FastIsomapVis: A Novel Approach for Nonlinear Manifold Learning

Abstract

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.