Graph Feature Extraction via Adjacency Matrix Diagonal Concentration
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Solution Overview
Problem
Existing graph classification methods face challenges in capturing large multi-vertex subgraph structures and deep features from implicit correlation structures at both vertex and edge levels, leading to reduced accuracy due to computational complexity and limited window size constraints.
Innovation Solution
The system concentrates connection information in the adjacency matrix into a specific diagonal region, using a filter matrix to extract subgraph structures along the diagonal direction, and employs a stacked convolutional neural network to capture larger subgraph structures and deep features, reducing computational complexity and improving classification accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional graph classification methods use limited window size to extract features, then computational complexity is reduced, but the ability to capture large multi-vertex subgraph structures is limited
Solution Approach 1:
The patent transforms the graph adjacency matrix into a new representation space by computing powers of the adjacency matrix (A, A², A³, etc.), where each power represents connections at different hop distances. This dimensional transformation allows the model to capture large-scale subgraph structures indirectly through multiple small-window convolutions on the transformed features, resolving the contradiction between limited window size and large subgraph capture capability.
2Measurement precision
If the window size is increased to capture larger subgraph structures, then the capture accuracy improves, but computational complexity increases significantly
Solution Approach 1:
The patent segments the graph structure analysis into multiple hierarchical levels by using different powers of the adjacency matrix (A¹ for direct connections, A² for two-hop connections, etc.). Each level captures subgraph structures at a specific scale, and the combination of these segmented features enables comprehensive capture of large subgraph structures without requiring a single large window, thus reducing computational complexity while maintaining accuracy.
3Measurement precision
If deep features from implicit correlation structures are extracted, then classification accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent performs preliminary transformation of the graph data by computing powers of the adjacency matrix before applying convolutional operations. This preliminary action pre-computes and encodes implicit correlation structures at different distances, making them explicitly visible in the transformed feature space. Subsequent shallow convolutions can then efficiently extract deep features from these pre-processed representations without the computational burden of searching for implicit correlations during the main processing stage.
Data Source
AI summary
A method and system of graph feature extraction and graph classification based on adjacency matrix is provided. The invention first concentrates the connection information elements in the adjacency matrix into a specific diagonal region of the adjacency matrix which reduces the non-connection information elements in advance. Then the subgraph structure of the graph is further extracted along the diagonal direction using the filter matrix. Further, it uses a stacked convolutional neural network to extract a larger subgraph structure. On one hand, it greatly reduces the amount of computation and complexity, getting rid of the limitations caused by computational complexity and window size. On the other hand, it can capture large subgraph structure through a small window, as well as deep features from the implicit correlation structures at both vertex and edge level, which improves speed and accuracy of graph classification.