提出一种谱方法，精准分离多视角数据中的共性与个性特征子空间。
A spectral method for multi-view subspace learning using the product of projections
- 基于投影矩阵乘积的谱分析，识别子空间分离条件。
- 通过旋转自助法和随机矩阵理论，准确划分共性、个性与噪声子空间。
- 适用于多组学、多模态数据，提升下游预测性能。
多视角数据在相同观测上提供互补信息，如多组学与多模态传感器数据。分析此类数据需区分共享（联合）与独特（个体）信号子空间，但现有方法缺乏可靠的识别条件。本文严格量化了这些条件，涉及信号秩与环境维度比、真子空间间主角、噪声水平。方法通过分析各视角估计子空间的投影矩阵乘积的谱扰动，揭示子空间分离机制。据此提出一种易用且可扩展的估计算法，结合旋转自助法与随机矩阵理论，将观测谱划分为联合、个体与噪声子空间。诊断图可视化该划分，提供可解释的性能洞察。模拟实验显示，本方法在联合与个体子空间估计上优于现有方法。在结直肠癌患者多组学数据及小鼠营养基因组研究中的应用，亦提升了下游预测任务表现。
原文摘要 · Abstract (English)
Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique (individual) signal subspaces from noisy, high-dimensional measurements. Despite many proposed methods, the conditions for reliably identifying joint and individual subspaces remain unclear. We rigorously quantify these conditions, which depend on the ratio of the signal rank to the ambient dimension, principal angles between true subspaces, and noise levels. Our approach characterizes how spectrum perturbations of the product of projection matrices, derived from each view's estimated subspaces, affect subspace separation. Using these insights, we provide an easy-to-use and scalable estimation algorithm. In particular, we employ rotational bootstrap and random matrix theory to partition the observed spectrum into joint, individual, and noise subspaces. Diagnostic plots visualize this partitioning, providing practical and interpretable insights into the estimation performance. In simulations, our method estimates joint and individual subspaces more accurately than existing approaches. Applications to multi-omics data from colorectal cancer patients and nutrigenomic study of mice demonstrate improved performance in downstream predictive tasks.
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