【作者】 周丹；

【导师】 张运杰；

【作者基本信息】 大连海事大学 ， 应用数学， 2013， 硕士

【摘要】 非负矩阵分解(Non-negative Matrix Factorization, NMF)是一种处理大规模高维数据的矩阵分解方法,它以分解的结果中不出现负值,提取的特征是基于部分的、局部化的、纯加性的描述等独特的优势区别于其它的方法。作为一种新的特征提取的方法,自从Lee和口Seung提出以后,就被广泛应用于人脸识别领域。在人脸特征提取中,人们总是希望得到一个分解的结果更加稀疏化,局部特征更加明显,数据之间冗余更小,分解速度更快的矩阵分解方法。为此,在经典NMF的基础上人们进行了大量的研究实验,提出了很多的改进算法。这些算法使得分解的结果更加适合我们的需求,但也还存在一定的缺陷。例如,提取的局部特征不够明显,权值矩阵的稀疏性不强,算法的收敛速度慢等,这些都使得非负矩阵分解在人脸识别中的应用不是很完美。针对NMF算法提取的局部特征不够明显的缺陷,本文提出了一种增强基矩阵稀疏性的非负矩阵分解算法。通过将经典的NMF目标函数与稀疏约束条件相结合,利用梯度下降法得到了算法的迭代公式。该算法使得基矩阵中数据之间的差异更大,从而局部特征更加突出。在人脸特征提取中,H稀疏可以减少数据之间的冗余,加快识别的效率,增大所包含的关于原图像的信息量。因此,与增强基矩阵稀疏性方法类似,本文还给出一种增强权矩阵稀疏性的非负矩阵分解算法,并给出了相应的迭代公式。该算法提高了权值矩阵的稀疏度,使得权矩阵中数据之间的差异更大,零的数量增多,识别的效率提高,所包含的关于原图像的信息量明显增大。针对NMF算法运行速度慢的缺陷,本文提出了一种降低人脸图像矩阵向量之间相关性的非负矩阵分解算法。由于人脸图像矩阵相邻行(列)之间的相关性很强,所以通过降低他们之间的相关性,可以达到降低矩阵的维数,提高算法运行速度的目的。该算法不仅使得识别效率大大提高,并且识别率也有一定的提高。本文利用ORL人脸数据库对三个算法进行了验证实验,从实验的结果可以看到算法的有效性。更多还原

【Abstract】 Nonnegative matrix factorization (Non-negative Matrix Factorization, NMF) is a kind of matrix decomposition method which to deal with a large-scale and high-dimensional data. The results of the decomposition is not negative, the extracted features are based on the part, localization and pure additive description. These and other unique advantages make NMF different from other methods. As a kind of new method of feature extraction, since Lee and Seung proposed have already widely used in the field of face recognition.In face feature extraction, people always want to get a matrix decomposition method with the result more sparseness, local characteristics obvious, smaller data redundancy and a faster speed. Therefore, a large number of studies and experiments have been conducted and proposed a lot of improved algorithms. These algorithms results in more suitable decomposition for us, but there are also have some shortcomings. For example, local features is not obvious enough, the sparseness of the weighted matrix is not strong, slow convergence speed and so on. These all make nonnegative matrix decomposition in the application of face recognition is not very perfect.For solving the NMF algorithm extract the local features not obvious enough, in this paper we propose a base matrix sparseness reinforced algorithm. Through combine the sparse constraint with the classic NMF Objective function and using the gradient desce-nt method obtain the iterative formula. This algorithm resulted in the distance between the basis matrixes bigger, thus local characteristics is more outstanding.In face feature extraction, the sparseness of H can reduce the redundancy between the data, improve the recognition efficiency, and increase the information of the original image. Therefore, similar to the algorithm of enhance basis matrix sparseness method, this paper give an algorithm for learning more sparseness information of the weighted matrix, and given the iterative formula. The algorithm improves the sparseness degree of the weighted matrix, which makes the distance between the basis matrixes bigger, the number of zero increased, recognition efficiency improved and the information of the original image increased. For solving the speed of NMF is slow, in this paper we propose A Decorrelation-based nonnegative matrix factorization algorithm for face recognition. Because of the correlation between the adjacent rows (column) of a face image matrix is very strong. So by reducing the correlation between them, reduced the dimensions of the matrix at the same time, and improve the speed of algorithm. This algorithm not only improves identification efficiency greatly, but also recognition rate has improved a little.Experiment have done on the ORL face database for these three algorithms, form the experiment we can see the algorithm is effective.更多还原