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Electroencephalogram (EEG) is a pivotal diagnostic tool for epilepsy. EEG signals have complex sources, significant individual differences, and data distribution varies across different domains are also easily influenced by noise. This study develops a low-rank sparse representation-based transition subspace learning (LRSRTS) algorithm. Based on low-rank reconstruction transfer subspace learning, the LRSRTS algorithm uses subspace projection and low-rank constraints to ensure that multiple domains are aligned in the subspace and uses sparse constraints to ensure reconstruction from the source domain to the target domain. Separating the noise information in the subspace, the LRSRTS algorithm uses the source domain samples to establish a discriminative classifier. Since the label information is non-negative, the LRSRTS imposes non-negative constraints on the transition subspace. With the more flexible subspace and classifier, the LRSRTS algorithm demonstrates satisfactory recognition performance on the CHB-MIT dataset.

Matrix completion is critical in a wide range of scientific and engineering applications, such as image restoration and recommendation systems. This topic is commonly expressed as a low-rank matrix optimization framework. In this paper, a universal and effective rank approximation method for matrix completion (RAMC) is provided. Fundamental to this strategy is developing a general function that meets specific conditions in order to directly approach the rank function and subsequently utilizing it to build a RAMC model. The major goal is to investigate a more accurate estimate of the rank function, allowing for more effective acquisition of the low-rank structure of incomplete data. Further, the RAMC model is easily implemented by a viable iterative method that may be successfully used to matrix completion tasks. Extensive experiments using the synthetic data and natural images reveal the excellent applicability of RAMC over the existing methods.

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on truncation of the frequency range solution and is incorporated into two well-known iterative solvers - BiCGstab and GMRes. The proposed method is applied to two acoustic interior problems as well as to an exterior problem in order to assess the underlying approximations and to study the convergence behavior. While this paper provides the proof of concept, its application to large-scale acoustic problems necessitates efficient preconditioning for multi-frequency systems, which are yet to be developed.