Eigenvalue bounds for an alignment matrix in manifold learning

详细信息	查看全文 | 推荐本文 |

• 作者：Qiang Ye ^{qye@ms.uky.edu} ; Weifeng Zhi ; ^{wzhi@ms.uky.edu}
• 关键词：Eigenvalue bound ; Smallest nonzero eigenvalue ; Alignment matrix ; Manifold learning ; Dimensionality reduction
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：15 April, 2012
• 卷：436
• 期：8
• 页码：2944-2962
• 文件大小：407 K

摘要

This paper presents a spectral analysis for an alignment matrix that arises in reconstruction of a global coordinate system from local coordinate systems through alignment in manifold learning. Some characterizations of its eigenvalues and its null space as well as a lower bound for the smallest positive eigenvalue are given, which generalize earlier results of Li et al. (2007) to include a more general situation that arises in alignments of local sections of different dimensions. Our results provide a theoretical understanding of the Local Tangent Space Alignment (LTSA) method (Zhang and Zha (2004) ) for nonlinear manifold learning and address some computational issues related to the method.