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Answers for “在这个 PCA 介绍中,符号 D = 2 -> D' = 1 是什么意思?”

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Projecting onto the blue line loses less information because the spread along that direction is smaller. Clamping all points onto one line in that direction would not lose that much information.

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