ISOLLE: LLE with geodesic distance

We propose an extension of the algorithm for nonlinear dimensional reduction locally linear embedding (LLE) based on the usage of the geodesic distance (ISOLLE). In LLE, each data point is reconstructed from a linear combination of its n nearest neighbors, which are typically found using the Euclidean distance. We show that the search for the neighbors performed with respect to the geodesic distance can lead to a more accurate preservation of the data structure. This is confirmed by experiments on both real-world and synthetic data.