Nonlinear transfer functions (like hyperbolic tangents) in the hidden layers empower the network to characterize arbitrary continuous curves. 2. Principal Curves and Manifolds
The network typically utilizes five layers: an input layer, an encoding layer, a narrow "bottleneck" layer, a decoding layer, and an output layer. Nonlinear Principal Component Analysis and Rela...
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. Because the bottleneck layer contains fewer nodes than
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) Unlike the rigid orthogonal vectors of linear PCA,
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 better understand when to deploy each technique, consider this scannable breakdown of their structural and operational differences: Nonlinear principal component analysis by neural networks