Linear Discriminant Analysis
A supervised projection maximizing between-class scatter over within-class scatter, separating known classes rather than maximizing overall data variance.
Where PCA ranks directions by how much the data spreads overall, LDA ranks them by how well they separate labeled classes — tight classes that sit far apart score highest, using label information PCA never looks at.
At most one fewer direction than the number of classes carries any separating information at all, a firm ceiling PCA's component count doesn't share.