Embedding new data points for manifold learning via coordinate propagation |
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Authors: | Shiming Xiang Feiping Nie Yangqiu Song Changshui Zhang Chunxia Zhang |
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Affiliation: | (1) Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, 3-120 Room, FIT Building, Beijing, 100084, People’s Republic of China;(2) Software School, School of Computer Science, Beijing Institute of Technology, Beijing, 100081, China |
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Abstract: | In recent years, a series of manifold learning algorithms have been proposed for nonlinear dimensionality reduction. Most
of them can run in a batch mode for a set of given data points, but lack a mechanism to deal with new data points. Here we
propose an extension approach, i.e., mapping new data points into the previously learned manifold. The core idea of our approach
is to propagate the known coordinates to each of the new data points. We first formulate this task as a quadratic programming,
and then develop an iterative algorithm for coordinate propagation. Tangent space projection and smooth splines are used to
yield an initial coordinate for each new data point, according to their local geometrical relations. Experimental results
and applications to camera direction estimation and face pose estimation illustrate the validity of our approach.
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Keywords: | Manifold learning Out-of-sample Coordinate propagation Tangent space projection Smooth spline Quadratic programming |
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