A Tangent Distance Preserving Dimensionality Reduction Algorithm

2019/02/04 by Xu Zhao, Zongli Jiang, Zhao, Xu +1
Computer Science · Mathematics · #Advanced Image and Video Retrieval Techniques #Algorithm #Artificial intelligence #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Dimensionality reduction #FOS: Computer and information sciences #Face and Expression Recognition #Geometry #Image Retrieval and Classification Techniques #Mathematics #Reduction (mathematics) #Tangent #cs.CV

paper · pdf · doi:10.48550/arxiv.1902.05373

Signal and Image Processing (SIP 2008)

arxiv created 2019/02/04 · openalex publication_date 2019/02/04 · arxiv updated 2019/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear structure of the manifold, and shows how the manifold is folded in the high dimensional space. We call this method Tangent Distance Preserving Mapping (TDPM). TDPM uses tangent distance instead of geodesic distance, and then applies MDS to the tangent distance matrix to map the manifold into a low dimensional space in which we can get its nonlinear structure.

Citations

• Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment
• A Global Geometric Framework for Nonlinear Dimensionality Reduction

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