National Laboratory for Parallel and Distributed Processing, School of Computer Science, National University of Defense Technology, Changsha, Hunan, China.
Centre for Quantum Computation and Intelligent Systems and the Faculty of Engineering and Information Technology, University of Technology, Sydney, Sydney, New South Wales, Australia.
PLoS One. 2013 Dec 20;8(12):e83291. doi: 10.1371/journal.pone.0083291. eCollection 2013.
Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W(T) X as their coefficients, i.e., X≈WW(T) X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher's criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.
投影非负矩阵分解 (PNMF) 将高维非负样本 X 投影到由非负基 W 张成的低维子空间，并将 W(T) X 视为它们的系数，即 X≈WW(T) X。由于 PNMF 学习了 X 的基于自然部分的表示 W，因此它已被广泛应用于模式识别和计算机视觉等多个领域。然而，PNMF 在分类任务中的表现并不理想，因为它完全忽略了数据集的标签信息。本文提出了一种判别性 PNMF 方法（DPNMF）来克服这一不足。具体来说，DPNMF 利用 Fisher 准则对 PNMF 进行了利用标签信息的扩展。与 PNMF 类似，DPNMF 学习单个非负基矩阵，并且比 NMF 具有更少的计算负担。与 PNMF 不同的是，DPNMF 最大化了任意两类样本中心之间的距离，同时最小化了低维子空间中同一类的任意两个样本之间的距离，因此具有更强的判别能力。我们开发了一种乘法更新规则来解决 DPNMF 问题，并证明了其收敛性。在四个流行的人脸图像数据集上的实验结果表明，与代表性的 NMF 和 PNMF 算法相比，它具有更好的效果。
