Key concepts of PCA
PCA produces multiple linear combinations of features and each linear combination is a component. It identifies a component that captures the largest amount of variance, and a second component that captures the largest amount of remaining variance, and then a third component, and so on until a stopping point we specify is reached. The stopping point can be based on the number of components, the percent of the variation explained, or domain knowledge.
One very useful characteristic of principal components is that they are mutually orthogonal. This means that they are uncorrelated, which is really good news for modeling. Figure 15.1 shows two components constructed from the features x1 and x2. The maximum variance is captured with PC1, the maximum remaining variance with PC2. (The data points in the figure are made up.) Notice that the two vectors are orthogonal (perpendicular).
Figure 15.1 – An illustration of PCA with two features...
