & Sajjadi, Z. S. (2026). Investigating social influence using embedding-based similarity and spatial homophily on the location based social networks. Journal of Big Data. https://doi.org/10.1186/s40537-026-01546-x

Image Credits: AI Generated

DOI: 10.1186/s40537-026-01546-x

Keywords: social influence, location-based social networks, node embeddings, spatial homophily, GeoSocial2Vec, heterogeneous graph, random walk, Gowalla, Brightkite, Foursquare, representation learning, targeted advertising