Non-linear Dimensionality Reduction by Locally Linear Isomaps

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 lowdimensional 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.

• Type: Conference
• Year: 2004
• Where: ICONIP
• Authors: Ashutosh Saxena, Abhinav Gupta, Amitabha Mukerjee
• Keywords: Algorithm, ICONIP 2004, ICONIP 2007, Isomap Algorithm, Local Linear