论文标题
基于L1-norm PCA的强大奇异值
Robust Singular Values based on L1-norm PCA
论文作者
论文摘要
单数值分解（SVD）是工程，科学和统计中无处不在的数据分析方法。尤其是，在一系列工程应用中，奇异值估计至关重要，例如通信系统中的通道估计，肌电图信号分析和图像压缩，仅举几例。数据矩阵的常规SVD与标准主组件分析（PCA）一致。 PCA的L2-norm（平方值总和）促进了外围数据点，从而使PCA对异常值敏感。自然，SVD继承了这种异常敏感性。在这项工作中，我们提出了一种基于L1-norm（绝对值之和）公式的SVD和单数值估计的新型鲁棒非参数方法，我们将其命名为L1-CSVD。因此，提出的方法表明了对异常值的坚固耐药性，并可以促进更可靠的数据分析和处理在广泛的工程应用中。
Singular-Value Decomposition (SVD) is a ubiquitous data analysis method in engineering, science, and statistics. Singular-value estimation, in particular, is of critical importance in an array of engineering applications, such as channel estimation in communication systems, electromyography signal analysis, and image compression, to name just a few. Conventional SVD of a data matrix coincides with standard Principal-Component Analysis (PCA). The L2-norm (sum of squared values) formulation of PCA promotes peripheral data points and, thus, makes PCA sensitive against outliers. Naturally, SVD inherits this outlier sensitivity. In this work, we present a novel robust non-parametric method for SVD and singular-value estimation based on a L1-norm (sum of absolute values) formulation, which we name L1-cSVD. Accordingly, the proposed method demonstrates sturdy resistance against outliers and can facilitate more reliable data analysis and processing in a wide range of engineering applications.
