Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment

• DOI: 10.48550/arxiv.cs/0212008
• Publication Date: 2002-01-01
• Authors: Zhenyue Zhang; Hongyuan Zha
• Keywords: Manifold (fluid mechanics); Manifold alignment; Data point

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised and visualization problem with great variety of applications. In this paper we present new algorithm for nonlinear dimension reduction. Based on set sampled noise the manifold, represent local geometry using tangent spaces learned by fitting an affine subspace in neighborhood each point. Those are aligned to give internal global coordinates respect underlying way partial eigendecomposition connection matrix. We careful error analysis our show that reconstruction errors second-order accuracy. illustrate curves surfaces both 2D/3D higher dimensional Euclidean spaces, 64-by-64 pixel face images various pose lighting conditions. also address several theoretical algorithmic issues further research improvements.