learning topology
Learning Topology with the Generative Gaussian Graph and the EM Algorithm
Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learning theory. In this work, we propose a generative model based on the Delaunay graph of the prototypes and the ExpectationMaximization algorithm to learn the parameters. This work is a first step towards the construction of a topological model of a set of points grounded on statistics.
Learning Topology of Curves with Application to Clustering
Mobahi, Hossein (University of Illinois at Urbana Champaign) | Rao, Shankar (University of Illinois at Urbana Champaign) | Ma, Yi (University of Illinois at Urbana Champaign)
We propose a method for learning the intrinsic topology 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 situation where extant manifold learning methods are expected to fail. We formulate a loss function based on the smoothness of a curve, and derive a greedy procedure for minimizing this loss function. We compare the efficacy of our approach with representative manifold learning and hierarchical clustering methods on both real and synthetic data.
Learning Topology with the Generative Gaussian Graph and the EM Algorithm
Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learning theory. In this work, we propose a generative model based on the Delaunay graph of the prototypes and the Expectation-Maximization algorithm to learn the parameters. This work is a first step towards the construction of a topological model of a set of points grounded on statistics.
Learning Topology with the Generative Gaussian Graph and the EM Algorithm
Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learningtheory. In this work, we propose a generative model based on the Delaunay graph of the prototypes and the Expectation-Maximization algorithm to learn the parameters. This work is a first step towards the construction of a topological model of a set of points grounded on statistics.