Residual-Based Sampling for Online Outlier-Robust PCA
Residual-Based Sampling for Online Outlier-Robust PCA
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发表时间：
2022
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通讯作者：
Tianhao Zhu;Jie Shen
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作者：
Tianhao Zhu;Jie Shen
离群稳健主成分分析（OR-PCA）在科学发现中得到了广泛的应用。在本文中，我们研究了在线ORPCA，这是一个重要的变体，它解决了数据点以顺序方式到达的实际挑战，目标是用一次数据传递来恢复干净数据的底层子空间。我们的主要贡献是第一个可证明的算法，享有可比的恢复保证最知名的批处理算法，同时显着改善后，最先进的在线ORPCA算法。核心技术是残差规范的鲁棒版本，非正式地说，它不仅利用数据点的重要性，还利用它作为异常值的可能性。
Outlier-robust principal component analysis (OR-PCA) has been broadly applied in scientific discovery in the last decades. In this paper, we study online ORPCA, an important variant that addresses the practical challenge that the data points arrive in a sequential manner and the goal is to recover the underlying subspace of the clean data with one pass of the data. Our main contribution is the first provable algorithm that enjoys comparable recovery guarantee to the best known batch algorithm, while significantly improving upon the state-of-the-art online ORPCA algorithms. The core technique is a robust version of the residual norm which, informally speaking, leverages not only the importance of a data point, but also how likely it behaves as an outlier.