提出新方法直接识别稀疏成分支撑集，提升视频与高光谱数据的异常检测性能。
Robust Principal Component Completion
- 通过变分贝叶斯推断间接确定稀疏成分支持区域
- 在合成数据上接近最优，在真实视频和高光谱数据中表现稳健
- 无需事后阈值处理，适合需要精准前景提取的场景
鲁棒主成分分析（RPCA）旨在从和中分离出低秩成分与稀疏成分。然而，在许多实际应用中，稀疏前景会替换或遮挡低秩背景元素，导致传统方法不匹配。为此，本文提出一种新框架——鲁棒主成分补全（RPCC），通过概率化贝叶斯稀疏张量分解，利用变分贝叶斯推断间接识别稀疏成分的支持集。理论上证明其收敛至硬分类器，避免了以往方法所需的后处理阈值操作。实验表明，该方法在合成数据上实现近似最优估计，在真实彩色视频数据上表现优异的前景提取能力，在高光谱数据上具备强健的异常检测性能。源代码与附录见：https://github.com/WongYinJ/BCP-RPCC。
原文摘要 · Abstract (English)
Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank background. To address this mismatch, a new framework is proposed in which the sparse component is identified indirectly through determining its support. This approach, called robust principal component completion (RPCC), is solved via variational Bayesian inference applied to a fully probabilistic Bayesian sparse tensor factorization. Convergence to a hard classifier for the support is shown, thereby eliminating the post-hoc thresholding required of most prior RPCA-driven approaches. Experimental results reveal that the proposed approach delivers near-optimal estimates on synthetic data as well as robust foreground-extraction and anomaly-detection performance on real color video and hyperspectral datasets, respectively. Source implementation and Appendices are available at https://github.com/WongYinJ/BCP-RPCC.
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