Frequency Domain-Oriented Complex Graph Neural Networks for Graph Classification.

Area of Science:

• Machine Learning
• Graph Neural Networks
• Complex Analysis

Background:

• Current Graph Neural Networks (GNNs) are limited to the spatial domain.
• GNNs typically learn real-valued, low-dimensional embeddings for graph classification.
• There is a need for GNNs that can capture richer representations beyond the spatial domain.

Purpose of the Study:

• To explore frequency domain-oriented complex Graph Neural Networks (cGNNs).
• To address challenges in designing graph pooling for complex embeddings.
• To improve the representational power and efficiency of GNNs for graph classification tasks.

Main Methods:

• Proposed a mirror-connected design for complex GNNs where node embeddings are complex vectors.
• Introduced squared singular value pooling (SSVP) to address parameter reduction.
• Developed a feasible method for complex gradient backpropagation to handle complex embeddings.
• Incorporated a mixture of pooling strategies with first-order statistics.

Main Results:

• Proved the representational equivalence of SSVP followed by a specific fully connected layer to a mirror-connected layer.
• Provided a theoretical guarantee for solving singular values of complex embeddings.
• Demonstrated the effectiveness of the proposed complex GNNs with mirror-connected layers on benchmark datasets.

Conclusions:

• Complex GNNs operating in the frequency domain offer enhanced capabilities for graph representation learning.
• The proposed mirror-connected design and SSVP effectively address key challenges in complex GNNs.
• The developed methods show significant improvements in graph classification tasks.