Learning Neural Representations and Local Embedding for Nonlinear Dimensionality Reduction Mapping

This work explores neural approximation for nonlinear dimensionality reduction mapping based on internal representations of graph-organized regular data supports. Given training observations are assumed as a sample from high-dimensional space with an embedding low-dimensional manifold. An approximating function consisting adaptable built-in parameters is optimized subject to given by the proposed learning process, and verified transformation novel testing images in output space. Optimized sketch supports distributed clusters their representative On basis, able operate without reserving original massive observations. The model contains multiple modules. Each activates non-zero response input inside its correspondent local support. Graph-organized have lateral interconnections representing neighboring relations, inferring minimal path between centroids any two supports, proposing distance constraints all Following distance-preserving principle, this proposes Levenberg-Marquardt optimizing constraints, further develops during execution phase. Numerical simulations show effective reliable mapping.