@misc{GaoZhangPanetal., author = {Gao, Yunlong and Zhang, Yisong and Pan, Jinyan and Luo, Sizhe and Yang, Chengyu}, title = {Discriminant analysis based on reliability of local neighborhood}, series = {Expert Systems with Applications}, volume = {175}, journal = {Expert Systems with Applications}, issn = {1873-6793}, doi = {10.1016/j.eswa.2021.114790}, abstract = {To obtain a compact and effective low-dimensional representation, recently, most existing discriminant manifold learning methods have integrated manifold learning into discriminant analysis (DA) for extracting the intrinsic structure of data. These methods learn two kinds of adjacency graphs, such as intrinsic graph and penalty graph, to characterize the similarity between samples from intraclass and the pseudo similarity of interclass. However, they treat every sample equally, which results in the following defects: (1) These methods cannot accurately characterize the marginal region among different classes only through penalty graphs. (2) They can not identify the noisy and outlier samples which reduce the robustness of these methods. To address these problems, we introduce an adaptive adjacency factor to perform the discriminative based reliability analysis for each sample. By integrating the adjacency factor into discriminant manifold learning methods, we propose a novel method for DA namely discriminant analysis based on reliability of local neighborhood (DA-RoLN). We mainly have three contributions in this paper: (1) By the introduction of adjacency factor, sample points can be divided into three parts: intraclass samples, marginal samples, and outliers. Therefore, DA-RoLN emphasizes the effect of valid samples and filters the influence of outliers. (2) We adaptively calculate the adjacency factor in low-dimensional space, thus, the margin between different classes in low-dimensional space is emphasized. (3) An iterative algorithm is developed to solve the objective function of DA-RoLN, and it is easy to solve with a low computational cost. Extensive experimental results show the effectiveness of DA-RoLN.}, language = {en} } @misc{GaoLuoPanetal., author = {Gao, Yunlong and Luo, Si-Zhe and Pan, Jin-Yan and Chen, Bai-Hua and Zhang, Yi-Song}, title = {Robust PCA Using Adaptive Probability Weighting}, series = {Acta Automatica Sinica}, volume = {47}, journal = {Acta Automatica Sinica}, number = {4}, issn = {0254-4156}, doi = {10.16383/j.aas.c180743}, pages = {825 -- 838}, abstract = {Principal component analysis (PCA) is an important method for processing high-dimensional data. In recent years, PCA models based on various norms have been extensively studied to improve the robustness. However, on the one hand, these algorithms do not consider the relationship between reconstruction error and covariance; on the other hand, they lack the uncertainty of considering the principal component to the data description. Aiming at these problems, this paper proposes a new robust PCA algorithm. Firstly, the L2,p-norm is used to measure the reconstruction error and the description variance of the projection data. Based on the reconstruction error and the description variance, the adaptive probability error minimization model is established to calculate the uncertainty of the principal component's description of the data. Based on the uncertainty, the adaptive probability weighting PCA is established. The corresponding optimization method is designed. The experimental results of artificial data sets, UCI data sets and face databases show that RPCA-PW is superior than other PCA algorithms.}, language = {en} } @misc{GaoLinZhangetal., author = {Gao, Yunlong and Lin, Tingting and Zhang, Yisong and Luo, Sizhe and Nie, Feiping}, title = {Robust principal component analysis based on discriminant information}, series = {IEEE Transactions on Knowledge and Data Engineering}, volume = {35}, journal = {IEEE Transactions on Knowledge and Data Engineering}, number = {2}, publisher = {IEEE}, issn = {1558-2191}, doi = {10.1109/TKDE.2021.3093447}, pages = {1991 -- 2003}, abstract = {Recently, several robust principal component analysis (RPCA) models were presented to enhance the robustness of PCA by exploiting the robust norms as their loss functions. But an important problem is that they have no ability to discriminate outliers from correct samples. To solve this problem, we propose a robust principal component analysis based on discriminant information (RPCA-DI). RPCA-DI disentangles the robust PCA with a two-step fashion: the identification and the processing of outliers. To identity outliers, a sample representation model based on entropy regularization is constructed to analyze the membership of data belonging to the principal component space(PC) and its orthogonal complement(OC), the discriminative information of data will be extracted based on measuring the differences of retained information on PC(or OC) of data. By this way, we can discriminate correct samples when we deal with outliers, which is more reasonable for robustness learning respective to previous works. In the noise processing step, in addition to considering the levels of noise, the resistance of the sample points to noise is also considered to prevent overfitting, thereby improving the generalization performance of RPCA-DI. Finally, an iterative algorithm is designed to solve the corresponding model. Compared with some state-of-art RPCA methods on artificial datasets, UCI datasets and face databases that verifies the effectiveness of our proposed algorithm.}, language = {en} }