矩阵低秩逼近的快速增量算法及其在人脸图像中的应用

针对矩阵数据降维或低秩逼近问题,提出了一种快速增量算法.假设矩阵数据存在双边分解,建立了两个相互耦合的特征子空间模型,因此增量算法由两个特征子空间的迭代更新构成.每一步迭代,新载入的矩阵数据沿着行(列)特征子空间进行正交分解,从而获得了行(列)协方差矩阵更紧致的表达.一旦该表达被建立,行(列)特征子空间的更新就可以通过解一个和矩阵数据的行(列)数相比更小规模的特征值问题来完成,算法的高效率得以实现.该算法被应用到人脸图像重构和人脸跟踪问题中,一系列实验表明了算法的有效性.

A fast incremental algorithm for low rank approximations of matrices and its applications in facial images

A fast incremental algorithm for low rank approximations or dimensionality reduction of matrices was presented.Assuming that matrices can be double-sided and decomposed,an incremental solution that constitutes two coupled eigenmodels and thus a two-step updating procedure was set up.At each step,row-row or column-column covariance matrices as the form of eigen-decomposition were represent firstly and then new available matrices were orthogonally decomposed along existing eigenspaces in order to obtain a more compact representation of updated row-row or column-column covariance matrices.Thus,the eigenmodel could be updated properly by solving an eigenvalue problem with a smaller number of eigenvalues.The algorithm was applied to perform the tasks of both image reconstruction on facial image databases and face tracking on videos.These examples provided extensive illustrations of the algorithms performance.