Non-negative Matrix Factorization (NMF) has been one of the most popular clustering techniques in machine leaning, and involves various real-world applications. Most existing works perform matrix factorization on high-dimensional data directly. However, the intrinsic data structure is always hidden within the low-dimensional subspace. And, the redundant features within the input space may affect the final result adversely. In this paper, a new unsupervised matrix factorization method, Discrimination-aware Projected Matrix Factorization (DPMF), is proposed for data clustering. The main contributions are threefold: (1) The linear discriminant analysis is jointly incorporated into the unsupervised matrix factorization framework, so the clustering can be accomplished in the discriminant subspace. (2) The manifold regularization is introduced to perceive the geometric information, and the ${\ell _{2,1}}$ℓ2,1-norm is utilized to improve the robustness. (3) An efficient optimization algorithm is designed to solve the proposed problem with proved convergence. Experimental results on one toy dataset and eight real-world benchmarks show the effectiveness of the proposed method.

中文翻译：

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歧视感知投影矩阵分解

非负矩阵分解(NMF) 一直是机器学习中最流行的聚类技术之一，涉及各种实际应用。大多数现有工作直接对高维数据进行矩阵分解。然而，内在数据结构总是隐藏在低维子空间中。并且，输入空间中的冗余特征可能会对最终结果产生不利影响。在本文中，一种新的无监督矩阵分解方法，歧视感知投影矩阵分解(DPMF)，被提议用于数据聚类。主要贡献有三方面： (1) 线性判别分析结合到无监督矩阵分解框架中，因此可以在判别子空间中完成聚类。(2) 引入流形正则化感知几何信息，${\ell _{2,1}}$ℓ2,1-norm 用于提高鲁棒性。(3) 设计了一种有效的优化算法来解决所提出的问题，并证明收敛性。一个玩具数据集和八个真实世界基准的实验结果表明了所提出方法的有效性。