Local Node Embeddings via Submodular Hypergraphs
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Solution Overview
Problem
Existing methods for obtaining local node embeddings in heterogeneous graphs are inefficient, particularly for large hypergraphs, as they often rely on global embeddings, are not scalable, and introduce approximation errors or require complex tuning, failing to capture nuanced relationships and user-defined patterns effectively.
Innovation Solution
The method employs submodular hypergraphs and 1-regularized personalized PageRank to compute local node embeddings, allowing for efficient processing without reducing hypergraphs to simpler graphs, and using submodular cut-cost functions to discriminate hyperedge cuts, thereby capturing complex relationships and improving scalability and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If global embeddings are used for heterogeneous graphs, then comprehensive graph representation is achieved, but computational efficiency and scalability deteriorate for large graphs
Solution Approach 1:
The patent segments the graph processing into local neighborhoods around seed nodes rather than processing the entire graph globally. This is achieved through personalized PageRank that confines computations to ε- neighborhoods, dividing the large-scale problem into smaller, manageable local regions that can be processed independently and efficiently
Solution Approach 2:
The patent applies local quality by computing embeddings specifically for local neighborhoods rather than uniform global embeddings. Each node's embedding is computed based on its local structural context and relationships, allowing the representation to adapt to local graph characteristics while maintaining computational efficiency
2Device complexity
If standard graph algorithms are applied to heterogeneous graphs, then algorithm simplicity is maintained, but ability to capture fine-grained relationships deteriorates
Solution Approach 1:
The patent changes key parameters of the PageRank algorithm to suit heterogeneous graphs: introducing teleportation probability α to seed nodes, modifying the transition matrix to handle hyperedges, and adjusting the embedding dimensionality. These parameter changes enable the algorithm to capture fine-grained relationships while maintaining the iterative simplicity of PageRank
Solution Approach 2:
The patent introduces submodular functions as intermediaries to bridge simple iterative computation and complex relationship capture. The submodular objective function serves as a mediator that encodes higher-order relationships and graph structure complexity, allowing the simple PageRank iteration to achieve sophisticated relationship modeling
3Productivity
If hypergraphs are reduced to simpler graphs for processing, then computational scalability is improved, but approximation errors increase
Solution Approach 1:
Instead of reducing hypergraphs to simpler graphs as conventional approaches do, the patent inverts the approach by developing algorithms that work directly on the hypergraph structure. The personalized PageRank is computed on the original hypergraph with hyperedges intact, and embeddings are derived without any reduction or approximation, thereby maintaining both scalability and accuracy
4Measurement precision
If complex tuning parameters are introduced to capture nuanced relationships, then relationship capture accuracy is improved, but ease of operation deteriorates
Solution Approach 1:
The patent enables the algorithm to self-adjust and adapt to the graph structure through the inherent properties of personalized PageRank and submodular optimization. The teleportation probability α and embedding dimension k are the primary parameters, while the algorithm automatically adapts to different graph structures through the diffusion process and submodular objective, reducing the need for extensive manual tuning
Data Source
AI summary
Provided are computing systems, methods, and platforms that obtain local node embeddings for heterogeneous graphs. A heterogeneous graph comprising a plurality of nodes can be obtained. Weight values respectively associated with subgraphs of the heterogeneous graph can be determined. At least one node from among the plurality of nodes can be selected. An embedding for the at least one selected node can be learned using an embedding objective computed based on the weight values. The heterogeneous graph can be processed based on the embedding. Submodular hypergraphs can be used to represent heterogeneous graphs and their cuts. The 1-regularized personalized PageRank can be applied to hypergraphs, where the optimal solution gives the node embedding for the given seed nodes. The resulting 1-regularized personalized PageRank can be solved in running time without depending on the size of the whole graph.