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We propose a method for learning the intrinsic topol- ogy of a point set sampled from a curve embedded in a high-dimensional ambient space. Our approach does not rely on distances in the ambient space, and thus can recover the topology of sparsely sampled curves, a sit- uation where extant manifold learning methods are ex- pected to fail. We formul...
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... this performance significantly deteriorates when the sample size is reduced. For example, consider the instance of the problem shown in Figure 1 This observation is not very surprising as these kernels are well suited for spherical-shaped distributions while here each spiral is a thin curve. Thus, manifold learning seems to be a more promising avenue for learning such structure of more sparsely sampled datasets. ...
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