Unsupervised Manifold Alignment with Joint Multidimensional Scaling
This addresses the challenge of aligning data across domains without correspondences, useful for tasks like visualization and domain adaptation, but it is incremental as it builds on existing methods like MDS and Wasserstein Procrustes.
The paper tackles the problem of unsupervised manifold alignment for datasets from different domains without known correspondences, introducing Joint Multidimensional Scaling to map them to a common low-dimensional space, and demonstrates effectiveness in applications like domain adaptation and graph matching.
We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common low-dimensional Euclidean space. Our approach integrates Multidimensional Scaling (MDS) and Wasserstein Procrustes analysis into a joint optimization problem to simultaneously generate isometric embeddings of data and learn correspondences between instances from two different datasets, while only requiring intra-dataset pairwise dissimilarities as input. This unique characteristic makes our approach applicable to datasets without access to the input features, such as solving the inexact graph matching problem. We propose an alternating optimization scheme to solve the problem that can fully benefit from the optimization techniques for MDS and Wasserstein Procrustes. We demonstrate the effectiveness of our approach in several applications, including joint visualization of two datasets, unsupervised heterogeneous domain adaptation, graph matching, and protein structure alignment. The implementation of our work is available at https://github.com/BorgwardtLab/JointMDS