提出新方法提升非负矩阵分解抗噪能力，速度比现有技术快10倍。
The Target Polish: A New Approach to Outlier-Resistant Non-Negative Matrix Factorization
- 用加权中位数动态修正数据，保持快速加法更新结构。
- 在含块状和随机噪声图像上精度达顶尖水平，计算耗时减少90%。
- 适合需要快速处理含异常值图像数据的科研与工程场景。
本文提出「目标抛光」（Target Polish）框架，一种鲁棒且高效的非负矩阵分解（NMF）方法。传统加权NMF虽能抵抗异常值，但因采用乘法更新导致收敛缓慢。而目标抛光通过基于加权中位数的数据自适应变换，兼容以高速著称的Fast-HALS算法，保留其高效的加法更新机制。实验证明，在含结构化（块状）与非结构化（盐粒状）噪声的图像数据集上，该方法精度达到或超过当前最优鲁棒NMF方法，同时在测试场景下计算时间降低一个数量级。
原文摘要 · Abstract (English)
This paper introduces the "Target Polish," a robust and computationally efficient framework for Non-Negative Matrix Factorization (NMF). Although conventional weighted NMF approaches are resistant to outliers, they converge slowly due to the use of multiplicative updates to minimize the objective criterion. In contrast, the Target Polish approach remains compatible with the Fast-HALS algorithm, which is renowned for its speed, by adaptively "polishing" the data with a weighted median-based transformation. This innovation provides outlier resistance while maintaining the highly efficient additive update structure of Fast-HALS. Empirical evaluations using image datasets corrupted with structured (block) and unstructured (salt) noise demonstrate that the Target Polish approach matches or exceeds the accuracy of state-of-the-art robust NMF methods while reducing computational time by an order of magnitude in the studied scenarios.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。