论文标题
基于切线空间的非负低等级矩阵近似值的交替预测
Tangent Space Based Alternating Projections for Nonnegative Low Rank Matrix Approximation
论文作者
论文摘要
在本文中，我们开发了一种新的交替投影方法，以计算非负矩阵的非负低等级矩阵近似。在非负低秩矩阵近似方法中，由于需要单数值分解，因此对固定秩矩阵的歧管的投影可能很昂贵。我们建议使用歧管中点的切线空间，以将投影近似于歧管上，以降低计算成本。我们表明，交替的投影产生的序列在固定级别矩阵歧管的切线和非负矩阵歧管上生成的序列，将线性收敛到两个歧管的交汇处，其中收敛点足够接近最佳解决方案。基于对歧管的不精确投影的这种收敛结果是新的，并且在文献中没有研究。在计算时间和准确性方面，给出了数据聚类，模式识别和高光谱数据分析中的数值示例，以证明所提出的方法的性能优于非负矩阵分解方法。
In this paper, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices. In the nonnegative low rank matrix approximation method, the projection onto the manifold of fixed rank matrices can be expensive as the singular value decomposition is required. We propose to use the tangent space of the point in the manifold to approximate the projection onto the manifold in order to reduce the computational cost. We show that the sequence generated by the alternating projections onto the tangent spaces of the fixed rank matrices manifold and the nonnegative matrix manifold, converge linearly to a point in the intersection of the two manifolds where the convergent point is sufficiently close to optimal solutions. This convergence result based inexact projection onto the manifold is new and is not studied in the literature. Numerical examples in data clustering, pattern recognition and hyperspectral data analysis are given to demonstrate that the performance of the proposed method is better than that of nonnegative matrix factorization methods in terms of computational time and accuracy.
