Dimensionality Reduction in Statistical Learning

Many statistical learning tasks deal with data which are presented in high-dimensional spaces, and the ´curse of dimensionality´ phenomenon is often an obstacle to the use of many methods for solving these tasks. To avoid this phenomenon, various dimensionality reduction algorithms are used as the first key step in solving these tasks. The algorithms transform original high-dimensional data into lower dimensional representations in such a way that the initial task can be reduced to a lower dimensional one. The dimensionality reduction problems have varying formulations depending on their initial statistical learning tasks. A new geometrically motivated algorithm that solves various dimensionality reduction problems is presented.