Active Neighborhood Selection for Locally Linear Embedding

In this paper, we propose metric locally linear embedding (LLE) to handling the problem of multiple manifolds through learning neighborhood. LLE succeeds in extracting the low-dimensional representation of data in a single manifold, but fails in the case of multiple manifolds. This paper makes use of the strategy of active neighborhood selection to extend LLE. The strategy requires partial information of similarity among data to find an appropriate Mahalanobis distance to replace Euclidean distance. The use of new distance metric aims to diminish the distance of data points within the same manifold and enlarge the distance between different manifolds, while preserving the intrinsic structure of each manifold as faithfully as possible. Experimental results demonstrate that metric LLE usually performs better than LLE in feature extraction.