The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique that is widely used for its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in a low-dimensional embedding. We show that the reconstruction weights computed by LLE capture the high-dimensional structure of the neighborhoods, and not the low-dimensional manifold structure. Consequently, the weight vectors are highly sensitive to noise. Moreover, this causes LLE to converge to a linear projection of the input, as opposed to its non-linear embedding goal. To resolve both of these problems, we propose to compute the weight vectors using a low-dimensional neighborhood representation. We call this technique LDR-LLE. We present numerical examples of the perturbation and linear projection problems, and of the improved outputs resulting from the low-dimensional neighborhood representation. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Goldberg, Y., & Ritov, Y. (2008). LDR-LLE: LLE with low-dimensional neighborhood representation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5359 LNCS, pp. 43–54). https://doi.org/10.1007/978-3-540-89646-3_5
Mendeley helps you to discover research relevant for your work.