nlpca-updates-both-weights-and-inputs
IN premise — summaries/2026/08/24/wiki-Nonlinear_dimensionality_reduction-chunk-2.md
Created 2026-08-24T17:11:21+00:00
Nonlinear PCA (NLPCA) trains an MLP via backpropagation but uniquely updates both the network weights and the input values (treated as latent variables), where the learned latent inputs form the low-dimensional embedding
Summary
NLPCA finds a compressed representation of data by jointly learning the network's internal mapping and the coordinates of each data point in that lower-dimensional space, rather than fixing one and solving for the other. This matters because the resulting embedding is co-optimized end-to-end: the best low-dimensional coordinates and the best nonlinear projection are discovered together, which can capture structure that a two-step approach (embed first, then map) would miss.