Domain adaptation has found widespread applications in real-life scenarios, especially when the target domain has limited labeled samples. However, most of the domain adaptation models only utilize one type of knowledge from the source domain, which is usually achieved by strong mode of convergence. To fully incorporate multiple knowledge from the source domain, for binary classification, this paper studies a novel learning paradigm for Domain Adaptation via Learning Using Statistical Invariant by simultaneously combining the strong and weak modes of convergence in a Hilbert space. The strong mode of convergence undertakes the mission of learning a least squares probability output binary classification task in a general hypothesis space, while the weak mode of convergence integrates diverse knowledge by constructing meaningful statistical invariants that embody the concept of intelligence. The utilization of weak convergence shrinks the admissible set of approximation functions, and subsequently accelerates the learning process. In this paper, several statistical invariants that represent sample, feature and parameter information from the source domain are constructed. By taking an appropriate statistical invariant, DLUSI realizes some existing methods. Experimental results on synthetic data as well as the widely used Amazon Reviews and 20 News data demonstrate the superiority of the proposed method.

Two-dimensional linear discriminant analysis (2DLDA) is a widely applied extension of LDA that can cope with matrix input samples directly. However, its construction is based on a squared F $F$ -norm which will lead to sensitivity to noise and outliers. In this paper, a square-free F $F$ -norm 2DLDA is proposed to improve the robustness of 2DLDA. By losing the squared operation, the proposed method weakens the influence of outliers and noise and at the same time keeps the geometric structure of data. It can be solved through an effective nongreedy iterative algorithm, with each subproblem having a closed-form solution. The algorithm is further proved to be convergent. Experiments on several human face image databases demonstrate the effectiveness and robustness of the proposed method.

When solving many regression problems, there exist a large number of input features. However, not all features are relevant for current regression, and sometimes, including irrelevant features may deteriorate the learning performance. Therefore, it is essential to select the most relevant features, especially for high-dimensional regression. Feature selection is an effective way to solve this problem. It tries to represent original data by extracting relevant features that contain useful information. In this paper, aiming to effectively select useful features in least squares support vector regression (LSSVR), we propose a novel sparse LSSVR based on L p -norm (SLSSVR), 0 < p ≤ 1 . Different from the existing L 1 -norm LSSVR ( L 1 -LSSVR) and L p -norm LSSVR ( L p -LSSVR), SLSSVR uses a smooth approximation of the nonsmooth nonconvex L p -norm term along with an effective solving algorithm. The proposed algorithm avoids the singularity issue that may encounter in L p -LSSVR, and its convergency is also guaranteed. Experimental results support the effectiveness of SLSSVR on both feature selection ability and regression performance.