Non-linear dimensionality reduction by locally linear isomaps

Abstract

Algorithms for nonlinear dimensionality reduction (NLDR) find meaningful hidden low-dimensional structures in a high-dimensional space. Current algorithms for NLDR are Isomaps, Local Linear Embedding and Laplacian Eigenmaps. Isomaps are able to reliably recover low-dimensional nonlinear structures in high-dimensional data sets, but suffer from the problem of short-circuiting, which occurs when the neighborhood distance is larger than the distance between the folds in the manifolds. We propose a new variant of Isomap algorithm based on local linear properties of manifolds to increase its robustness to short-circuiting. We demonstrate that the proposed algorithm works better than Isomap algorithm for normal, noisy and sparse data sets.