School of Computer Science and School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi'an 710072, Shaanxi, PR China.
Neural Netw. 2022 Aug;152:347-352. doi: 10.1016/j.neunet.2022.05.005. Epub 2022 May 16.
The kernel principal component analysis (KPCA) serves as an efficient approach for dimensionality reduction. However, the KPCA method is sensitive to the outliers since the large square errors tend to dominate the loss of KPCA. To strengthen the robustness of KPCA method, we propose a novel robust kernel principal component analysis with optimal mean (RKPCA-OM) method. RKPCA-OM not only possesses stronger robustness for outliers than the conventional KPCA method, but also can eliminate the optimal mean automatically. What is more, the theoretical proof proves the convergence of the algorithm to guarantee that the optimal subspaces and means are obtained. Lastly, exhaustive experimental results verify the superiority of our method.
核主成分分析（KPCA）是一种有效的降维方法。然而，由于大的平方误差往往会主导 KPCA 的损失，因此 KPCA 方法对外点很敏感。为了增强 KPCA 方法的鲁棒性，我们提出了一种新的具有最优均值的鲁棒核主成分分析（RKPCA-OM）方法。RKPCA-OM 不仅比传统的 KPCA 方法对外点具有更强的鲁棒性，而且可以自动消除最优均值。更重要的是，理论证明证明了算法的收敛性，以保证最优子空间和均值的获得。最后，详尽的实验结果验证了我们方法的优越性。
