Hierarchical Optimal Transport for Robust Multi-View Learning
This addresses robustness issues in multi-view learning for applications where data assumptions are violated, but it appears incremental as it builds on existing optimal transport techniques.
The paper tackles the problem of multi-view learning when samples are unaligned and have different distributions by proposing a hierarchical optimal transport (HOT) method, which shows robust performance on synthetic and real-world tasks.
Traditional multi-view learning methods often rely on two assumptions: ($i$) the samples in different views are well-aligned, and ($ii$) their representations in latent space obey the same distribution. Unfortunately, these two assumptions may be questionable in practice, which limits the application of multi-view learning. In this work, we propose a hierarchical optimal transport (HOT) method to mitigate the dependency on these two assumptions. Given unaligned multi-view data, the HOT method penalizes the sliced Wasserstein distance between the distributions of different views. These sliced Wasserstein distances are used as the ground distance to calculate the entropic optimal transport across different views, which explicitly indicates the clustering structure of the views. The HOT method is applicable to both unsupervised and semi-supervised learning, and experimental results show that it performs robustly on both synthetic and real-world tasks.