Abstract
Manifold based metric learning methods have become increasingly popular in recent years. In almost all these methods, however, the underlying manifold is approximated by a point cloud, and the matric tensor, which is the most basic concept to describe the manifold, is neglected. In this paper, we propose a non-linear metric learning framework based on metric tensor. We construct a Riemannian manifold and its metric tensor on sample space, and replace the Euclidean metric by the learned Riemannian metric. By doing this, the sample space is twisted to a more suitable form for classification, clustering and other applications. The classification and clustering results on several public datasets show that the learned metric is effective and promising.
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Yin, L., Pei, M. (2015). Non-linear Metric Learning Using Metric Tensor. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9489. Springer, Cham. https://doi.org/10.1007/978-3-319-26532-2_4
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DOI: https://doi.org/10.1007/978-3-319-26532-2_4
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