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.

中文翻译：

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使用基于角度的自适应权重方法进行鲁棒的局部保持投影

局部保留投影（LPP）方法是用于降维的经典流形学习方法。但是，LPP对离群值敏感，因为平方L2-范数可能会夸大离群值的距离。此外，LPP的归一化约束可能会削弱其在嵌入过程中的鲁棒性。基于这一观察结果，作者提出了一种使用基于角度的自适应权重（RLPP-AAW）方法的新型鲁棒LPP。RLPP-AAW不仅考虑训练样本的距离度量，而且考虑了重构误差，以减少离群值和噪声在嵌入过程中的影响。在RLPP-AAW中，基于距离度量与重构误差之间的夹角，采用一种新颖的方法将它们组合到目标函数中。此外，RLPP-AAW采用L21规范标准，保留旋转不变性，并且比平方L2-范数更健壮。提出了一种求解RLPP-AAW目标函数的迭代算法。在基准数据库上的实验结果说明了该算法的有效性。