Abstract:

Non-negative matrix factorization (NMF) adds non-negative constraints to matrix decomposition, and its decomposed sub-matrices are easier to interpret. The optimization target of many traditional NMF algorithms is based on L₂ norm, and they are not easy to identify the nonlinearly distributed data structures. In order to solve this problem, we propose a regularized non-negative matrix factorization algorithm based on L₂₁ norm. The objective function of the proposed algorithm is written into the form of L₂₁ norm, and we add graph regularization term to the objective function to handle complex nonlinear data sets. Finally, several benchmark data sets are used to test the performance of the proposed algorithm on the clustering task. The experimental results show that the proposed algorithm can extract the key features of the data, obtain the low-dimensional representation of the original data, and produce better clustering results.

Key words: Nonnegative Matrix Factorization, L₂₁ Norm, Regularization Method, Clustering

摘要： 非负矩阵分解(Nonnegative Matrix Factorization，NMF)给矩阵分解加了非负的约束条件，其分解的子矩阵更容易解释。传统的NMF算法使用基于L₂范数的优化目标，不容易识别非线性分布的数据结构。为了解决这一问题，提出一种基于L₂₁范数的正则化非负矩阵分解算法，将非负矩阵分解的目标函数写成L₂₁范数的形式，并在目标函数中加入图正则化项，使其能更好地处理复杂的非线性数据。最后，使用基准数据集，在聚类任务上测试所提出算法的性能。实验结果表明，所提出的算法可以提取数据的关键特征，获得原始数据的低维表示，产生更好的聚类结果。

关键词: 非负矩阵分解, L₂₁范数, 正则化, 聚类