An Extended Isomap Approach for Nonlinear Dimension Reduction

Nowadays, Isomap is one of the most popular nonlinear manifold dimension reductions which have applied to the real-world datasets. However, it has various limitations for the high-dimensional and large-scale dataset. Two main limitations of the Isomap are: it may make incorrect links in the neighborhood graph G and high computational cost. In this paper, we have introduced a novel framework, which we called the FastIsomap. The main purpose of the FastIsomap is to increase the accuracy of the graph by using two state-of-the-art algorithms: a randomized division tree and NN-Descent. The basic idea of FastIsomap is to construct an accurate approximated KNN graph from millions and hundreds of dimensional’ data points and then project the graph into low-dimensional space. We have compared the FastIsomap framework with the existing Isomap algorithm to verify its efficiency and performance, which provided accurate results of the high and large-dimensional datasets. © 2020, Springer Nature Singapore Pte Ltd.