ISOLLE: Locally Linear Embedding with Geodesic Distance

Locally Linear Embedding (LLE) has recently been proposed as a method for dimensional reduction of high-dimensional nonlinear data sets. 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 propose an extension of LLE which consists in performing the search for the neighbors with respect to the geodesic distance (ISOLLE). In this study we show that the usage of this metric can lead to a more accurate preservation of the data structure. The proposed approach is validated on both real-world and synthetic data.

• Type: Conference
• Year: 2005
• Where: PKDD
• Authors: Claudio Varini, Andreas Degenhard, Tim W. Nattkemper
• Keywords: Data Point, Euclidean Distance, Nearest Neighbors, PKDD 2005