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
this https URL

该论文介绍了一种新的方法 —— 联合多维标度，它可以将来自两个不同领域的数据集映射到一个低维欧几里得空间中，同时只需要每个数据集内部的成对不相似性作为输入，并展示了其在联合可视化、异质领域自适应、图形匹配和蛋白质结构对齐等多个应用中的有效性。