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Sample-based Estimation of Jacobian Matrix on Manifold

Student: Illarion Petrov

Supervisor: Yury Yanovich

Faculty: Faculty of Computer Science

Educational Programme: Data Science (Master)

Year of Graduation: 2017

In many applications, the real high-dimensional data occupy only a very small part in the high dimensional ‘observation space’ whose intrinsic dimension is small. The most popular model of such data is Manifold model which assumes that the data lie on or near an unknown manifold Data Manifold, (DM) of lower dimensionality embedded in an ambient high-dimensional input space (Manifold assumption about highdimensional data).Manifold Learning is a Dimensionality Reduction problem under the Manifold assumption about the processed data and its goal is to construct a low-dimensional parameterization of the DM (global low-dimensional coordinates on the DM) from a finite dataset sampled from the DM. One of the tasks that can arise in the process of investigating a manifold is estimation of Jacobian of function on Manifold. In this paper, the algorithm estimation of Jacobian of function on Manifold is proposed and implemented. Numerical experiments have also been conducted to evaluate the quality of estimates.

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