Hands-On Machine Learning for Algorithmic Trading

Visualizing PCA in 2D

The following screenshot illustrates several aspects of PCA for a two-dimensional random dataset (see the pca_key_ideas notebook):

• The left panel shows how the first and second principal components align with the directions of maximum variance while being orthogonal.
• The central panel shows how the first principal component minimizes the reconstruction error, measured as the sum of the distances between the data points and the new axis.
• Finally, the right panel illustrates supervised OLS, which approximates the outcome variable (here we choose x₂) by a (one-dimensional) hyperplane computed from the (single) feature. ...