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.