Globalizing Local Neighborhood for Locally Linear Embedding

Hessian locally linear embedding (HLLE) has good representational capacity and high computational efficiency, but it still fails to nicely deal with the sparsely sampled or noise contaminated datasets, where the local neighborhood structure is critically distorted. To solve this problem, this paper proposes a new approach that takes the general conceptual framework of HLLE so as to guarantee its correctness in the setting of local isometry, and then employs the geodesic distance instead of Euclidean distance to determine the local neighborhood so as to give the global representation to the local data. This approach can be regarded as the integration of both local approaches and global approaches, so that it have the better performance and stability. The conducted experiments on both synthetic and real datasets have validated the proposed approach.