Why does projecting onto the blue line lose less information than projecting onto the red line?

Conditions

• Demonstrated on a 2D scatter plot.
• The explanation is geometric and intuitive rather than algebraic.

Reasoning, step by step

1. Observe the 2D scatter plot of green points.
2. Project the points onto the blue direction and note that they remain distributed along that line.
3. Project the points onto the red direction and note that they collapse almost completely.
4. Conclude that the blue direction has smaller spread and thus loses less information when projected onto.

Example

The animation maps the cloud onto one candidate axis to test what remains visible after reduction. The narrator says this direction has smaller spread and that clamping onto one line there would not lose that much information, and the animation shows a retained 1D distribution.

Common misconceptions

• The clip gives an intuitive description only; no covariance matrix, eigenvalue equation, or optimization objective is shown in this excerpt.

Watch the explanation

Explore next

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