Unsupervised domain adaptation aims to classify unlabeled data points in the target domain using labeled data points from the source domain, while the distributions of data points in two domains are different. To address this issue, we propose a novel method called the anchor guided unsupervised domain adaptation method (AGDA). We minimize distribution divergence in a latent feature subspace using the Maximum Mean Discrepancy (MMD) criterion. Unlike existing unsupervised domain adaptation methods, we introduce anchor points in the original space and impose domains data to the same anchor points rather than center points to further reduce the domain difference. We optimize the anchor-based graph in the subspace to obtain discriminative transformation matrices. This enables our model to perform better on non-Gaussian distribution than methods focusing on global structure. Furthermore, the sparse anchor-based graph reduces time complexity compared to the fully connected graph, enabling exploration of local structure. Experimental results demonstrate that our algorithm outperforms several state-of-the-art methods on various benchmark datasets.

Feature selection has achieved unprecedented success in obtaining sparse discriminative features. However, the existing methods almost use the$\ell _{2,p}$-norm constraint on transformation matrix to obtain sparse features, which introduces extra parameters and cannot obtain the features directly. In addition, existing algorithms only focused on the global structure and ignored the local structure, leading to poor performance when solving data with non-Gaussian distributions which a single center point cannot describe precisely. Based on above considerations, we propose a supervised feature selection via multi-center and local structure learning. We further introduce trace ratio criterion into our model in favor of improving the discriminant of features selected. In order to address the overlap problem, we use multiple center points to match the distribution of data and construct a$k$-Nearest Neighbor graph to explore the local structure of the data. In addition, we also propose an efficient method to optimize the transformation matrix with the$\ell _{2,0}$-norm constraint and can directly obtain the sparse features. We evaluate our method on Toy datasets and several real-world datasets, show improvement over state-of-the-art feature selection methods, and demonstrate the effectiveness of our model in dealing with non-Gaussian distributed data problems.

In recent decades, unsupervised feature selection methods have become increasingly popular. Nevertheless, most of the existing unsupervised feature selection methods suffer from two major problems that lead to suboptimal solutions. Many methods impose a hard linear projection constraint on original data, which is overly strict in nature and not suitable for dealing with data sampled from nonlinear manifolds. Second, most existing methods usel2,p-norm (02S and SF2SOG, which can simultaneously learn optimal flexible projections and obtain an orthogonal sparse projection to directly select discriminative features by applyingl2,0-norm constraint. Moreover, we propose to explore the local structure of flexible embedding through preserving the manifold structure of original data and adaptively constructing an optimal graph in subspace. Thirdly, the novel iterative optimization algorithms are presented to solve objective functions guaranteeing convergence theoretically. Various evaluation experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of our proposed methods.