Why does the video use an ellipse to explain principal components?

Conditions

• The data are approximated by an ellipse.
• The ellipse is described verbally as 'basically a two-dimensional Gaussian.'

Reasoning, step by step

1. Fit an ellipse around the scatter plot.
2. Identify the main axes of the ellipse.
3. Label the axes as principal component 1 and principal component 2.
4. Understand that these axes represent the directions of interest for reduction.

Example

A scatter plot of green points is enclosed by a gray ellipse. The speaker describes this ellipse as 'basically a two-dimensional Gaussian' and says the goal is to find its main axes. Two arrows are drawn from the center of the ellipse: a longer red axis and a shorter blue axis. These are labeled 'principal component 1' and 'principal component 2'.

Common misconceptions

• The statement is presented intuitively in this clip; no formal proof is given here.

Watch the explanation

Explore next

• How is the data matrix X organized in the PCA setup shown here?
• Why does the PCA algorithm subtract the mean from the data before continuing?