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鲁棒主成分分析和协同过滤：剔除异常值，识别操纵器Robust PCA and Collaborative Filtering: Rejecting Outliers, Identifying Manipulators |
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| 课程网址: | http://videolectures.net/nipsworkshops2010_caramanis_rcf/ |
| 主讲教师: | Constantine Caramanis |
| 开课单位: | 德克萨斯大学 |
| 开课时间: | 2011-01-13 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Principal Component Analysis is one of the most widely used techniques for dimensionality reduction. Nevertheless, it is plagued by sensitivity to outliers; finding robust analogs, particularly for high-dimensional data, is critical. We discuss the challenges posed by the high dimensional setting, where dimensionality is of the same order, or greater, than the number of samples. We detail why existing techniques fail -- indeed, no known algorithm can provide provable bounds to any constant fraction of outliers -- and then present two very different algorithms for High Dimensional Robust PCA. Our first algorithm achieves a breakdown point of 50% -- the best possible using any algorithm, and a stark improvement from the previous best-known result of 0%. Our second algorithm is based on ideas from convex optimization, and in addition to recovering the principal components, is also able to identify the corrupted points. We extend this to the partially observed setting, significantly extending matrix completion results to the setting of corrupted rows or columns. |
| 关 键 词: | 主成分分析; 异常值; 高维数据; 凸优化; 扩展矩阵 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-06-02：毛岱琦(课程编辑志愿者) |
| 阅读次数: | 71 |