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Answers for “为什么向蓝线投影比向红线投影丢失的信息更少?”

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The clip explains that PCA chooses which directions to keep based on the spread of the data. It uses a 2D scatter plot to show that projecting along the smaller-spread direction leaves the points separated, while projecting along the larger-spread direction collapses them.

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