Robust and Stable Locally Linear Embedding

Recently, some manifold learning methods have aroused a great of interest in many fields of information processing. However, these manifold learning methods are not robust against outliers. In this paper, an outlier detection algorithm is proposed, and we propose a robust and stable locally liner embedding(RSLLE) algorithm by introducing multiple linearly independent local weight vectors to represent the local geometry for each neighborhoods of clean data points. For the outlier points, RSLLE learns the local geometry by using a single weight vector. Numerical examples are given to show the improvement and efficiency of the proposed algorithm.