HARP: Hierarchical Representation Learning for Networks (1706.07845v2)

Abstract: We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively avoiding troublesome embedding configurations (i.e. local minima) which can pose problems to non-convex optimization. HARP works by finding a smaller graph which approximates the global structure of its input. This simplified graph is used to learn a set of initial representations, which serve as good initializations for learning representations in the original, detailed graph. We inductively extend this idea, by decomposing a graph in a series of levels, and then embed the hierarchy of graphs from the coarsest one to the original graph. HARP is a general meta-strategy to improve all of the state-of-the-art neural algorithms for embedding graphs, including DeepWalk, LINE, and Node2vec. Indeed, we demonstrate that applying HARP's hierarchical paradigm yields improved implementations for all three of these methods, as evaluated on both classification tasks on real-world graphs such as DBLP, BlogCatalog, CiteSeer, and Arxiv, where we achieve a performance gain over the original implementations by up to 14% Macro F1.

• The paper introduces a hierarchical paradigm that progressively coalesces graphs to capture both local and global structures, reducing optimization pitfalls.
• The methodology integrates edge and star collapsing techniques with proven algorithms like DeepWalk, LINE, and Node2vec to refine node embeddings.
• Empirical results show up to a 14% Macro F1 score improvement in tasks like classification and clustering, demonstrating HARP's practical impact.

An Analysis of HARP: Hierarchical Representation Learning for Networks

The paper "HARP: Hierarchical Representation Learning for Networks" presents a novel approach to graph representation learning that meticulously addresses key limitations present in existing methodologies. Traditional approaches, while successful in several domains, primarily focus on learning local neighborhood structures and are often susceptible to optimization issues associated with non-convex problems. HARP innovatively introduces a hierarchical paradigm that preserves higher-order structural features of a graph to enhance the quality of node embeddings and achieve superior performance in downstream tasks.

Methodological Framework

The principal contribution of HARP lies in its multilevel representation learning paradigm, which leverages a hierarchy of coalesced graphs. This method recursively coalesces nodes and edges of the original graph to create smaller but structurally similar graphs, revealing the global structure often overlooked by traditional methods. The embeddings are learned progressively, from the coarsest graph to the finest, using well-established algorithms like DeepWalk, LINE, and Node2vec as the baseline methods. HARP's refinement mechanism allows these embeddings to serve as effective initializations for embedding the original graph, potentially avoiding local minima that afflict non-convex optimization processes.

HARP strategically combines two key graph coarsening techniques: edge collapsing, which preserves first-order proximities, and star collapsing, which attends to second-order proximities. These methods ensure computational efficiency and maintain the essential structural information of a graph even after significant size reduction.

Strong Numerical Results

The empirical results outlined in the paper underscore the efficacy of the HARP approach. On multiple real-world datasets such as DBLP, BlogCatalog, and CiteSeer, HARP-enhanced versions of DeepWalk, LINE, and Node2vec consistently outperform their traditional counterparts. Notably, HARP led to performance improvements up to 14% Macro F1 score in a classification context. Such gains are significant and highlight HARP's potential to deliver more reliable embeddings suitable for various graph analytic tasks.

Practical and Theoretical Implications

From a practical standpoint, the ability to accurately capture and leverage the higher-order structure in graphs opens new avenues for network analysis, offering critical enhancements in tasks like multi-label classification, clustering, and link prediction. The methodological integration of existing neural algorithms with HARP not only facilitates improved embedding quality but also preserves the scalability necessary for large networks, a notorious challenge for traditional graph representation methods.

Theoretically, the hierarchical representation learning paradigm introduced by HARP could redefine how researchers conceptualize graph embeddings, encouraging further exploration into global structural features and their impact on learning quality. Future research may delve into integrating HARP with more intricate deep learning architectures, moving beyond the confines of shallow models like Skip-gram, to potentially unlock new layers of abstraction and insight within network data.

Concluding Remarks

HARP presents a methodical and well-founded innovation in the field of graph representation learning, seamlessly marrying the robustness of traditional neural methods with an intuitive hierarchical learning approach. By addressing both local and global graph structures, HARP effectively positions itself as a versatile toolkit for researchers and practitioners aiming to navigate the complexities of networked data with enhanced precision and reliability.