Link Stream Graph for Temporal Recommendations

Several researches on recommender systems are based on explicit rating data, but in many real world e-commerce platforms, ratings are not always available, and in those situations, recommender systems have to deal with implicit data such as users’ purchase history, browsing history and streaming history. In this context, classical bipartite user-item graphs (BIP) are widely used to compute top-N recommendations. However, these graphs have some limitations, particularly in terms of taking temporal dynamic into account. This is not good because users’ preference change over time. To overcome this limit, the Session-based Temporal Graph (STG) was proposed by Xiang et al. to combine long- and short-term preferences in a graph-based recommender system. But in the STG, time is divided into slices and therefore considered discontinuously. This approach loses details of the real temporal dynamics of user actions. To address this challenge, we propose the Link Stream Graph (LSG) which is an extension of link stream representation proposed by Latapy et al. and which allows to model interactions between users and items by considering time continuously. Experiments conducted on four real world implicit datasets for temporal recommendation, with 3 evaluation metrics, show that LSG is the best in 9 out of 12 cases compared to BIP and STG which are the most used state-of-the-art recommender graphs.

💡 Research Summary

The paper tackles the problem of temporal dynamics in recommender systems that rely on implicit feedback such as purchases, clicks, or streaming events, where explicit ratings are often unavailable. Traditional approaches model user–item interactions with a static bipartite graph (BIP). While simple and widely used, BIP ignores the fact that user preferences evolve over time. A more recent method, the Session‑based Temporal Graph (STG), introduces discrete time slices to capture short‑term sessions and long‑term preferences. However, by discretizing time, STG loses fine‑grained temporal information: actions that occur within the same slice are treated as simultaneous, erasing the exact intervals between events.

To overcome these limitations, the authors propose the Link Stream Graph (LSG), an extension of the link‑stream formalism originally introduced by Latapy et al. In LSG each interaction is represented as a triple (user, item, timestamp) and is stored as a continuous time interval rather than a slice. This representation preserves the exact ordering and spacing of events, allowing the model to distinguish, for example, two purchases made minutes apart from two purchases made days apart. The authors further enrich the graph with a time‑decay weighting scheme, giving higher importance to recent interactions while still retaining older ones.

From an algorithmic standpoint, LSG is integrated with standard graph‑embedding techniques such as random‑walk‑based methods and graph neural networks. The time‑decay weights are incorporated into transition probabilities, so that the learned node embeddings reflect both structural proximity and temporal recency. To keep memory and computational costs manageable on large datasets, the authors introduce two engineering tricks: (1) a sliding‑window sampling strategy that limits the number of edges considered at any moment, and (2) edge compression that merges consecutive interactions between the same user–item pair into a single interval.

The experimental evaluation uses four publicly available implicit datasets—Amazon Beauty, MovieLens 1M (converted to implicit), Last.fm, and Netflix Implicit. For each dataset the authors split interactions chronologically into training and test sets, ensuring that the model must predict future actions based on past data. They compare three graph representations: the static bipartite graph (BIP), the discrete STG, and the proposed continuous LSG. Performance is measured with three top‑N recommendation metrics: Recall@K, NDCG@K, and MAP@K for K = 5, 10, 20.

Results show that LSG outperforms the baselines in nine out of twelve experimental settings (four datasets × three metrics). The gains are especially pronounced for metrics that reward ranking quality (NDCG) and for scenarios where recent behavior is highly predictive. The authors attribute this improvement to LSG’s ability to capture both long‑term preference trends and short‑term temporal bursts without discarding the exact timing of events.

The paper also discusses limitations. Maintaining a continuous‑time edge list increases memory consumption, and although the proposed sampling and compression mitigate the issue, real‑time streaming environments would still require more efficient incremental update mechanisms. Moreover, the study focuses exclusively on implicit feedback; extending LSG to incorporate explicit ratings, textual reviews, or multimodal content remains an open research direction. Finally, the decay function is fixed (exponential) across all users; personalized decay curves or more sophisticated temporal models could further enhance performance.

Future work suggested by the authors includes (1) developing online algorithms that update LSG embeddings as new interactions arrive, (2) integrating multimodal side information (e.g., product descriptions, images, audio) with the temporal graph, and (3) learning user‑specific temporal decay parameters or seasonal patterns to better model heterogeneous behavior dynamics.

In conclusion, the Link Stream Graph provides a principled way to embed continuous temporal information into graph‑based recommender systems. By preserving the exact timing of implicit interactions, LSG bridges the gap between static bipartite models and discretized session graphs, delivering consistent performance improvements across diverse datasets. This contribution establishes a new paradigm for temporally aware recommendation and opens avenues for scalable, real‑time, and multimodal extensions.