Mahalanobis-based Adaptive Nonlinear Dimension Reduction

We define a new adaptive embedding approach for data dimension reduction applications. Our technique entails a local learning of the manifold of the initial data, with the objective of defining local distance metrics that take into account the different correlations between the data points. We choose to illustrate the properties of our work on the isomap algorithm. We show through multiple simulations that the new adaptive version of isomap is more robust to noise than the original non-adaptive one.