Anonymous Walk Embeddings (1805.11921v3)

Abstract: The task of representing entire graphs has seen a surge of prominent results, mainly due to learning convolutional neural networks (CNNs) on graph-structured data. While CNNs demonstrate state-of-the-art performance in graph classification task, such methods are supervised and therefore steer away from the original problem of network representation in task-agnostic manner. Here, we coherently propose an approach for embedding entire graphs and show that our feature representations with SVM classifier increase classification accuracy of CNN algorithms and traditional graph kernels. For this we describe a recently discovered graph object, anonymous walk, on which we design task-independent algorithms for learning graph representations in explicit and distributed way. Overall, our work represents a new scalable unsupervised learning of state-of-the-art representations of entire graphs.

• The paper introduces a novel unsupervised method leveraging anonymous walks to efficiently capture and represent graph structures.
• It presents both feature-based and data-driven embedding techniques, drawing parallels to language models like word2vec.
• Empirical evaluations show competitive classification accuracy across social and biochemical datasets, highlighting the method's versatility.

Analysis of Anonymous Walk Embeddings in Network Representation

In the presented paper, Ivanov and Burnaev explore the domain of network representations through the utilization of anonymous walk embeddings (AWE). The paper addresses the challenge of effectively representing graph-structured data, which has proven invaluable in a wide array of machine learning applications, particularly in tasks involving graph classification. The authors introduce an approach that incorporates anonymous walks derived from graph structures to develop both feature-based and data-driven embeddings, contributing to the scalability and effectiveness of network representation.

The paper posits that traditional network embeddings often rely on supervised learning models that may not capture task-agnostic characteristics inherent in graph structures. The authors aim to resolve this by proposing a scalable, unsupervised method that leverages the inherent characteristics of anonymous walks, which are random walks that abstract away node identifiers, thus capturing unique and characteristic patterns of the graph topology.

Core Contributions

1. Feature-based Network Embeddings: This approach abstracts graph features through the lens of anonymous walks, which are analyzed to establish a probabilistic feature vector for the graph representation. The authors provide an efficient sampling strategy to approximate the distribution of these walks, thereby circumventing the computationally intensive task of calculating exact distributions, especially in large networks.
2. Data-driven Network Embeddings: Inspired by natural language processing techniques such as word2vec, the paper builds graph representations by treating anonymous walks as analogous to words and graphs as documents. This method relies on maximizing the probability of context co-occurrence within the graph, employing gradient descent for optimizing the embeddings, and demonstrating robustness when used with standard machine learning classifiers such as SVM.

Empirical Evaluation

The paper presents empirical evaluations on several graph classification tasks to benchmark the performance of AWE against existing models like the Weisfeiler-Lehman kernel, deep graph kernels, and convolutional neural network-based methods. In many cases, AWE exhibits competitive classification accuracy, indicating its potential efficacy in domains requiring robust network representations. Specifically, AWE shows promise in both social and biochemical datasets, highlighting its versatility across different graph types.

Theoretical Implications

The proposed method of anonymous walks theoretically underscores an intriguing property whereby the presence and frequency of anonymous walks in a subgraph can be sufficient to reconstruct its topology, barring ambiguity or isomorphism. This offers an implicit verification of the robustness of anonymous walks in capturing essential structural features, which serve as a foundation for constructing graph embeddings.

Future Directions

Potential future directions include exploring the extension of anonymous walk embeddings for more fine-grained applications such as node and edge embeddings, thereby generalizing the applicability of AWE within detailed graph analytics. Additionally, investigating the parameterization of anonymous walks and optimizing sampling techniques could further enhance computational efficiency and embedding quality.

In conclusion, the paper by Ivanov and Burnaev provides a compelling method for network representation via anonymous walks, achieving notable performance without requiring supervised learning, thus opening pathways for more flexible and scalable graph-based learning systems.