Hierarchical Graph Pooling via Grouping Matrix Decomposition
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Solution Overview
Problem
Existing graph neural networks face challenges in hierarchically aggregating information beyond local convolutions, particularly in graph-level prediction tasks, due to the standard procedure of globally pooling all node features without weighing differences.
Innovation Solution
A learning processing device and method that generate a grouping matrix based on the similarity of pairwise nodes in graph data, and decompose this matrix in a square-root form to obtain a pooling operator, allowing for hierarchical pooling of graph data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If globally pooling all node features into a single graph representation is used, then the graph-level prediction task can be performed, but the model cannot hierarchically aggregate information beyond local convolutions
Solution Approach 1:
The patent segments the graph data into multiple hierarchical levels using grouping matrices at different scales. Instead of a single global pooling operation, the method applies sequential pooling operations with grouping matrices that operate at different hierarchical levels, allowing information to be aggregated progressively from local to global scales while preserving structural relationships.
Solution Approach 2:
The patent introduces a hierarchical dimension to the pooling process by applying multiple grouping matrices with different ranks and structures. This transforms the single-dimensional global pooling into a multi-dimensional hierarchical aggregation process, enabling information to flow through multiple levels of abstraction while maintaining graph structure.
2Device complexity
If standard global pooling is applied, then computation is simplified, but the number of clusters cannot be automatically determined and hierarchical structure is lost
Solution Approach 1:
The patent makes the pooling operation dynamic by using learnable grouping matrices whose structure and rank are determined during the training process. The model adaptively learns the appropriate number of clusters and their configurations based on the input graph data, rather than requiring fixed pre-defined parameters. This dynamic approach allows the system to adjust to different graph structures automatically.
Solution Approach 2:
The patent changes the parameters of the pooling operation by using multiple grouping matrices with different ranks and structures. Instead of a fixed pooling operation, the method employs a series of pooling operations with varying parameters that are learned during training, enabling automatic adaptation to different graph sizes and structures while maintaining computational efficiency.
3Ease of operation
If all node features are pooled equally into a single representation, then the pooling process is simple, but differences between nodes are not weighted
Solution Approach 1:
The patent applies local quality by using grouping matrices that assign different weights to different nodes based on their local structural properties and similarities. Each grouping matrix operates locally to identify and weight nodes with similar characteristics, creating differentiated representations that capture local graph structures while maintaining overall simplicity through matrix operations.
Data Source
AI summary
A learning processing device and method for pooling graph data of a hierarchical structure based on a grouping matrix, and a method for learning an artificial intelligence model. The learning processing device includes a memory and a processor in communication with the memory. The processor generates a grouping matrix of a secondary form, grouped based on a similarity of a pairwise nodes by inputting graph data into a pre-learned first artificial intelligence model; and decomposes the grouping matrix to generate a pooling matrix. The grouping matrix is decomposed in a square-root form to obtain a pooling operator.