Title: MIMO Graph Filters for Convolutional Neural Networks,
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.