Temporal Link Prediction using Matrix and Tensor Factorizations (1005.4006v2)

Abstract: The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T+1? If our data has underlying periodic structure, can we predict out even further in time, i.e., links at time T+2, T+3, etc.? In this paper, we consider bipartite graphs that evolve over time and consider matrix- and tensor-based methods for predicting future links. We present a weight-based method for collapsing multi-year data into a single matrix. We show how the well-known Katz method for link prediction can be extended to bipartite graphs and, moreover, approximated in a scalable way using a truncated singular value decomposition. Using a CANDECOMP/PARAFAC tensor decomposition of the data, we illustrate the usefulness of exploiting the natural three-dimensional structure of temporal link data. Through several numerical experiments, we demonstrate that both matrix- and tensor-based techniques are effective for temporal link prediction despite the inherent difficulty of the problem. Additionally, we show that tensor-based techniques are particularly effective for temporal data with varying periodic patterns.

• The paper demonstrates that tensor techniques outperform matrix methods for long-term link prediction in evolving bipartite graphs.
• The methodology employs truncated singular value decomposition and CP tensor decomposition to capture complex temporal and periodic patterns.
• Numerical experiments show that tensor methods maintain high predictive accuracy in noisy environments, while matrix methods excel at immediate predictions.

Analyzing Temporal Link Prediction with Matrix and Tensor Techniques

The paper "Temporal Link Prediction using Matrix and Tensor Factorizations" by Dunlavy, Kolda, and Acar explores the problem of predicting future links in evolving bipartite graphs. By leveraging link data across time, the authors aim to forecast links at future time points, particularly for datasets with periodic structures. The paper evaluates matrix- and tensor-based methodologies, providing a comprehensive comparative analysis through numerical experiments.

Methodological Approaches

The paper meticulously examines both matrix and tensor approaches for temporal link prediction:

1. Matrix-Based Methods: The paper utilizes the Katz measure, extending its applicability to bipartite graphs. A notable aspect is the scalable approximation using truncated singular value decomposition (TSVD), facilitating efficient computation of Katz scores. The authors also introduce a weight-based method for temporal data aggregation, outperforming simple summation in link prediction contexts.
2. Tensor-Based Methods: The CANDECOMP/PARAFAC (CP) tensor decomposition is employed to exploit the three-dimensional structure inherent in temporal link data. This approach enables capturing complex temporal patterns, particularly effective for data with periodic variations. Forecasting methods, such as Holt-Winters, are used to predict beyond a single time step, showcasing the robustness of tensor analysis in capturing periodicity.

Results and Implications

The numerical experiments underscore the efficacy of the proposed methods:

• Matrix vs. Tensor Performance: Despite matrix methods like Katz-CWT demonstrating strong AUC values for immediate predictions, tensor methods provide unparalleled predictive capability over extended periods. The experiments with simulated data highlight tensor methods' ability to maintain prediction accuracy even amidst significant noise.
• Prediction of New Links: Tensor techniques showed a substantial advantage in predicting unseen links, indicating their potential in identifying emergent relationships.

The paper elucidates that temporal and periodic patterns, which are inadequately captured by matrix-based aggregation, can be effectively modeled using tensor techniques. This distinction becomes particularly critical for domains involving dynamic interactions over time, such as social networks and communication systems.

Future Directions

The research opens doors for further explorations in temporal link prediction by:

• Investigating alternative tensor models and decompositions that might capture even more nuanced temporal patterns.
• Expanding approaches to multi-mode networks where more than two types of entities interact.
• Addressing scalability challenges, particularly in high-dimensional datasets, to improve computational efficiency while maintaining accuracy.

In conclusion, the application of tensor-based methods in temporal link prediction presents promising avenues for further research, particularly in domains with intricate temporal dynamics. The work invites continued exploration into the integration of advanced tensor decomposition techniques with time-series analysis, potentially revolutionizing predictive analytics in complex networks.