Search Results (107)

In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient use of unlabeled data, low pseudo-label accuracy, and inefficient label propagation. To address these issues, this paper proposes dual label propagation-driven least squares regression with feature selection, named DLPLSR, which is a pseudo-label-free SSL framework. DLPLSR employs a fuzzy-graph-based clustering strategy to capture global relationships among all samples, and manifold regularization preserves local geometric consistency, so that it implements the dual label propagation mechanism for comprehensive utilization of unlabeled data. Meanwhile, a dual-feature selection mechanism is established by integrating orthogonal projection for maximizing feature information with an ℓ_2,1-norm regularization for eliminating redundancy, thereby jointly enhancing the discriminative power. Benefiting from these two designs, DLPLSR boosts learning performance without pseudo-labeling. Finally, the objective function admits an efficient closed-form solution solvable via an alternating optimization strategy. Extensive experiments on multiple benchmark datasets show the superiority of DLPLSR compared to state-of-the-art LSR-based SSL methods. Full article

This study addresses the problem of simultaneous variable selection and model estimation in multivariate failure time data, a common challenge in clinical trials with multiple correlated time-to-event endpoints. We propose a unified framework that identifies predictors shared across outcomes, applicable to both low- and high-dimensional settings. For linear marginal hazard models, we develop a penalized pseudo-partial likelihood approach with a group LASSO-type penalty applied to the ${\mathsf{\ell }}_2$ norms of coefficients corresponding to the same covariates across marginal hazard functions. To capture potential nonlinear effects, we further extend the approach to a sparse-input neural network model with structured group penalties on input-layer weights. Both methods are optimized using a composite gradient descent algorithm combining standard gradient steps with proximal updates. Simulation studies demonstrate that the proposed methods yield superior variable selection and predictive performance compared to traditional and outcome-specific approaches, while remaining robust to violations of the common predictor assumption. In an application to advanced prostate cancer data, the framework identifies both established clinical factors and potentially novel prognostic single-nucleotide polymorphisms for overall and progression-free survival. This work provides a flexible and robust tool for analyzing complex multivariate survival data, with potential utility in prognostic modeling and personalized medicine. Full article

This paper concerns a class of robust factorization models of low-rank matrix recovery, which have been widely applied in various fields such as machine learning and imaging sciences. An ${\ell }_1$-loss robust factorized model incorporating the ${\ell }_{2,0}$-norm regularization term is proposed to address the presence of outliers. Since the resulting problem is nonconvex, nonsmooth, and discontinuous, an approximation problem that shares the same set of stationary points as the original formulation is constructed. Subsequently, a proximal alternating minimization method is proposed to solve the approximation problem. The global convergence of its iterate sequence is also established. Numerical experiments on matrix completion with outliers and image restoration tasks demonstrate that the proposed algorithm achieves low relative errors in shorter computational time, especially for large-scale datasets. Full article

Data acquisition and high-dimensional signal processing often require the recovery of sparse representations of signals to minimize the resources needed for data collection. ${\ell }_p$ quasi-norm minimization excels in exactly reconstructing sparse signals from fewer measurements, but it is NP-hard and challenging to solve. In this paper, we propose two distinct Iteratively Re-weighted ${\ell }_1$ Minimization (IR${\ell }_1$) formulations for solving this non-convex sparse recovery problem by introducing two novel reweighting strategies. These strategies ensure that the $ϵ$-regularizations adjust dynamically based on the magnitudes of the solution components, leading to more effective approximations of the non-convex sparsity penalty. The resulting IR${\ell }_1$ formulations provide first-order approximations of tighter surrogates for the original ${\ell }_p$ quasi-norm objective. We prove that both algorithms converge to the true sparse solution under appropriate conditions on the sensing matrix. Our numerical experiments demonstrate that the proposed IR${\ell }_1$ algorithms outperform the conventional approach in enhancing recovery success rate and computational efficiency, especially in cases with small values of p. Full article

This article explores two distinct function spaces: Hilbert spaces and mixed-Orlicz–Zygmund spaces with variable exponents. We first examine the relational properties of Hilbert spaces in a tensorial framework, utilizing self-adjoint operators to derive key results. Additionally, we extend a Maclaurin-type inequality to the tensorial setting using generalized convex mappings and establish various upper bounds. A non-trivial example involving exponential functions is also presented. Next, we introduce a new function space, the mixed-Orlicz–Zygmund space $\left({\ell }_{\mathtt{q}(·)}{log}^{\beta }\left({\mathtt{L}}^{\mathtt{p}(·)}\right)\right)$, which unifies Orlicz–Zygmund spaces of integrability and sequence spaces. We investigate its fundamental properties including separability, compactness, and completeness, demonstrating its significance. This space generalizes the existing structures, reducing to mixed-norm Lebesgue spaces when $\beta =0$ and to classical Lebesgue spaces when $\mathtt{q}=\infty ,\beta =0$. Given the limited research on such spaces, our findings contribute valuable insights to the functional analysis. Full article

Hyperspectral band selection plays a key role in reducing the high dimensionality of data while maintaining essential details. However, existing band selection methods often encounter challenges, such as high memory consumption, the need for data matricization that disrupts inherent data structures, and difficulties in preserving crucial spatial–spectral relationships. To address these challenges, we propose a tensor-based band selection model using Generalized 3D Total Variation (G3DTV), which utilizes the ${\ell }_1^p$ norm to promote smoothness across spatial and spectral dimensions. Based on the Alternating Direction Method of Multipliers (ADMM), we develop an efficient hyperspectral band selection algorithm, where the tensor low-rank structure is captured through tensor CUR decomposition, thus significantly improving computational efficiency. Numerical experiments on benchmark datasets have demonstrated that our method outperforms other state-of-the-art approaches. In addition, we provide practical guidelines for parameter tuning in both noise-free and noisy data scenarios. We also discuss computational complexity trade-offs, explore parameter selection using grid search and Bayesian Optimization, and extend our analysis to evaluate performance with additional classifiers. These results further validate the proposed robustness and accuracy of the model. Full article

A novel method for the direction of arrival (DOA) estimation of coherent signals under a space–time–coding metasurface (STCM) is proposed in this paper. Noticeably, the STCM can replace multi-channel arrays with a single channel, which can be utilized to modulate incident electromagnetic waves and generate harmonics. However, coherent signals are overlapping in the frequency spectrum and cannot achieve DOA estimation through subspace methods. Therefore, the proposed method transforms the angle information in the time domain into amplitude and phase information at harmonics in the frequency domain by modulating incident coherent signals using the STCM and performing a fast Fourier transform (FFT) on these signals. Based on the harmonics in the frequency spectrum of the coherent signals, appropriate harmonics are selected. Finally, the ℓ₁ norm singular value decomposition (ℓ₁-SVD) algorithm is utilized for achieving high-precision DOA estimation. Simulation experiments are conducted to show the performance of the proposed method under the condition of different incident angles, harmonic numbers, signal-to-noise ratios (SNRs), etc. Compared to the traditional algorithms, the performance of the proposed algorithm can achieve more accurate DOA estimation under a low SNR. Full article

This paper introduces a novel capped separable difference of two norms (CSDTN) method for sparse signal recovery, which generalizes the well-known minimax concave penalty (MCP) method. The CSDTN method incorporates two shape parameters and one scale parameter, with their appropriate selection being crucial for ensuring robustness and achieving superior reconstruction performance. We provide a detailed theoretical analysis of the method and propose an efficient iteratively reweighted ${\ell }_1$ (IRL1)-based algorithm for solving the corresponding optimization problem. Extensive numerical experiments, including electrocardiogram (ECG) and synthetic signal recovery tasks, demonstrate the effectiveness of the proposed CSDTN method. Our method outperforms existing methods in terms of recovery accuracy and robustness. These results highlight the potential of CSDTN in various signal-processing applications. Full article

Compressed Sensing SAR Imaging is based on an accurate observation matrix. As the observed scene enlarges, the resource consumption of the method increases exponentially. In this paper, we propose a weighted ℓ_2/3-norm regularization SAR imaging method based on approximate observation. Initially, to address the issues brought by the precise observation model, we employ an approximate observation operator based on the Chirp Scaling Algorithm as a substitute. Existing approximate observation models typically utilize ℓ_q(q = 1, 1/2)-norm regularization for sparse constraints in imaging. However, these models are not sufficiently effective in terms of sparsity and imaging detail. Finally, to overcome the aforementioned issues, we apply ℓ_2/3 regularization, which aligns with the natural image gradient distribution, and further constrain it using a weighted matrix. This method enhances the sparsity of the algorithm and balances the detail insufficiency caused by the penalty term. Experimental results demonstrate the excellent performance of the proposed method. Full article

Robust face clustering enjoys a wide range of applications for gate passes, surveillance systems and security analysis in embedded sensors. Nevertheless, existing algorithms have limitations in finding accurate clusters when data contain noise (e.g., occluded face clustering and recognition). It is known that in subspace clustering, the ${\ell }_1$- and ${\ell }_2$-norm regularizers can improve subspace preservation and connectivity, respectively, and the elastic net regularizer (i.e., the mixture of the ${\ell }_1$- and ${\ell }_2$-norms) provides a balance between the two properties. However, existing deterministic methods have high per iteration computational complexities, making them inapplicable to large-scale problems. To address this issue, this paper proposes the first accelerated stochastic variance reduction gradient (RASVRG) algorithm for robust subspace clustering. We also introduce a new momentum acceleration technique for the RASVRG algorithm. As a result of the involvement of this momentum, the RASVRG algorithm achieves both the best oracle complexity and the fastest convergence rate, and it reaches higher efficiency in practice for both strongly convex and not strongly convex models. Various experimental results show that the RASVRG algorithm outperformed existing state-of-the-art methods with elastic net and ${\ell }_1$-norm regularizers in terms of accuracy in most cases. As demonstrated on real-world face datasets with different manually added levels of pixel corruption and occlusion situations, the RASVRG algorithm achieved much better performance in terms of accuracy and robustness. Full article

Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the ${\ell }_{2,1}$ norm to depict the sparsity of the error matrix, and they usually ignore the global structure embedded in each single view, compromising the clustering performance. Here, we design a robust tensor learning method for multi-view spectral clustering (RTL-MSC), which employs the weighted tensor nuclear norm to regularize the essential tensor for exploiting the high-order correlations underlying multiple views and adopts the nuclear norm to constrain each frontal slice of the essential tensor as the block diagonal matrix. Simultaneously, a novel column-wise sparse norm, namely, ${\ell }_{2,p}$, is defined in RTL-MSC to measure the error tensor, making it sparser than the one derived by the ${\ell }_{2,1}$ norm. We design an effective optimization algorithm to solve the proposed model. Experiments on three widely used datasets demonstrate the superiority of our method. Full article

In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary control for the specified hyperbolic system is given. A difference scheme is constructed for the numerical solution of the considered initial boundary value problem. The definition of the exponential stability of the numerical solution in ${\ell }^2$-norm with respect to a discrete perturbation of the equilibrium state of the initial boundary value difference problem is given. A discrete Lyapunov function for a numerical solution is constructed, and a theorem on the exponential stability of a stationary solution of the initial boundary value difference problem in ${\ell }^2$-norm with respect to a discrete perturbation is proved. Full article

The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model composed of a single qubit inside an external magnetic field. We show that the ${\mathsf{\ell }}_1$ norm of energy coherence $\mathcal{C}$ is invariant with respect to the unitary evolution of the quantum state. Thus, the ${\mathsf{\ell }}_1$ norm of energy coherence $\mathcal{C}$ of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal ${\mathsf{\ell }}_1$ norm of energy coherence, $\mathcal{C}<1$, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal ${\mathsf{\ell }}_1$ norm of energy coherence, $\mathcal{C}=1$, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance. Full article

Representation-based classification methods (RBCM) have recently garnered notable attention in the field of pattern classification. Diverging from conventional methods reliant on ${\mathsf{\ell }}_1$ or ${\mathsf{\ell }}_2$-norms, the nonnegative representation-based classifier (NRC) enforces a nonnegative constraint on the representation vector, thus enhancing the representation capabilities of positively correlated samples. While NRC has achieved substantial success, it falls short in fully harnessing the discriminative information associated with the training samples and neglects the locality constraint inherent in the sample relationships, thereby limiting its classification power. In response to these limitations, we introduce the locality-constraint discriminative nonnegative representation (LDNR) method. LDNR extends the NRC framework through the incorporation of a competitive representation term. Recognizing the pivotal role played by the estimated samples in the classification process, we include estimated samples that involve discriminative information in this term, establishing a robust connection between representation and classification. Additionally, we assign distinct local weights to different estimated samples, augmenting the representation capacity of homogeneous samples and, ultimately, elevating the performance of the classification model. To validate the effectiveness of LDNR, extensive comparative experiments are conducted on various pattern classification datasets. The findings demonstrate the competitiveness of our proposed method. Full article

Effective information transmission is a central element in quantum information protocols, but the quest for optimal efficiency in channels with symmetrical characteristics remains a prominent challenge in quantum information science. In light of this challenge, we introduce a hybrid channel that encompasses thermal, magnetic, and local components, each simultaneously endowed with characteristics that enhance and diminish quantum correlations. To investigate the symmetry of this hybrid channel, we explored the quantum correlations of a simple two-qubit Heisenberg spin state, quantified using measures such as negativity, ${\ell }_1$-norm coherence, entropic uncertainty, and entropy functions. Our findings revealed that the hybrid channel can be adeptly tailored to preserve quantum correlations, surpassing the capabilities of its individual components. We also identified optimal parameterizations to attain maximum entanglement from mixed entangled/separable states, even in the presence of local dephasing. Notably, various parameters and quantum features, including non-Markovianity, exhibited distinct behaviors in the context of this hybrid channel. Ultimately, we discuss potential experimental applications of this configuration. Full article