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Sample-Based Orientation of Manifold Choice

Student: Evgeniy Abramov

Supervisor: Yury Yanovich

Faculty: Faculty of Computer Science

Educational Programme: Mathematical Methods of Optimization and Stochastics (Master)

Final Grade: 9

Year of Graduation: 2018

The real data usually has a high dimensionality. However, due to presence of different dependencies between data points, they occupy only a small part of high-dimensional space of observations. The most common model is the assumption, that data lie on or near a manifold of a smaller dimension. This assumption is called the Manifold Hypothesis. Often we are interested not only in reconstruction such manifold, but also it's topological and geometric properties. In the work was given an algorithm to define an orientation of manifold for sufficiently large number of samples . Also was proposed an algorithm, checking the orientability of manifold .

Full text (added May 28, 2018)

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