论文标题
基于日志的稀疏非负矩阵分解数据表示
Log-based Sparse Nonnegative Matrix Factorization for Data Representation
论文作者
论文摘要
非负矩阵分解（NMF）在近年来已广泛研究其在表示具有基于零件表示的非负数据方面的有效性。 For NMF, a sparser solution implies better parts-based representation.However, current NMF methods do not always generate sparse solutions.In this paper, we propose a new NMF method with log-norm imposed on the factor matrices to enhance the sparseness.Moreover, we propose a novel column-wisely sparse norm, named $\ell_{2,\log}$-(pseudo) norm to enhance the robustness $ \ ell_ {2，\ log} $ - - （伪）规范是不变的，连续的且可区分的。对于$ \ ell_ {2，\ log} $正常的收缩问题，我们得出了封闭形式的解决方案，可用于其他一般乘法规则的封闭形式解决方案，用于效率的乘法规则。序列。扩展的实验结果证实了所提出的方法的有效性，以及增强的稀疏性和鲁棒性。
Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. For NMF, a sparser solution implies better parts-based representation.However, current NMF methods do not always generate sparse solutions.In this paper, we propose a new NMF method with log-norm imposed on the factor matrices to enhance the sparseness.Moreover, we propose a novel column-wisely sparse norm, named $\ell_{2,\log}$-(pseudo) norm to enhance the robustness of the proposed method.The $\ell_{2,\log}$-(pseudo) norm is invariant, continuous, and differentiable.For the $\ell_{2,\log}$ regularized shrinkage problem, we derive a closed-form solution, which can be used for other general problems.Efficient multiplicative updating rules are developed for the optimization, which theoretically guarantees the convergence of the objective value sequence.Extensive experimental results confirm the effectiveness of the proposed method, as well as the enhanced sparseness and robustness.
