The classical Isomap is the most common unsupervised nonlinear manifold method and widely being used in visualizations and dimension reductions. However, when it applied to real-world datasets, it shows shortcomings for the shortest path between all pairs of data points, which are based on the nearest neighborhood G graph via the Dijkstra algorithm, which makes it a very time-consuming step. The other critical problem is the classical Isomap has a lack of topological stability on the nearest neighborhood G graph. In this paper, we propose a novel technique called the FastIsomapVis for the above problems of the classical Isomap. The FastIsomapVis uses hierarchal divide, conquer, and combine approach through two algorithms, which are randomized division tree (KD-tree) and Dijkstra Buckets Double (DKD). The primary aim of the FastIsomapVis is to increase the efficiency and accuracy of the graph. This research paper focuses on transforming the high dimensional datasets into a low dimensional Isomap visualization. The FastIsomapVis makes it easy to construct an accurate K nearest neighborhood G graph and scale high dimensional data points into low dimensional space. Our proposed method is compared to the classical Isomap to verify its effectiveness and provide highly authentic results of the high dimensional datasets. The finding of the current study shows that our proposed method is much fastened than classical Isomap.

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.