基于鉴别流形的不相关稀疏投影非负矩阵分解

Discriminative manifold-based uncorrelated sparse projective nonnegative matrix factorization

基于流形学习、稀疏表示和鉴别分析理论,提出一种基于鉴别流形的统计不相关稀疏投影非负矩阵分解(discriminative manifold—based uncorrelated sparse projective NMF,DMUPNMF)算法。该方法继承了线性投影NM F优点,充分利用了数据集的局部和非局部几何鉴别信息,能够从数据集中抽取不相关鉴别特征,且分解结果具有良好的数据局部表示和稀疏性;给出多乘更新规则求解优化算法并证明其收敛性,还给出投影梯度优化算法以提高收敛速度。为解决大规模数据处理中计算量和存储空间过大问题,提出一种从训练集选取少量代表性样本学习DMUPNMF方法。大量的实验表明,该算法优于现有的改进NMF算法。

Inspired by manifold learning,sparse representation and discriminant analysis theories,a discriminative manifold-based uncorrelated sparse projective nonnegative matrix factorization（ DM UPNM F） algorithm was developed in this work. By exploiting local and nonlocal geometric discriminant information of the data and the merits of the linear projective NM F,the extracted features were approximately uncorrelated and the decomposition results of DM UPNM F were sparse and better part-based representation. Multiplicative updating rules were introduced to slove the optimization problem of DM UPNM F and its convergence proof was given as well. Moreover,projected gradient decent optimization method was developed to enhance the convergence speed of the method. An approach was proposed to select the informative data points from training dataset,which reduces the computation burden and storage space resulted from a large amount of objects for traditional NM F. Simulations demonstrated that the proposed algorithm outperforms the state-ofthe-art algorithms on real-w orld problems.