Traditional PCA finds the lower-dimensional hyperplane that minimizes the sum of squared orthogonal deviations from the dataset. In contrast, NLPCA maps the data to a lower-dimensional curved surface.
To accomplish this, three primary methodologies have emerged over the decades: 1. Autoassociative Neural Networks (Autoencoders) Nonlinear Principal Component Analysis and Rela...
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) principal curves are smooth
The most widely used implementation of NLPCA involves a multi-layer feed-forward neural network trained to perform an identity mapping. Nonlinear Principal Component Analysis and Rela...