具有离群值的NMF的Bregman近端ADMM：估计具有缺失值和离群值的特征：用于稳健非负矩阵分解的Bregman近端算法及其在基因表达分析中的应用
A Bregman Proximal ADMM for NMF with Outliers: Estimating features with missing values and outliers: a Bregman-proximal point algorithm for robust Non-negative Matrix Factorization with application to gene expression analysis
摘要：
在给定的数据集中提取相关特征是一个困难的任务，最近解决了非负数据情况下的非负矩阵分解（NMF）方法。这项研究工作的目的是将这种方法扩展到由于离群值而丢失和/或损坏数据的情况。为此，对数据进行去噪，插补缺失值，并在对恢复的矩阵进行低秩非负矩阵分解时检测离群值。为了实现这一目标，混合使用Bregman近似方法和增广拉格朗日方案，以类似的方式，所谓的交替方向的乘数方法。最后提出了一个应用程序的膀胱癌患者的基因表达数据的分析。
英文摘要：
To extract the relevant features in a given dataset is a difficult task, recently resolved in the non-negative data case with the Non-negative Matrix factorization (NMF) method. The objective of this research work is to extend this method to the case of missing and/or corrupted data due to outliers. To do so, data are denoised, missing values are imputed, and outliers are detected while performing a low-rank non-negative matrix factorization of the recovered matrix. To achieve this goal, a mixture of Bregman proximal methods and of the Augmented Lagrangian scheme are used, in a similar way to the so-called Alternating Direction of Multipliers method. An application to the analysis of gene expression data of patients with bladder cancer is finally proposed.
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