将PCA和ICA推广到连续时间信号，支持不规则采样数据分解
Continuous-Time Signal Decomposition: An Implicit Neural Generalization of PCA and ICA
- 用隐式神经网络建模连续时间信号，统一处理PCA与ICA问题
- 通过对比损失项强制源信号具备去相关或独立性统计特性
- 适用于点云和非均匀采样信号，突破传统方法适用限制
我们将低秩分解问题（如主成分分析和独立成分分析）推广至连续时间向量信号，并提出一种模型无关的隐式神经信号表示框架，用于学习数值近似解。通过将信号建模为连续时间随机过程，我们在网络损失中引入对比函数项，统一了连续场景下PCA与ICA的求解方法，强制分解出的源信号满足所需的统计特性（如去相关性、独立性）。该连续域扩展使此类分解可应用于点云和非均匀采样信号，而传统方法在这些场景下无法适用。
原文摘要 · Abstract (English)
We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to learn numerical approximations to solve the problem. Modeling signals as continuous-time stochastic processes, we unify the approaches to both the PCA and ICA problems in the continuous setting through a contrast function term in the network loss, enforcing the desired statistical properties of the source signals (decorrelation, independence) learned in the decomposition. This extension to a continuous domain allows the application of such decompositions to point clouds and irregularly sampled signals where standard techniques are not applicable.
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