Robust locality preserving projections using angle‐based adaptive weight method

Abstract

Locality preserving projections (LPP) method is a classical manifold learning method for dimensionality reduction. However, LPP is sensitive to outliers since squared L2‐norm may exaggerate the distance of outliers. Besides, the normalisation constraint of LPP may impair its robustness during embedding. Motivated by this observation, the authors propose a novel robust LPP using angle‐based adaptive weight (RLPP‐AAW) method. RLPP‐AAW not only considers the distance metric of training samples, but also take the reconstruction error into account, so as to reduce the influence of outliers and noise in the embedding process. In the RLPP‐AAW, based on the angle between distance metric and reconstruction error, a novel way is used to combine them in the objective function. Besides, RLPP‐AAW employs the L21‐norm criterion, which retains rotational invariance and is more robust than squared L2‐norm. An iterative algorithm is presented to solve the objective function of RLPP‐AAW. Experimental results on the benchmark databases illustrate the effectiveness of the proposed algorithm.

Adaptive Metric Learning for Dimensionality Reduction

“…To deal with this problem, Zhao et al [37] use 2,1 l -norm to develop a new LDA formulation for improving robustness. Also, some other linear dimensionality reduction approaches using local information of data have been proposed, such as locality preserving projections [38] and local linear embedding [39] [40]. These methods achieve significant discriminant performance to deal with linear problems.…”