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K-means Principal Geodesic Analysis on Riemannian Manifolds

  • Youshan ZhangEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1069)

Abstract

Principal geodesic analysis (PGA) has been proposed for data dimensionality reduction on manifolds. However, a single PGA model is limited to data with a single modality. In this paper, we are the first to propose a generalized K-means-PGA model on manifolds. This model can analyze multi-mode nonlinear data, which applies to more manifolds (Sphere, Kendall’s shape and Grassmannian). To show the applicability of our model, we apply our model to spherical, Kendall’s shape and Grassmannian manifolds. Our K-means-PGA model offers correct geometry geodesic recovery than K-means-PCA model. We also show shape variations from different clusters of human corpus callosum and mandible data. To demonstrate the efficiency of our model, we perform face recognition using ORL dataset. Our model has a higher accuracy (99.5%) than K-means-PCA model (95%) in Euclidean space.

Keywords

K-means Principal Geodesic Analysis Manifolds 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Computer Science and EngineeringLehigh UniversityBethlehemUSA

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