基于流形正则化判别的因子分解

Manifold regularized-based discriminant concept factorization

通过对非负矩阵分解(non-negative matrix factorization,NMF)和因子分解(concept factorization,CF)的分析,针对它们无法核化或忽略数据几何结构和判别信息的问题,提出了基于流形正则化判别的因子分解算法(manifold regularized-based discriminant concept factorization,MRCF)。该算法用CF算法对数据进行低维非负分解时,根据流形学习的图框架理论,构建邻接矩阵保持数据局部几何结构;利用样本的标签信息,进行监督学习,给出算法多步更新规则,理论上证明了MRCF算法的收敛性。在人脸数据库ORL、图像库COIL20和手写体数据库USPS上的仿真结果表明,相对于NMF、CF及其一些改进算法,MRCF均具有更高的聚类精度。

Non-negative matrix factorization（NMF） and concept factorization（CF） can be found not to make use of the power of kernelization or pay any attention to the geometric structure and the label information of the data.A novel algorithm called manifold regularized-based discriminant concept factorization（MRCF）.When original data is factorized in lower dimensional space using CF,MRCF preserves the intrinsic geometry of data,using the label information as supervised learning,producing an efficient multiplicative updating procedure and providing the convergence proof of our algorithm.Compared with NMF,CF and its improved algorithms,experimental results of ORL face database,COIL20 image database and USPS handwrite database have shown that the proposed method achieves more highly clustering precision.