Globally-Preserving Based Locally Linear Embedding

The locally linear embedding (LLE) algorithm is considered as a powerful method for the problem of nonlinear dimensionality reduction. In this paper, a new method called globally-preserving based LLE (GPLLE) is proposed. It not only preserves the local neighborhood, but also keeps those distant samples still far away, which solves the problem that LLE may encounter, i.e. LLE only makes local neighborhood preserving, but can´t prevent the distant samples from nearing. Moreover, GPLLE can estimate the intrinsic dimensionality d of the manifold structure. The experiment results show that GPLLE always achieves better classification performances than LLE based on the estimated d.