Matrix analysis
Robust locally linear embedding
Pattern Recognition
Efficient locally linear embeddings of imperfect manifolds
MLDM'03 Proceedings of the 3rd international conference on Machine learning and data mining in pattern recognition
Local smoothing for manifold learning
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
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The locally linear embedding (LLE) is an effective algorithm for dimensional reduction, visualization and classification, which can automatically discover the low-dimensional nonlinear manifold in a high-dimensional data space and then embed the data points into a low-dimensional embedding space, using tractable linear algebraic techniques that are easy to implement. Despite its appealing properties, LLE is not robust against outliers in the data, yet so far very little has been done to address the robustness problem. To improve the performance of LLE, some modified LLE algorithms were proposed by rigidly restraining the influence of the noise and outliers in the data embedding. In this paper, a weighted LLE (WLLE) is proposed. The experiments on synthetic data and real plant leaf image data demonstrate that WLLE is effective and feasible.