Dimensionality Reduction

Abstract:

There are times when a dataset has a sort of symmetry that can be used to remove some of its redundant variables. Conceptually, it is like trying to describe the surface of a sphere in 3 dimensions. If we use the x-y-z coordinate we need to work with 3 variables. But, in a spherical coordinate, we only need \(\theta\) and \(\phi\) variables. That means the symmetry has removed one of the variables. The same concep exist in data science. Just like in coordinate transformations in physics we can define new variables (features) as linear or non-linear combination of the original variables such that a smaller set of the new variables remain important.