Because the bottleneck layer contains fewer nodes than the input or output layers, the network is forced to compress the data. The values extracted at this bottleneck represent the nonlinear principal component scores.

To accomplish this, three primary methodologies have emerged over the decades: 1. Autoassociative Neural Networks (Autoencoders)

Nonlinear transfer functions (like hyperbolic tangents) in the hidden layers empower the network to characterize arbitrary continuous curves. 2. Principal Curves and Manifolds

Initially proposed by Hastie and Stuetzle, principal curves are smooth, self-consistent curves that pass through the "middle" of a data cloud. Unlike the rigid orthogonal vectors of linear PCA, a principal curve bends and twists to accommodate the global shape of the data. 3. Kernel PCA (kPCA)