Geometric Multimodal Deep Learning With Multiscaled Graph Wavelet Convolutional Network

Multimodal data provide complementary information of a natural phenomenon by integrating data from various domains with very different statistical properties. Capturing the intramodality and cross-modality information of multimodal data is the essential capability of multimodal learning methods. The geometry-aware data analysis approaches provide these capabilities by implicitly representing data in various modalities based on their geometric underlying structures. Also, in many applications, data are explicitly defined on an intrinsic geometric structure. Generalizing deep learning methods to the non-Euclidean domains is an emerging research field, which has recently been investigated in many studies. Most of those popular methods are developed for unimodal data. In this article, a multimodal graph wavelet convolutional network (M-GWCN) is proposed as an end-to-end network. M-GWCN simultaneously finds intramodality representation by applying the multiscale graph wavelet transform to provide helpful localization properties in the graph domain of each modality and cross-modality representation by learning permutations that encode correlations among various modalities. M-GWCN is not limited to either the homogeneous modalities with the same number of data or any prior knowledge indicating correspondences between modalities. Several semisupervised node classification experiments have been conducted on three popular unimodal explicit graph-based datasets and five multimodal implicit ones. The experimental results indicate the superiority and effectiveness of the proposed methods compared with both spectral graph domain convolutional neural networks and state-of-the-art multimodal methods.