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首页> 外文会议>European conference on machine learning and knowledge discovery in databases >Efficient Rank-one Residue Approximation Method for Graph Regularized Non-negative Matrix Factorization
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Efficient Rank-one Residue Approximation Method for Graph Regularized Non-negative Matrix Factorization

机译：图正则化非负矩阵分解的有效秩一残差逼近方法

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Nonnegative matrix factorization (NMF) aims to decompose a given data matrix X into the product of two lower-rank nonnegative factor matrices UV~T. Graph regularized NMF (GNMF) is a recently proposed NMF method that preserves the geometric structure of X during such decomposition. Although GNMF has been widely used in computer vision and data mining, its multiplicative update rule (MUR) based solver suffers from both slow convergence and non-stationarity problems. In this paper, we propose a new efficient GNMF solver called rank-one residue approximation (RRA). Different from MUR, which updates both factor matrices (U and V) as a whole in each iteration round, RRA updates each of their columns by approximating the residue matrix by their outer product. Since each column of both factor matrices is updated optimally in an analytic formulation, RRA is theoretical and empirically proven to converge rapidly to a stationary point. Moreover, since RRA needs neither extra computational cost nor parametric tuning, it enjoys a similar simplicity to MUR but performs much faster. Experimental results on real-world datasets show that RRA is much more efficient than MUR for GNMF. To confirm the stationarity of the solution obtained by RRA, we conduct clustering experiments on real-world image datasets by comparing with the representative solvers such as MUR and NeNMF for GNMF. The experimental results confirm the effectiveness of RRA.
机译：非负矩阵分解（NMF）旨在将给定数据矩阵X分解为两个低级非负因子矩阵UV〜T的乘积。图形正则化NMF（GNMF）是最近提出的NMF方法，其在这种分解期间保留X的几何结构。虽然GNMF已广泛用于计算机视觉和数据挖掘，但其乘法更新规则（MUR）的求解器遭受了缓慢的收敛和非公平问题。在本文中，我们提出了一种称为Rank-One Reside Quentmation（RRA）的新高效GNMF解算器。与MUR不同，在每个迭代轮中将因子矩阵（U和V）更新，RRA通过其外部产品近似残留矩阵来更新每个列。由于两种因子矩阵的每列在分析制剂中最佳地更新，因此RRA是理论和经验证明的，以便迅速收敛到静止点。此外，由于RRA既不需要额外的计算成本也不需要参数调整，因此它享有类似的简单性，但表现得更快。实验结果对现实世界数据集表明，RRA比GNMF更有效。为了确认RRA获得的解决方案的实质性，我们通过与代表性求解器（如MUR和NENMF为GNMF）来对现实世界图像数据集进行聚类实验。实验结果证实了RRA的有效性。

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