Abstract
The locally linear embedding (LLE) is one of the most promising algorithm among nonlinear dimensionality reduction technique. When the number of the nearest neighbor k is larger than the input dimension D, LLE will make the local covariance matrix Ci singular in the process of calculating local reconstruction weights vectors Wi. In this case, regularization is needed, but at the same time, which leads Wi can not reflect optimally intrinsic structure of neighbours. To solve the problem, we propose NWLLE (New Weighted LLE) to improve LLE algorithm and test the new algorithm from embedded performance and quantitative error. The numerical experiment results show that the NWLLE yields less error than LLE and can produce a good embedding effect.
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