L1-norm locally linear embedding
L1范局部线性嵌入

The problem of dimensionality reduction arises in many fields of information processing, including machine learning, pattern recognition, data mining etc. Locally linear embedding (LLE) is an unsupervised and nonlinear learning algorithm for dimensionality reduction, well-known for its outperformance. Unlike classical LLE, which is based on the L2-norm, a novel L1-norm based LLE (L1-LLE) algorithm is proposed in this article, which is robust to outliers because it utilizes the L1-norm, which is less sensitive to outliers. The proposed L1-norm optimization technique is intuitive, simple, and easy to implement. It is also proven to find a globally minimal solution. The proposed method is applied to several data sets and the performance is compared to those of other conventional methods.