Multilevel Approximate Robust Principal Component Analysis
Multilevel Approximate Robust Principal Component Analysis
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DOI：
10.1109/iccvw.2017.70
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发表时间：
2017-10
期刊：
影响因子：
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通讯作者：
Vahan Hovhannisyan;Yannis Panagakis;S. Zafeiriou;P. Parpas
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文献类型：
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作者：
Vahan Hovhannisyan;Yannis Panagakis;S. Zafeiriou;P. Parpas
鲁棒主成分分析（RPCA）是目前从稀疏损坏中恢复低秩矩阵的首选方法，这些损坏具有未知的价值并通过将观察矩阵分解为低秩和稀疏矩阵来支持。 RPCA 有很多应用，包括背景扣除、从视觉数据中学习鲁棒子空间等。然而，SVD 在优化方法的每次迭代中的应用使得 RPCA 在数据量较大的情况下的应用具有挑战性。在本文中，据我们所知，我们提出了第一个用于求解凸和非凸 RPCA 模型的多级方法。其基本思想是构建较低维的模型并对其进行SVD，而不是原来的高维问题。我们表明，所提出的方法为凸和非凸公式的原始问题提供了良好的近似解决方案，同时在几个现实世界数据集中比原始 RPCA 方法快很多倍。
Robust principal component analysis (RPCA) is currently the method of choice for recovering a low-rank matrix from sparse corruptions that are of unknown value and support by decomposing the observation matrix into low-rank and sparse matrices. RPCA has many applications including background subtraction, learning of robust subspaces from visual data, etc. Nevertheless, the application of SVD in each iteration of optimisation methods renders the application of RPCA challenging in cases when data is large. In this paper, we propose the first, to the best of our knowledge, multilevel approach for solving convex and non-convex RPCA models. The basic idea is to construct lower dimensional models and perform SVD on them instead of the original high dimensional problem. We show that the proposed approach gives a good approximate solution to the original problem for both convex and non-convex formulations, while being many times faster than original RPCA methods in several real world datasets.