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The compressed coordinates are obtained by taking the dot product of the original 3D feature vector with the two principal component direction vectors. This projects the 3D data onto the 2D principal plane.

Conditions: The original sample $\mathbf{x}$ lies in $\mathbb{R}^3$.; Principal directions $\mathbf{e}_1$ and $\mathbf{e}_2$ define the 2D coordinate system.; Coordinates are obtained by dot products with those directions.

The compressed coordinates are obtained by taking the dot product of the original 3D feature vector with the two principal component direction vectors. This projects the 3D data onto the 2D principal plane.

Conditions: The original sample $\mathbf{x}$ lies in $\mathbb{R}^3$.; Principal directions $\mathbf{e}_1$ and $\mathbf{e}_2$ define the 2D coordinate system.; Coordinates are obtained by dot products with those directions.