Shamap: Shape-based Manifold Learning

2018/02/15 by Fenglei Fan, Fan, Fenglei, Ziyu Su +5
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Vision and Imaging #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1802.05386

openalex publication_date 2018/02/15 · arxiv created 2019/09/18 · arxiv updated 2019/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying shape-oriented information or a topological similarity between high- and low-dimensional representations of a data cloud. Our results demonstrate the feasibility and merits of the proposed dimensionality reduction scheme.

Citations

• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Representation Learning: A Review and New Perspectives

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