EXPERIMENTAL STUDY OF MANIFOLD LEARNING AND TANGENT PROPAGATION

Abstract

In the Data Science routine, we often face the curse of dimensionality, dealing with high-dimensional data which, in turn, can be very difficult. The problems of this nature can be approached by methods of Dimensionality Reduction. These methods assume that data can be interpreted in a smaller dimension. The hypothesis proposed in this work is that data is located exactly or near along with a low dimension manifold and the tool for finding this manifold is auto-encoders. In particular, we calculate the basis of the tangent space of the low-dimensional manifold at each data point and up towards using it to the regularization of the regression task. All calculations are implemented via Python 3 since this programming language in cludes a wide range of packages for dealing with Big Data.