NR-Isomap: An Incremental Approach with Gaussian Process Kernels for Denoising

The Isomap is a popular nonlinear dimensionality reduction method often used for low-dimensional embedding space. When the big data is noisy, Isomap often fails because of the graph structure’ Short-Circuit Edges (SCE) problem. In this paper, an incremental Noise-Reduction Isomap (NR-Isomap) approach is to address the SCE problem in a graph structure. The GP kernels are combined with the manifold learning approach and provide significant results. NR-Isomap is based on the Hessian Locally Linear Embedding (HLLE) algorithm with Gaussian Process (GP) kernels. The HLLE algorithm provides the optimal solution to the SCE problem caused by an overly noisy dataset. NR-Isomap provides an answer to the Isomap SCE problem in noisy big data problems that cannot be handled using existing methods. Therefore, the GP kernel significantly improves and measures the performance of the NRI-somap accuracy. Our NR-Isomap method outperforms experiments on SK-Learn datasets and shows efficient results compared to Isomap. Our NR Isomap is much more efficient and faster compared to Isomap. The efficiency and accuracy of the NR-Isomap method are demonstrated theoretically and compared with other manifold learning methods.