Robust Principal Component Analysis with Adaptive Neighbors
Robust Principal Component Analysis with Adaptive Neighbors
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发表时间：
2019
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通讯作者：
Rui Zhang;Hanghang Tong
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作者：
Rui Zhang;Hanghang Tong
假设某些数据点被过度污染，那么现有的主成分分析（PCA）方法往往无法过滤和消除过度污染的数据点，这可能导致相应模型的功能退化。为了解决这个问题，我们提出了一个通用框架，即具有自适应邻居的鲁棒权重学习（RWL-AN），通过该框架，可以自动获得具有鲁棒性和稀疏邻居的自适应权重向量。更重要的是，稀疏程度是可控制的，使得在优化过程中仅激活具有最小重构误差的精确k个拟合良好的样本，而为了全局鲁棒性而消除剩余样本，即极端噪声样本。此外，该框架进一步应用于PCA问题，以证明所提出的RWL-AN模型的优越性和有效性。
Suppose certain data points are overly contaminated, then the existing principal component analysis (PCA) methods are frequently incapable of filtering out and eliminating the excessively polluted ones, which potentially lead to the functional degeneration of the corresponding models. To tackle the issue, we propose a general framework namely robust weight learning with adaptive neighbors (RWL-AN), via which adaptive weight vector is automatically obtained with both robustness and sparse neighbors. More significantly, the degree of the sparsity is steerable such that only exact k well-fitting samples with least reconstruction errors are activated during the optimization, while the residual samples, i.e., the extreme noised ones are eliminated for the global robustness. Additionally, the framework is further applied to PCA problem to demonstrate the superiority and effectiveness of the proposed RWL-AN model.