Review of Linear Projection Methods

Abstract

Exploratory data analysis is a set of methods with which we try to extract as much information as possible from a data set of high dimension and huge volume. However, performing analysis of complex data usually involves a large number of variables and analysis with a large number of variables generally requires a large amount of memory and computational power and may generalize poorly to new samples. Many techniques change the basis of the considered data space by projecting the data to a lower dimensional space. The basic idea is to find some suitable function $\varphi : \Re^D \mapsto \Re^d , d\ll D$, which maps the original data sample ${\bf x}\in \Re^D$ into a d-dimensional manifold by ϕ(x) = y, where ${\bf x}\in \Re^D,{\bf y}\in \Re^d$. In this section, we review several projection methods in detail.