Chapter 6. Dimensionality Reduction: Squashing the Data Pancake with PCA
With automatic data collection and feature generation techniques, one can quickly obtain a large number of features. But not all of them are useful. In Chapters 3 and 4, we discussed frequency-based filtering and feature scaling as ways of pruning away uninformative features. Now we will take a close look at the topic of feature dimensionality reduction using principal component analysis (PCA).
This chapter marks an entry into model-based feature engineering techniques. Prior to this point, most of the techniques can be defined without referencing the data. For instance, frequency-based filtering might say, “Get rid of all counts that are smaller than n,” a procedure that can be carried out without further input from the data itself.
Model-based techniques, on the other hand, require information from the data. For example, PCA is defined around the principal axes of the data. In previous chapters, there was always a clear-cut line between data, features, and models. From this point forward, the difference gets increasingly blurry. This is exactly where the excitement lies in current research on feature learning.
Dimensionality reduction is about getting rid of “uninformative information” while retaining the crucial bits. There are many ways to define “uninformative.” PCA focuses on the notion of linear dependency. In “The Anatomy of a Matrix”, we describe the column space of a data matrix as the ...