We present a planar waveguide model and a mechanism based on standing wave resonances to interpret the unity absorptions of ultrathin planar metamaterial absorbers. The analytical model predicts that the available absorption peaks of the absorber are corresponding to the fundamental mode and only its odd harmonic modes of the standing wave. The model is in good agreement with numerical simulation and can explain the main features observed in typical ultrathin planar metamaterial absorbers. Based on this model, ultrathin planar metamaterial absorbers with multi-band absorptions at desired frequencies can be easily designed.

Anomaly detection (AD) aims to distinguish the data points that are inconsistent with the overall pattern of the data. Recently, unsupervised anomaly detection methods have aroused huge attention. Among these methods, feature representation (FR) plays an important role, which can directly affect the performance of anomaly detection. Sparse representation (SR) can be regarded as one of matrix factorization (MF) methods, which is a powerful tool for FR. However, there are some limitations in the original SR. On the one hand, it just learns the shallow feature representations, which leads to the poor performance for anomaly detection. On the other hand, the local geometry structure information of data is ignored. To address these shortcomings, a graph regularized deep sparse representation (GRDSR) approach is proposed for unsupervised anomaly detection in this work. In GRDSR, a deep representation framework is first designed by extending the single layer MF to a multilayer MF for extracting hierarchical structure from the original data. Next, a graph regularization term is introduced to capture the intrinsic local geometric structure information of the original data during the process of FR, making the deep features preserve the neighborhood relationship well. Then, a L1-norm-based sparsity constraint is added to enhance the discriminant ability of the deep features. Finally, a reconstruction error is applied to distinguish anomalies. In order to demonstrate the effectiveness of the proposed approach, we conduct extensive experiments on ten datasets. Compared with the state-of-the-art methods, the proposed approach can achieve the best performance.

No abstract

In this paper, we present a novel unsupervised feature selection method termed robust matrix factorization with robust adaptive structure learning (RMFRASL), which can select discriminative features from a large amount of multimedia data to improve the performance of classification and clustering tasks. RMFRASL integrates three models (robust matrix factorization, adaptive structure learning, and structure regularization) into a unified framework. More specifically, a robust matrix factorization-based feature selection (RMFFS) model is proposed by introducing an indicator matrix to measure the importance of features, and the L21-norm is adopted as a metric to enhance the robustness of feature selection. Furthermore, a robust adaptive structure learning (RASL) model based on the self-representation capability of the samples is designed to discover the geometric structure relationships of original data. Lastly, a structure regularization (SR) term is designed on the learned graph structure, which constrains the selected features to preserve the structure information in the selected feature space. To solve the objective function of our proposed RMFRASL, an iterative optimization algorithm is proposed. By comparing our method with some state-of-the-art unsupervised feature selection approaches on several publicly available databases, the advantage of the proposed RMFRASL is demonstrated.

As one of the most effective feature learning methods, Nonnegative Matrix Factorization (NMF) has been widely used in many scientific fields, such as computer vision, data mining, and bioinformatics. However, NMF is an unsupervised method that cannot fully utilize the label information of data. Thus, its performance is limited in some recognition and classification problems. To remedy this shortcoming, this paper proposes a Semisupervised Discriminative NMF (SDNMF) method. First, we design a Soft‐Labeled NMF (SLNMF) model by introducing a soft‐label matrix‐based regression term into the original NMF, so that the relationship between the soft‐label matrix and low‐dimensional features can be constructed to improve the discriminative ability of low‐dimensional features. Second, to effectively estimate the soft‐label matrix, a Label Propagation (LP) model is adopted to fully explore the spatial distribution relationship between the labeled and unlabeled samples. Third, an Adaptive Graph Learning (AGL) model is proposed to exploit the geometric relationship of samples well, which could enhance the performance of LP. Finally, the above three models (i.e., SLNMF, LP, and AGL) are integrated into a unified framework for effective feature learning, which can not only effectively explore the structural relationship matrix between data, but also predict the labels for unknown samples. Moreover, an iterative optimization algorithm is presented to solve our objective function. The convergence and computational complexity analysis of the proposed SDNMF method are also provided. Extensive experiments are conducted on several standard data sets. Compared with related methods, the experimental results verify that the proposed SDNMF method achieves better performance.