Multi-modal learning aims to learn predictive models based on the data from different modalities. However, due to the requirement of data security and privacy protection, real-world multi-modal data are often scattered to different agents and cannot be shared across the agents, which limits the application of existing multi-modal learning methods. To achieve robust multi-modal learning in such a challenging scenario, we propose a novel optimal transport-based mixer (OTM), which works as an effective latent code alignment and augmentation method for unaligned and distributed multi-modal data. In particular, we train a Wasserstein autoencoder (WAE) for each agent, which encodes its single modal samples in a latent space. Through a central server, the proposed OTM computes a stochastic fused Gromov-Wasserstein barycenter (FGWB) to mix different modalities' latent codes, so that each agent applies the barycenter to reconstruct its samples. This method neither requires well-aligned multi-modal data nor assumes the data to share the same latent distribution, and each agent can learn a specific model based on multi-modal data while achieving inference based on its local modality. Experiments on multi-modal clustering and classification demonstrate that the models learned with the OTM method outperform the corresponding baselines.

Domain adaptation aims to align the data scattered in different domains, which is important for developing generalizable machine learning models. However, real-world data in different domains are often heterogeneous, requiring alignment at both sample and feature levels. In this study, we develop a new optimal transport-based method, unbalanced co-relational optimal transport (UCROT), to achieve robust heterogeneous data alignment. Given the data in different domains, we define a co-relational optimal transport problem, jointly inferring the optimal transport (OT) plans defined at the sample and feature levels. The OT plans indicate the sample correspondence and feature correlation across different domains. In addition, we relax the doubly stochastic constraints of the OT plans to the KL-divergence regularization of their marginals, which enhances the robustness of our method to the sample- and feature-level outliers and leads to the proposed UCROT method. Experiments on the heterogeneous domain adaptation and co-clustering tasks demonstrate the superiority of UCROT.

Multi-modal clustering aims at finding a clustering structure shared by the data of different modalities in an unsupervised way. Currently, solving this problem often relies on two assumptions: i) the multi-modal data own the same latent distribution, and ii) the observed multi-modal data are well-aligned and without any missing modalities. Unfortunately, these two assumptions are often questionable in practice and thus limit the feasibility of many multi-modal clustering methods. In this work, we develop a new multi-modal clustering method based on the Gromovization of optimal transport distance, which relaxes the dependence on the above two assumptions. In particular, given the data of different modalities, whose correspondence is unknown, our method learns the Gromov-Wasserstein (GW) barycenter of their kernel matrices. Driven by the modularity maximization principle, the GW barycenter helps to explore the clustering structure shared by different modalities. Moreover, the GW barycenter is associated with the GW distances between the different modalities to the clusters, and the optimal transport plans corresponding to the GW distances help to achieve the alignment and the clustering of the multi-modal data jointly. Experimental results show that our method outperforms state-of-the-art multi-modal clustering methods, especially when the data are (partially or completely) unaligned. The code is available at https://github.com/rucnyz/GWMAC.