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An Information Geometry of Statistical Manifold Learning

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Published in Proceedings of the 31 st International Conference on Machine Learning. Beijing, China. 2014, p. 1-9
Collection JMLR: Workshop and Conference Proceedings; 32
Abstract Manifold learning seeks low-dimensional representations of high-dimensional data. The main tactics have been exploring the geometry in an input data space and an output embedding space. We develop a manifold learning theory in a hypothesis space consisting of models. A model means a specific instance of a collection of points, e.g., the input data collectively or the output embedding collectively. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions. There, manifold learning is interpreted as a trajectory of intermediate models. The volume of a continuous region reveals an amount of information. It can be measured to define model complexity and embedding quality. This provides deep unified perspectives of manifold learning theory.
Keywords Information geometryManifold learning
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Research groups Viper group
Computer Vision and Multimedia Laboratory
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SUN, Ke, MARCHAND-MAILLET, Stéphane. An Information Geometry of Statistical Manifold Learning. In: Proceedings of the 31 st International Conference on Machine Learning. Beijing, China. [s.l.] : [s.n.], 2014. p. 1-9. (JMLR: Workshop and Conference Proceedings; 32) https://archive-ouverte.unige.ch/unige:73194

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Deposited on : 2015-06-15

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