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• W2125003829 startingPage "796" @default.
• W2125003829 abstract "Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, that is, how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low- dimensional space. Experiments on synthetic data, as well as real-world images, demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings." @default.
• W2125003829 created "2016-06-24" @default.
• W2125003829 creator A5017031914 @default.
• W2125003829 creator A5040989553 @default.
• W2125003829 date "2008-05-01" @default.
• W2125003829 modified "2023-09-30" @default.
• W2125003829 title "Riemannian Manifold Learning" @default.
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• W2125003829 doi "https://doi.org/10.1109/tpami.2007.70735" @default.
• W2125003829 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/18369250" @default.
• W2125003829 hasPublicationYear "2008" @default.
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