基于大间隔编码的空间非负矩阵分解

Spatial Non-Negative Matrix Factorization Based on Max-Margin Coding

虽然基于局部的表示方法在图像处理中具有很好的鲁棒性,但非负矩阵分解只有隐式局部约束,导致分解不唯一和基图像不够局部.另外,局部性与判别性作为样本表示的重要性质几乎没有在非负矩阵分解中被同时考虑过.为此,文中提出了基于大间隔编码的空间非负矩阵分解,将图像数据看作像素构成的二维网络,借鉴网络中的知识将空间信息嵌入基图像,不但施加了显式的局部约束,而且能够弥补数据向量化损失的空间信息.同时,利用大间隔约束学到的额外一维空间平衡重建误差和判别性约束对基图像的影响.在AR数据库和扩展的Yale B数据库上的人脸识别实验结果表明,相比于非负矩阵及其他几种典型的扩展方法,基于大间隔编码的空间非负矩阵分解更加鲁棒.

Although the parts-based representation results in strong robustness in image processing,the local constraint in non-negative matrix factorization（ NMF） is implicit,which leads to insufficient uniqueness and locality.Meanwhile,as two important property indexes,locality and discriminant in feature extraction are seldom considered in NMF simultaneously. In order to solve this problem,a discriminative NMF on the basis of max-margin coding is proposed. In this method,image data are regarded as a 2D network of pixels,and,on the basis of network knowledge,spatial information is embedded into basis images,which not only imposes an explicit local constraint but also compensates the spatial information loss caused by data vectorization. Additionally,an extra 1D space learned from maxmargin constraint is adopted to balance the effects of reconstruction error and discriminative constraint on basis images. Experimental results on AR and extended Yale B databases for face recognition show that,in comparison with NMF and some of its variants,the proposed max-margin coding-based spatial NMF is more robust.