Local-Aggregation Graph Networks.

Area of Science:

• Computer Science
• Machine Learning
• Graph Neural Networks

Background:

• Traditional Convolutional Neural Networks (CNNs) are limited to Euclidean domains due to their reliance on ordered, grid-like data.
• This limitation restricts CNNs from effectively processing non-Euclidean data such as graphs, traffic networks, and molecular structures.

Purpose of the Study:

• To develop a novel aggregation function capable of handling permutation-unordered and dimension-unequal inputs on non-Euclidean domains.
• To introduce Local-Aggregation Graph Networks (LAGNs) by replacing traditional convolution with this new function, enabling CNNs to operate on graph-structured data.

Main Methods:

• A local-aggregation function was designed as a sharable nonlinear operation.
• This function is parameterized using orthonormal polynomials, drawing from function approximation theory for efficiency.
• The new function replaces standard convolution in CNN architectures, creating LAGNs.

Main Results:

• LAGNs can fit nonlinear functions without requiring activation functions.
• The networks are trainable using standard back-propagation, demonstrating training efficiency.
• Extensive experiments showed superior performance of LAGNs across diverse tasks like text categorization, molecular activity detection, taxi flow prediction, and image classification.

Conclusions:

• Local-Aggregation Graph Networks (LAGNs) effectively extend CNN capabilities to non-Euclidean graph domains.
• The proposed local-aggregation function offers an efficient and effective method for processing complex, unordered graph data.
• LAGNs demonstrate significant potential for advancing pattern recognition and machine learning on graph-structured data.