PathFinder：链接多模态数据集的联合分解方法

中文摘要 AI 辅助

低秩矩阵分解能够揭示数据中的模式与结构，在众多学科中有着广泛应用。已有研究提出了“联合”低秩分解方法以链接不同模态的数据集，但这些方法要求所有多模态数据共享一个或多个维度。我们提出一种新的分析方法PathFinder，可对未必共享某一维度的数据集进行联合分析。核心思路是：只要矩阵对或矩阵子集确实共享某一维度，且存在一条或多条路径连接所有数据矩阵，即可寻求全局联合分解。这使得我们能够对不同模态、物种或尺度间的共同模式进行联合估计，而无需所有数据沿某一维度存在一一映射。研究表明，PathFinder是一个通用框架，许多矩阵分解方法都可作为其特例归入其中；该方法可用于发现不同数据集间的共同模式，也可对缺失数据或模态进行预测。

英文摘要

Low-rank matrix decompositions can uncover patterns and structure in data and have a number of different applications across many disciplines. Extensions to "joint" low-rank decompositions have been proposed to link datasets from different modalities. While these methods enable the discovery of common patterns across modalities, they require that all the multimodal data share one or more dimensions. We propose a new analysis method, PathFinder, that enables co-analysis of datasets that do not necessarily all share a dimension. The key insight is that as long as pairs or subgroups of matrices do share some dimension, and that there are one or more paths that link across the data matrices, a global joint decomposition can be sought out. This enables the joint estimation of common patterns across different modalities, species, or scales, where a one-to-one mapping across all data along some dimension is not necessarily available. We show that PathFinder is a general umbrella under which many matrix decomposition methods fall as special cases. It can be used to discover common patterns across disparate datasets and to make predictions for missing data or modalities.

发表机构

• Oxford Centre for Integrative Neuroimaging（牛津整合神经成像中心）
• University of Oxford（牛津大学）

机构由 AI 辅助整理，请以论文原文为准。