Autoencoder vs PCA Explorer Linear AE ≡ PCA
(A) 2D Data Space & Reconstruction $\hat{\mathbf{x}}$
Original $\mathbf{x}$ Decoded $\hat{\mathbf{x}}$ Manifold $\hat{\mathbf{x}}(z)$
(B) 1D Bottleneck Latent Space $z \in \mathbb{R}^1$ Cleanly Unrolled