[Paper Review] HONEM: Network Embedding Using Higher-Order Patterns in Sequential Data.

Mandana Saebi, Giovanni Luca Ciampaglia+2 more|arXiv (Cornell University)|Aug 15, 2019

Advanced Graph Neural Networks20 references4 citations

TL;DR

HONEM proposes a novel network embedding method that captures higher-order temporal and sequential dependencies in network data by constructing a higher-order neighborhood matrix, overcoming the limitations of first-order Markovian assumptions in existing methods. It outperforms state-of-the-art approaches in node classification, link prediction, network reconstruction, and visualization by modeling complex, long-range interaction patterns.

ABSTRACT

Representation learning offers a powerful alternative to the oft painstaking process of manual feature engineering, and as a result, has enjoyed considerable success in recent years. This success is especially striking in the context of graph mining, since networks can take advantage of vast troves of sequential data to encode information about interactions between entities of interest. But how do we learn embeddings on networks that have higher-order and sequential dependencies? Existing network embedding methods naively assume the Markovian property (first-order dependency) for node interactions, which may not capture the time-dependent and longer-range underlying complex interactions of the raw data. To address the limitation of current methods, we propose a network embedding method for higher-order networks (HON). We demonstrate that the higher-order network embedding (HONEM) method is able to extract higher-order dependencies from HON to construct the higher-order neighborhood matrix of the network, while existing methods are not able to capture these higher-order dependencies. We show that our method outperforms other state-of-the-art methods in node classification, network reconstruction, link prediction, and visualization.

Motivation & Objective

• To address the limitation of existing network embedding methods that assume first-order Markovian dependencies in node interactions.
• To model higher-order and time-dependent dependencies in sequential network data that are often overlooked by current approaches.
• To develop a method capable of extracting complex, long-range interaction patterns from raw sequential data in networks.
• To improve performance in downstream tasks such as node classification, link prediction, and network reconstruction by leveraging higher-order structures.
• To provide a more accurate representation of network dynamics through a higher-order neighborhood matrix construction.

Proposed method

• HONEM constructs a higher-order neighborhood matrix by analyzing sequential interaction patterns among nodes in the network.
• It models higher-order dependencies by capturing multi-step interaction sequences rather than relying on immediate neighbor relationships.
• The method transforms raw sequential data into a higher-order network (HON) structure that encodes complex temporal dependencies.
• It employs a matrix factorization approach on the higher-order neighborhood matrix to learn low-dimensional node embeddings.
• The embedding learning process preserves both structural and sequential information from the network's interaction history.
• The framework is designed to be compatible with standard downstream tasks such as node classification and link prediction.

Experimental results

Research questions

• RQ1 Can higher-order dependencies in sequential network data be effectively captured to improve network embedding quality?
• RQ2 How does modeling long-range interaction patterns impact performance in node classification and link prediction tasks?
• RQ3 To what extent does HONEM outperform first-order methods in network reconstruction and visualization?
• RQ4 Can the higher-order neighborhood matrix representation better reflect the true dynamics of real-world sequential networks?
• RQ5 What is the contribution of sequential interaction patterns to the overall representational power of learned embeddings?

Key findings

• HONEM successfully captures higher-order dependencies in sequential network data that first-order methods fail to model.
• The method achieves superior performance in node classification compared to state-of-the-art baselines on sequential network datasets.
• HONEM demonstrates improved link prediction accuracy by leveraging long-range interaction patterns beyond immediate neighbors.
• The network reconstruction task shows that HONEM preserves structural and sequential information more effectively than existing methods.
• Visualizations of HONEM embeddings reveal clearer and more meaningful cluster structures, indicating better semantic representation.
• The higher-order neighborhood matrix construction enables more accurate and informative low-dimensional node embeddings.