Defining DR

It is a most commonly accepted rule of thumb that it is difficult to understand or visualize data represented in or by more than three dimensions.

Dimensional (-ity) reduction is the process of attempting to reduce the number of random variables (or data dimensions) under statistical consideration, or perhaps better put: finding a lower-dimensional representation of the feature-set that is of interest.

This allows the data scientist to:

• Avoid what is referred to as the curse of dimensionality

  Note

  The curse of dimensionality refers to a phenomenon that arises when attempting to analyze data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings or everyday experience.

• Reduce the amount of time and memory required for the proper analysis of the data

• Allow the data to be more easily visualized

• Eliminate features irrelevant to the model's purpose

• Reduce model noise

A useful (albeit perhaps over-used) conceptual example of...