基于Cholesky分解的K2DPCA人脸识别研究

K2DPCA(kernel 2D principal component analysis)是基于非线性特征提取的重要人脸识别方法,具有成功的应用.但对大规模训练数据库,其因核矩阵K规模过大、计算代价高而不能有效实现.采用选主元Cholesky,分解方法,仅需计算核矩阵的对角线上元素和部分精选列,得到迹范数意义下核矩阵K的最优Nystr(o|¨)m型低秩近似LL~T来解决该问题.并只需计算小规模矩阵L~TL的特征值和特征向量,实现大规模K2DPCA/KPCA(kernel principal component anialysis)的非线性特征提取.在加噪ORL人脸数据库上的实验结果表明,较K2DPCA/KPCA方法,新方法显著提高了识别率,并可以很大程度上克服噪声的影响;在Extended YaleB大型人脸数据库上的实验结果表明,此算法解决了K2DPCA核矩阵过大而不能有效实现的缺点.

K2DPCA methods for face recognitionbased on Cholesky decomposition

K2DPCA (kernel 2D principal component analysis), with successful applications, is an important method for nonlinear face recognition. However, it will meet challenge for the large-scale training problems, because the kernel matrix K is too large to fit the memory and the eigenvalues and eigenvectors of the kernel matrix are not obtained freely. To answer this challenge, we propose a new method, where the kernel matrix K is decomposed as its Nyström-type low-rank approximation LL^T by the pivoted Cholesky decomposition. In the procedure, only the diagonals and some well-chosen columns of the kernel matrix are available, then the optimal Nyström-type approximation is obtained under the trace norm without the full kernel matrix. Owning to this, K2DPCA/KPCA (kernel principal component analysis) is implemented by calculating the eigenvalues and eigenvectors of the small size matrix L^TL. The experiments on noise dataset of ORL face database show that the proposed algorithm can significantly improve the recognition rates of K2DPCA/KPCA, and also decrease the effect of noise to some extend. The experimental results on a large scale Extended YaleB face database show that the proposed method overcomes the weakness of K2DPCA on the large-scale training set.