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2006 NeurIPS NeurIPS 2006

MLLE: Modified Locally Linear Embedding Using Multiple Weights

Abstract

The locally linear embedding (LLE) is improved by introducing multiple linearly independent local weight vectors for each neighborhood. We characterize the reconstruction weights and show the existence of the linearly independent weight vectors at each neighborhood. The modified locally linear embedding (MLLE) proposed in this paper is much stable. It can retrieve the ideal embedding if MLLE is applied on data points sampled from an isometric manifold. MLLE is also compared with the local tangent space alignment (LTSA). Numerical examples are given that show the improvement and efficiency of MLLE.

🚀 Conference Pioneer - NeurIPS 2006
📈 Trend Setter - Embedding Learning
🐣 Hot Topic Early Bird - manifold learning

Authors

Zhenyue Zhang, Jing Wang

Topics

Machine Learning > Core Methods > Representation Learning Machine Learning > Core Methods > Embedding Learning Machine Learning > Core Methods > Dimensionality Reduction Machine Learning > Core Methods > Feature Learning Machine Learning > Core Methods > Feature Extraction

Keywords

dimensionality reduction manifold learning feature extraction locally linear embedding nonlinear embedding isometric embedding isometric manifold reconstruction weight
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