跨模态数据无共同维度也能联合分析，发现共性模式并补全缺失信息。
PathFinder: Joint Decompositions of Linked Multimodal Datasets
- 通过数据矩阵间路径关系实现非对齐多模态联合分解
- 可在无统一维度的数据中发现跨物种/尺度的共同模式
- 适用于缺失数据补全，兼容多种传统分解方法
低秩矩阵分解能揭示数据中的模式与结构，广泛应用于多个领域。针对多模态数据的联合低秩分解方法虽可发现跨模态共性，但要求所有数据共享一个或多个维度。本文提出PathFinder新方法，使不共享统一维度的多源数据仍可进行联合分析。核心思想是：只要成对或子组矩阵间存在共享维度，且存在连接各矩阵的数据路径，即可实现全局联合分解。该方法支持跨模态、跨物种或跨尺度的共性模式发现，无需严格的一一对应关系。我们证明PathFinder是多种矩阵分解方法的通用框架，可用于发现异构数据中的共同规律，并预测缺失数据或模态。
原文摘要 · Abstract (English)
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.
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