A Unifying Framework and Comparison of Algorithms for Non-negative Matrix Factorisation

Non-negative matrix factorisation (NMF) is an increasingly popular unsupervised learning method. However, parameter estimation in the NMF model is a difficult high-dimensional optimisation problem. We consider algorithms of the alternating least squares type. Solutions to the least squares problem fall in two categories. The first category is iterative algorithms, which include algorithms such as the majorise–minimise (MM) algorithm, coordinate descent, gradient descent and the Févotte-Cemgil expectation–maximisation (FC-EM) algorithm. We introduce a new family of iterative updates based on a generalisation of the FC-EM algorithm. The coordinate descent, gradient descent and FC-EM algorithms are special cases of this new EM family of iterative procedures. Curiously, we show that the MM algorithm is never a member of our general EM algorithm. The second category is based on cone projection. We describe and prove a cone projection algorithm tailored to the non-negative least square problem. We compare the algorithms on a test case and on the problem of identifying mutational signatures in human cancer. We generally find that cone projection is an attractive choice. Furthermore, in the cancer application, we find that a mix-and-match strategy performs better than running each algorithm in isolation.     

以非负矩阵分解提取局部特征的SAR目标稀疏表示分类

合成孔径雷达（SAR）目标分类是自动目标识别系统的核心功能之一,对于战场监视等应用具有重要意义。利用SAR图像局部散射明显的特点,提出了通过训练样本的非负矩阵分解获得低维数局部特征编码,并以该编码作为字典进行稀疏表示分类的方法。采用Gotcha项目民用车辆目标的实测数据进行了验证,结果显示在不同信噪比条件下该方法的分类正确率均优于广泛采用的由降采样、随机投影、主成分分析提取低维数特征的稀疏表示分类方法,表明了该方法的性能优势。另外,还通过实验对比分析了非负约束的稀疏表示与标准稀疏表示在分类性能上的差别,结果显示非负约束的稀疏表示导致分类正确率下降,故针对分类问题不宜在稀疏表示时进行非负约束。     

结合多源特征与高斯过程模型的SAR图像目标识别

针对合成孔径雷达（Synthetic Aperture Radar，SAR）图像目标识别问题，提出结合多源特征和高斯过程模型的方法。分别利用主成分分析（Principal Component Analysis，PCA）、非负矩阵分解（Non-negative Matrix Factorization，NMF）以及单演信号提取SAR图像的特征矢量，并将它们串接为单一矢量。三类特征从不同角度描述SAR图像目标特性，从而为目标识别提供更为有效的信息。决策分类过程采用高斯过程模型进行多元分类，基于融合特征矢量获得概率意义上的最佳决策。实验中，采用MSTAR数据集设置3类目标、10类目标、型号差异以及俯仰角差异识别问题，结果验证了提出方法的优越性能。