论文标题
toeplitz惩罚的非负矩阵分解
Nonnegative Matrix Factorization with Toeplitz Penalty
论文作者
论文摘要
非负矩阵分解（NMF）是一种无监督的学习算法，它会产生数据矩阵的线性，基于零件的近似值。 NMF构建非负低等级基矩阵和非负低等级矩阵权重矩阵，当将其倍增时，使用某些成本函数近似关注的数据矩阵。可以修改NMF算法以包括辅助约束，这些约束对矩阵分解的成本函数施加特定于任务的惩罚或限制。在本文中，我们提出了一种新的NMF算法，该算法利用非数据依赖性辅助约束，该约束将toeplitz矩阵纳入基础和权重矩阵的乘法更新中。我们将新的Toeplitz非负矩阵分解（TNMF）算法的面部识别性能与Zellner非负矩阵分解（ZNMF）算法的性能进行比较，该算法使用数据依赖数据依赖性的辅助约束。我们还比较了上述两种算法的面部识别性能与几种具有非DATA依赖性惩罚的有限的NMF算法的性能。面部识别性能使用面部的剑桥ORL数据库和耶鲁大学的面部数据库进行评估。
Nonnegative Matrix Factorization (NMF) is an unsupervised learning algorithm that produces a linear, parts-based approximation of a data matrix. NMF constructs a nonnegative low rank basis matrix and a nonnegative low rank matrix of weights which, when multiplied together, approximate the data matrix of interest using some cost function. The NMF algorithm can be modified to include auxiliary constraints which impose task-specific penalties or restrictions on the cost function of the matrix factorization. In this paper we propose a new NMF algorithm that makes use of non-data dependent auxiliary constraints which incorporate a Toeplitz matrix into the multiplicative updating of the basis and weight matrices. We compare the facial recognition performance of our new Toeplitz Nonnegative Matrix Factorization (TNMF) algorithm to the performance of the Zellner Nonnegative Matrix Factorization (ZNMF) algorithm which makes use of data-dependent auxiliary constraints. We also compare the facial recognition performance of the two aforementioned algorithms with the performance of several preexisting constrained NMF algorithms that have non-data-dependent penalties. The facial recognition performances are evaluated using the Cambridge ORL Database of Faces and the Yale Database of Faces.
