Low dimensional approximation and generalization of multivariate functions on smooth manifolds using deep ReLU neural networks.
Demetrio LabateJi ShiPublished in: Neural Networks (2024)
Keyphrases
- low dimensional
- neural network
- manifold learning
- high dimensional
- euclidean space
- nonlinear manifold learning
- high dimensional data
- dimensionality reduction
- data points
- principal component analysis
- input space
- nonlinear dimensionality reduction
- dimension reduction
- self organizing maps
- low dimensional manifolds
- appearance manifolds
- artificial neural networks
- pattern recognition
- multidimensional scaling
- piecewise constant
- vector space
- neural network model
- laplacian eigenmaps
- continuous functions
- higher dimensional
- convex functions
- fuzzy logic
- linear subspace
- efficient computation
- feature space
- back propagation
- activation function
- locally linear embedding
- approximation algorithms
- pattern classification
- basis functions
- manifold learning algorithm
- low dimensional spaces
- feature selection