Robust low-rank approximation under row-wise adversarial corruption can be achieved with a single pass, randomized procedure that detects and removes outlier rows by thresholding their projected norms. We propose a scalable, non-iterative algorithm that efficiently recovers the underlying low-rank structure in the presence of row-wise adversarial corruption. By first compressing the data with a Johnson Lindenstrauss projection, our approach preserves the geometry of clean rows while dramatically reducing dimensionality. Robust statistical techniques based on the median and median absolute deviation then enable precise identification and removal of outlier rows with abnormally high norms. The subsequent rank-k approximation achieves near-optimal error bounds with a one pass procedure that scales linearly with the number of observations. Empirical results confirm that combining random sketches with robust statistics yields efficient, accurate decompositions even in the presence of large fractions of corrupted rows.

翻译：针对行级对抗性污染下的鲁棒低秩逼近问题，可通过单次扫描的随机化流程实现，该流程通过阈值化投影范数来检测并移除异常行。我们提出一种可扩展的非迭代算法，能在存在行级对抗性污染的情况下高效恢复底层低秩结构。通过约翰逊-林登斯特劳斯投影对数据进行压缩，我们的方法在显著降低维度的同时保持了干净行的几何特性。基于中位数和中位数绝对偏差的鲁棒统计技术，能够精确识别并移除具有异常高范数的异常行。随后的秩k逼近通过单次扫描流程达到接近最优的误差界，其计算复杂度与观测数量呈线性关系。实证结果表明，即使存在大比例污染行，将随机草图与鲁棒统计技术相结合仍能获得高效且精确的分解结果。