论文标题
与关节多维缩放的无监督歧管对齐
Unsupervised Manifold Alignment with Joint Multidimensional Scaling
论文作者
论文摘要
我们引入了联合多维缩放，这是一种无监督的歧管比对的新方法，该方法将数据集从两个不同的域绘制数据集，而在整个数据集中的数据实例之间没有任何已知的对应关系，请绘制到一个常见的低维欧几里得空间。我们的方法集成了多维缩放（MDS）和Wasserstein Procruster将分析分析成一个关节优化问题，以同时生成数据的等距嵌入数据，并从两个不同数据集中学习实例之间的对应关系，而仅需要内部范围内的成对差异差异作为输入。这种独特的特征使我们的方法适用于数据集，而无需访问输入功能，例如求解了不精确的图形匹配问题。我们提出了一种交替的优化方案，以解决可以从MDS和Wasserstein Procrustes的优化技术中完全受益的问题。我们证明了方法在几种应用中的有效性，包括两个数据集的联合可视化，无监督的异质域适应性，图形匹配和蛋白质结构对齐。我们的工作的实施可从https://github.com/borgwardtlab/jointmds获得
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
