Hyper-Laplacian regularized multi-view subspace clustering with jointing representation learning and weighted tensor nuclear norm constraint

In recent years, tensor-Singular Value Decomposition (t-SVD) based tensor nuclear norm has achieved remarkable progress in multi-view subspace clustering. However, most existing clustering methods still have the following shortcomings: (a) It has no meaning in practical applications for singular values to be treated equally. (b) They often ignore that data samples in the real world usually exist in multiple nonlinear subspaces. In order to solve the above shortcomings, we propose a hyper-Laplacian regularized multi-view subspace clustering model that joints representation learning and weighted tensor nuclear norm constraint, namely JWHMSC. Specifically, in the JWHMSC model, firstly, in order to capture the global structure between different views, the subspace representation matrices of all views are stacked into a low-rank constrained tensor. Secondly, hyper-Laplace graph regularization is adopted to preserve the local geometric structure embedded in the high-dimensional ambient space. Thirdly, considering the prior information of singular values, the weighted tensor nuclear norm (WTNN) based on t-SVD is introduced to treat singular values differently, which makes the JWHMSC more accurately obtain the sample distribution of classification information. Finally, representation learning, WTNN constraint and hyper-Laplacian graph regularization constraint are integrated into a framework to obtain the overall optimal solution of the algorithm. Compared with the state-of-the-art method, the experimental results on eight benchmark datasets show the good performance of the proposed method JWHMSC in multi-view clustering.

Sparsity Enhanced Beamforming in The Presence of Coherent Signals

In order to find the directions of coherent signals, a sparsity enhanced beam-forming method is proposed. Unlike the conventional minimum variance distortless response (MVDR) method, the minimum variance in the proposed method corresponds to the orthogonal relationship between the noise subspace and the sparse representation of the received signal vector, whereas the distortless response corresponds to the nonorthogonal relationship between the signal subspace and the sparse representation of the received signal vector. The proposed sparsity enhanced MVDR (SEMVDR) method is carried out by the iterative reweighted Lp-norm constraint minimization. for direction finding of coherent signals. Simulation results are shown that SEMVDR has better performance than the existing algorithms, such as MVDR and MUSIC, when coherent signals are present.

Hyperspectral Remote Sensing Image Feature Representation Method Based on CAE-H with Nuclear Norm Constraint

Due to the high dimensionality and high data redundancy of hyperspectral remote sensing images, it is difficult to maintain the nonlinear structural relationship in the dimensionality reduction representation of hyperspectral data. In this paper, a feature representation method based on high order contractive auto-encoder with nuclear norm constraint (CAE-HNC) is proposed. By introducing Jacobian matrix in the CAE of the nuclear norm constraint, the nuclear norm has better sparsity than the Frobenius norm and can better describe the local low dimension of the data manifold. At the same time, a second-order penalty term is added, which is the Frobenius norm of the Hessian matrix expressed in the hidden layer of the input, encouraging a smoother low-dimensional manifold geometry of the data. The experiment of hyperspectral remote sensing image shows that CAE-HNC proposed in this paper is a compact and robust feature representation method, which provides effective help for the ground object classification and target recognition of hyperspectral remote sensing image.

One-Class Classification Using lp-Norm Multiple Kernel Fisher Null-Space

The paper addresses the one-class classification (OCC) problem and advocates a one-class multiple kernel learning (MKL) approach for this purpose. To this aim, based on the Fisher null-space one-class classification principle, we present a multiple kernel learning algorithm where an $\ell_p$-norm constraint ($p\geq1$) on kernel weights is considered. We cast the proposed one-class MKL task as a min-max saddle point Lagrangian optimisation problem and propose an efficient method to solve it. An extension of the proposed one-class MKL approach is also considered where several related one-class MKL tasks are learned concurrently by constraining them to share common kernel weights. <br>An extensive assessment of the proposed method on a range of data sets from different application domains confirms its merits against the baseline and several other algorithms.<br>

One-Class Classification Using lp-Norm Multiple Kernel Fisher Null-Space

The paper addresses the one-class classification (OCC) problem and advocates a one-class multiple kernel learning (MKL) approach for this purpose. To this aim, based on the Fisher null-space one-class classification principle, we present a multiple kernel learning algorithm where an $\ell_p$-norm constraint ($p\geq1$) on kernel weights is considered. We cast the proposed one-class MKL task as a min-max saddle point Lagrangian optimisation problem and propose an efficient method to solve it. An extension of the proposed one-class MKL approach is also considered where several related one-class MKL tasks are learned concurrently by constraining them to share common kernel weights. <br>An extensive assessment of the proposed method on a range of data sets from different application domains confirms its merits against the baseline and several other algorithms.<br>

Criterion for the H∞ Suppression of Overflow Oscillations in Fixed Point Digital Filters Employing Saturation Nonlinearities and External Interference

This paper proposes a novel criterion for suppressing the [Formula: see text] overflow oscillations in fixed point state-space digital filters employing saturation nonlinearities and external interference. The proposed criterion can be used to ensure the exponential stability (ES) and diminish the external interference effects to an [Formula: see text] norm constraint. An example is given to exemplify the utility of the obtained results.