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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.

The storage reduction is claimed because each face's representation changes from storing three floating-point numbers (nose length, eye distance, jaw width) to storing only two floating-point numbers (the two principal coordinates).

Conditions: Each original sample stores 3 floating-point coordinates.; Each compressed sample stores 2 floating-point coordinates.

The storage reduction is claimed because each face's representation changes from storing three floating-point numbers (nose length, eye distance, jaw width) to storing only two floating-point numbers (the two principal coordinates).

Conditions: Each original sample stores 3 floating-point coordinates.; Each compressed sample stores 2 floating-point coordinates.