MIMO Graph Filters for Convolutional Neural Networks

TL;DR

This paper introduces MIMO graph filters for CNNs that operate on irregular data domains, reducing model complexity while maintaining performance.

Contribution

It proposes three new structured MIMO graph filter architectures that are more parsimonious and computationally efficient than previous models.

Findings

Achieve similar accuracy with fewer parameters

Reduce computational complexity of graph CNNs

Mitigate overfitting risk in training

Abstract

Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise nonlinearity. Since the two first operations are well-defined only on regular-structured data such as audio or images, application of CNNs to contemporary datasets where the information is defined in irregular domains is challenging. This paper investigates CNNs architectures to operate on signals whose support can be modeled using a graph. Architectures that replace the regular convolution with a so-called linear shift-invariant graph filter have been recently proposed. This paper goes one step further and, under the framework of multiple-input multiple-output (MIMO) graph filters, imposes additional structure on the adopted graph filters, to obtain three new (more parsimonious) architectures. The proposed architectures result in a lower number of model parameters, reducing the computational complexity, facilitating the training, and mitigating the risk of overfitting. Simulations show that the proposed simpler architectures achieve similar performance as more complex models.