Dimensionality reduction by LPP‐L21

Locality preserving projection (LPP) is one of the most representative linear manifold learning methods and well exploits intrinsic structure of data. However, the performance of LPP remarkably degenerate in the presence of outliers. To alleviate this problem, the authors propose a robust LPP, namely LPP‐L21. LPP‐L21 employs L2‐norm as the distance metric in spatial dimension of data and L1‐norm as the distance metric over different data points. Moreover, the authors employ L1‐norm to construct similarity graph, this helps to improve robustness of algorithm. Accordingly, the authors present an efficient iterative algorithm to solve LPP‐L21. The authors’ proposed method not only well suppresses outliers but also retains LPP's some nice properties. Experimental results on several image data sets show its advantages.