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The reconstruction error points precisely along the direction of the dropped principal components. In the 3D to 2D example, the error aligns with the third principal component (PC3), which was discarded during projection.

Conditions: A subset of principal components has been dropped during dimensionality reduction.; The data is reconstructed using only the retained principal components.

The reconstruction error points precisely along the direction of the dropped principal components. In the 3D to 2D example, the error aligns with the third principal component (PC3), which was discarded during projection.

Conditions: A subset of principal components has been dropped during dimensionality reduction.; The data is reconstructed using only the retained principal components.

The reconstruction error for a single data point is defined as the Euclidean distance between the original 3D point and its reconstructed approximation on the 2D subspace.

Conditions: The original data point $\mathbf{x}_i$ is in 3D space.; The reconstructed point $\hat{\mathbf{x}}_i$ is on the 2D subspace.; Distance is measured using the Euclidean norm.

The reconstruction error for a single data point is defined as the Euclidean distance between the original 3D point and its reconstructed approximation on the 2D subspace.

Conditions: The original data point $\mathbf{x}_i$ is in 3D space.; The reconstructed point $\hat{\mathbf{x}}_i$ is on the 2D subspace.; Distance is measured using the Euclidean norm.