图的鲁棒主成分分析
Robust Principal Component Analysis on Graphs
摘要：
主成分分析（PCA）是线性降维和聚类的最广泛使用的工具。尽管如此，它对离群值高度敏感，并且在数据样本数量方面不能很好地扩展。鲁棒PCA用稀疏惩罚项解决了第一个问题。第二个问题可以用矩阵分解模型来处理，但是它是非凸的。此外，基于PCA的聚类也可以通过使用数据相似性图来增强。在这篇文章中，我们介绍了一个新的模型，称为“鲁棒PCA图”，它将谱图正则化到鲁棒PCA框架。我们提出的模型受益于1）主成分对遮挡和缺失值的鲁棒性，2）增强的低秩恢复，3）由于低秩矩阵上的图平滑假设而改进的聚类特性，以及4）所得优化问题的凸性。在8个基准测试，3个视频和2个人工数据集上进行的大量实验清楚地表明，我们的模型在聚类和低秩恢复任务中优于其他10个最先进的模型。
英文摘要：
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
