Robust Spatial Filtering with Graph Convolutional Neural Networks (1703.00792v3)

Abstract: Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract information than the previous layer. The simplicity and elegance of the convolutional filtering process makes them perfect for structured problems such as image, video, or voice, where vertices are homogeneous in the sense of number, location, and strength of neighbors. The vast majority of classification problems, for example in the pharmaceutical, homeland security, and financial domains are unstructured. As these problems are formulated into unstructured graphs, the heterogeneity of these problems, such as number of vertices, number of connections per vertex, and edge strength, cannot be tackled with standard convolutional techniques. We propose a novel neural learning framework that is capable of handling both homogeneous and heterogeneous data, while retaining the benefits of traditional CNN successes. Recently, researchers have proposed variations of CNNs that can handle graph data. In an effort to create learnable filter banks of graphs, these methods either induce constraints on the data or require preprocessing. As opposed to spectral methods, our framework, which we term Graph-CNNs, defines filters as polynomials of functions of the graph adjacency matrix. Graph-CNNs can handle both heterogeneous and homogeneous graph data, including graphs having entirely different vertex or edge sets. We perform experiments to validate the applicability of Graph-CNNs to a variety of structured and unstructured classification problems and demonstrate state-of-the-art results on document and molecule classification problems.

• The paper introduces a novel Graph-CNN framework that extends traditional CNNs to graph data using vertex filters and a supervised graph embed pooling operation.
• It demonstrates superior performance on diverse benchmarks such as fMRI, chemical compounds, and image classification tasks.
• The study provides key insights into graph signal processing and neural network architectures, paving the way for efficient analysis of heterogeneous data.

Overview of Robust Spatial Filtering with Graph Convolutional Neural Networks

The paper "Robust Spatial Filtering with Graph Convolutional Neural Networks" presents an innovative Machine Learning framework, termed Graph-CNNs, which extends the capabilities of traditional Convolutional Neural Networks (CNNs) to handle graph data. By representing filters as polynomials of functions of the graph adjacency matrix, this framework addresses the challenges posed by heterogeneous data with varying graph structures. The authors aim to leverage the inherent advantages of CNNs, typically applied to structured data, for graph-based data that lacks a gridded structure.

Key Contributions

The primary contributions of this research are multi-faceted:

• Vertex Filters: The paper introduces vertex filters, which simultaneously learn properties from graph vertices and edges. By enabling learning from multiple adjacency matrices, this approach facilitates handling diverse types of graph data.
• Pooling Operation: A supervised graph embed pooling operation is proposed, enabling dimension reduction for heterogeneous graph data. This is crucial for graphs that do not have fixed-size representations.
• Empirical Validation: The efficacy of Graph-CNNs is demonstrated through extensive experimentation across a spectrum of datasets, including brain fMRI, chemical compounds, 3D facial graphics, and document citations. The results highlight the versatility and applicability of this new framework in various fields.

Experimental Findings

Experiments conducted on several benchmark datasets illustrate the superior classification performance of Graph-CNNs:

• Image Classification: When applied to CIFAR-10 and ImageNet datasets, Graph-CNNs achieve comparable performance with traditional CNNs, thereby validating the conceptual equivalence and practical performance for structured image data.
• Biomedical Data: The model successfully differentiates male from female subjects using functional MRI data, showcasing potential applications in biomedical research where understanding brain function is vital.
• Chemistry and Materials Science: Graph-CNNs demonstrate state-of-the-art results for chemical compound classification tasks, indicating its effectiveness in pharmaceutical and materials research.
• Facial Recognition: Although traditional CNNs outperformed Graph-CNNs in facial expression recognition using Bosphorus 3D facial data, the Graph-CNN framework still shows promise for further development and optimization.

Theoretical Implications

The theoretical implications of this work extend to graph signal processing and neural network architectures. By processing graph data natively in the spatial domain, Graph-CNNs eliminate the need for homogeneous graph structures typically required by spectral approaches. This shift could lead to more flexible and computationally efficient frameworks that can adapt to varied real-world data structures encountered in multiple domains.

Future Developments

Future avenues for research include enhancing the depth and receptive fields of Graph-CNNs and exploring additional applications where graph-based data structures are prevalent. There is potential for incorporating edge filtering alongside vertex filtering, which could further enrich the model's capacity to interpret complex graph data.

The authors position their framework as a pivotal methodological advancement poised to be applicable across various disciplines requiring graph analytics and pattern recognition. As the framework matures, it could serve as a robust method for entirely new realms of AI-driven graph processing tasks, introducing the dynamic and transformative capabilities of deep learning to areas traditionally limited by their data's heterogeneous nature.