Graph Classification via Adjacency Matrix Diagonal Concentration

The patent segments the graph extraction process into multiple stages with different window sizes. Small window sizes are used for initial feature extraction, while larger window sizes are applied in subsequent stages to capture larger subgraph structures. This multi-scale segmentation approach enables the system to handle both local detailed features and global structural patterns without overwhelming computational complexity at any single stage.

The patent introduces a hierarchical dimension to the feature extraction process by organizing features across multiple scales and levels. Instead of using a single window size, the system creates a multi-dimensional feature space where features are extracted at different resolution levels, allowing large subgraphs to be captured by combining information from multiple smaller window-based extractions across different hierarchical levels.

The patent divides the computational task into segments performed at different hierarchical levels. Rather than computing features over the entire graph at once (which would be computationally expensive), the system segments the computation into local neighborhood operations followed by progressive aggregation, reducing the computational burden while maintaining accuracy.

The patent performs preliminary feature extraction using small window sizes to capture local patterns first. These pre-extracted features are then aggregated and used as input for subsequent stages with larger effective window sizes. This preliminary action at smaller scales reduces the dimensionality of the problem for later stages, decreasing overall computational complexity.

The patent implements a nested hierarchical structure where small-window features are nested within larger-context features, which are in turn nested within even larger structural patterns. Each level of the hierarchy captures features at its appropriate scale, with deeper levels capturing implicit correlation structures that span multiple vertices. This nested arrangement allows efficient local computation at each level while progressively building up to capture deep structural features.

The patent maintains continuous feature extraction across multiple hierarchical levels rather than performing discrete independent extractions. The feature extraction process continues progressively from local to global scales, with each stage building upon and refining features from previous stages, ensuring that deep features are captured through continuous refinement rather than lost in discrete computational steps.

The patent segments high-dimensional graph data into lower-dimensional local neighborhoods that can be processed independently at each hierarchical level. By dividing the high-dimensional processing task into segments operating on local subgraphs, the system can represent complex global structures while keeping individual processing steps manageable in dimensionality.

The patent transforms the high-dimensional graph processing problem by introducing a hierarchical dimension. Instead of processing all vertices simultaneously in a single high-dimensional space, the system organizes processing across multiple hierarchical levels, effectively adding a hierarchical dimension that reduces the computational dimensionality at each level while preserving the ability to represent complex structures.