Extrinsic Kernel Ridge Regression Classifier for Planar Kendall Shape Space

2019/12/17 by Hwi-Young Lee, Lee, Hwiyoung, Vic Patrangenaru +1
Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Morphological variations and asymmetry #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1912.08202

openalex publication_date 2019/12/17 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty in dealing with non-Euclidean geometry. In this paper, motivated by the extrinsic framework of manifold-valued data analysis, we propose a new positive definite kernel on planar Kendall shape space Σ₂^k, called extrinsic Veronese Whitney Gaussian kernel. We show that our approach can be extended to develop Gaussian kernels on any embedded manifold. Furthermore, kernel ridge regression classifier (KRRC) is implemented to address the shape classification problem on Σ₂^k, and their promising performances are illustrated through the real data analysis.

Citations

• Metric spaces and positive definite functions
• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces

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