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Why is the feature direction chosen in the direction associated with largest eigenvalue of $Σ_T$ in case of more than two classes? Please see the following.

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  • $\begingroup$ I think it makes sense, but I don't think it is a universal rule even for two classes. Imagine your two classes are point-clouds in 3d, and they look like parallel pancakes separated by a small gap in the direction perpendicular to pancake plane. I don't think the eigenvector corresponding to largest eigenvalue will be along this vector $\endgroup$
    – Cryo
    Sep 28, 2023 at 20:16

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