用于图片特征分解的稀疏多因式非负矩阵分解算法

Algorithms of sparse multi-factor NMF for images decomposition

非负矩阵分解(NMF)是一种流行的数据分析方法,其目标是使其接近通过所有非负成分产生的两个非负矩阵。文中描述了一种对于多因式非负矩阵分解(mf NMF)问题新的且有效的算法,概括了原始NMF问题的一些因式。此外,将扩展的NMF算法合并为一个基于Dirichlet分布的正则化准则来激励获得的系数组成的稀疏性。文中的稀疏mf NMF算法提供一个近似且直观的解释,与之前的算法相比,使用修复点迭代的效率更高。最终证明了本算法在人造和真实数据集上的有效性。

Nonnegative matrix factorization （NMF） is a popular data analysis method, theobjective of which is to approximate a matrix with all nonnegative componentsinto the product of two nonnegative matrices. In this work, we describe a newsimple and efficient algorithm for multi-factor nonnegative matrix factorization （mfNMF） problem that generalizes the original NMF problem to more than twofactors. Furthermore, we extend the mfNMF algorithm to incorporate a regularizerbased on the Dirichlet distribution to encourage the sparsity of the components ofthe obtained factors. Our sparse mfNMF algorithm affords a closed form and anintuitive interpretation, and is more efficient in comparison with previous worksthat use fix point iterations. We demonstrate the effectiveness and efficiency ofour algorithms on both synthetic and real data sets.