Node Embeddings Using Polar Coordinates for Graph Processing
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Solution Overview
Problem
Machine-learning models that utilize graphs face increased computational time and memory requirements as graph size grows, leading to longer training times and data skew, necessitating an improved system for generating node embeddings that is fast, scalable, and memory-efficient.
Innovation Solution
The method involves generating node embeddings using polar coordinates with uniform random distributions, converting them to Cartesian coordinates, and pre-training machine-learning models based on negative samples, allowing for efficient processing and reduced computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If graph size increases to represent more data, then data coverage and model applicability improve, but computational time and memory requirements increase
Solution Approach 1:
The patent segments the graph embedding training process by using polar coordinate representations that divide the embedding space into angular sectors. This segmentation allows for more efficient processing of large graphs by organizing nodes in a structured polar format rather than traditional Cartesian coordinates, reducing computational overhead while maintaining comprehensive data coverage
Solution Approach 2:
The patent changes the coordinate system parameter from Cartesian to polar coordinates for representing node embeddings. This parameter change transforms the embedding representation, enabling more efficient computation and memory usage while handling larger graph sizes, thus improving data coverage without proportionally increasing computational time
2Adaptability or versatility
If graph size increases to include more nodes and edges, then model comprehensiveness improves, but memory requirements increase
Solution Approach 1:
The patent changes the embedding representation parameter from Cartesian coordinates to polar coordinates, which reduces the memory footprint required to store node embeddings in large graphs. This parameter transformation maintains model comprehensiveness while optimizing memory efficiency by exploiting the angular symmetry in graph structure data
3Ease of manufacture
If traditional embedding methods are used, then implementation simplicity is maintained, but training time increases
Solution Approach 1:
The patent modifies the embedding coordinate parameter from Cartesian to polar representation, which reduces training time while maintaining implementation simplicity. The polar coordinate system naturally accommodates graph embedding operations and allows for more efficient gradient computations during training, achieving faster convergence without significantly complicating the implementation
Data Source
AI summary
Provided are systems, methods, and computer program products for generating node embeddings. The system includes at least one processor programmed or configured to generate a graph comprising a plurality of nodes, generate an embedding for each node of the plurality of nodes, each embedding comprising at least one polar angle and a vector length, store each embedding of a plurality of embeddings in memory, and in response to processing the graph with a machine-learning algorithm, convert at least one embedding of the plurality of embeddings to Cartesian coordinates.