arXiv subjects

Xianchao Xiu

Publications and source records attributed to Xianchao Xiu.

29 records · Page 2Linked to original sources

arXiv2025

Lightweight Deep Unfolding Networks with Enhanced Robustness for Infrared Small Target Detection

Infrared small target detection (ISTD) is one of the key techniques in image processing. Although deep unfolding networks (DUNs) have demonstrated promising performance in ISTD due to their model interpretability and data adaptability, existing methods still face significant challenges in parameter lightweightness and noise robustness. In this regard, we propose a highly lightweight framework based on robust principal component analysis (RPCA) called L-RPCANet. Technically, a hierarchical bottleneck structure is constructed to reduce and increase the channel dimension in the single-channel input infrared image to achieve channel-wise feature refinement, with bottleneck layers designed in each module to extract features. This reduces the number of channels in feature extraction and improves the lightweightness of network parameters. Furthermore, a noise reduction module is embedded to enhance the robustness against complex noise. In addition, squeeze-and-excitation networks (SENets) are leveraged as a channel attention mechanism to focus on the varying importance of different features across channels, thereby achieving excellent performance while maintaining both lightweightness and robustness. Extensive experiments on the ISTD datasets validate the superiority of our proposed method compared with state-of-the-art methods covering RPCANet, DRPCANet, and RPCANet++. The code will be available at https://github.com/xianchaoxiu/L-RPCANet.

cs.CV↗

arXiv2025

Adaptive Multi-Order Graph Regularized NMF with Dual Sparsity for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is a critical yet challenging task in remote sensing. However, existing nonnegative matrix factorization (NMF) methods with graph learning mostly focus on first-order or second-order nearest neighbor relationships and usually require manual parameter tuning, which fails to characterize intrinsic data structures. To address the above issues, we propose a novel adaptive multi-order graph regularized NMF method (MOGNMF) with three key features. First, multi-order graph regularization is introduced into the NMF framework to exploit global and local information comprehensively. Second, these parameters associated with the multi-order graph are learned adaptively through a data-driven approach. Third, dual sparsity is embedded to obtain better robustness, i.e., $\ell_{1/2}$-norm on the abundance matrix and $\ell_{2,1}$-norm on the noise matrix. To solve the proposed model, we develop an alternating minimization algorithm whose subproblems have explicit solutions, thus ensuring effectiveness. Experiments on simulated and real hyperspectral data indicate that the proposed method delivers better unmixing results.

cs.CV↗

arXiv2025

Bi-Sparse Unsupervised Feature Selection

To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure of datasets by embedding a single sparse regularization or constraint on the transformation matrix. In this paper, we introduce a novel bi-sparse method called BSUFS to improve the performance of UFS. The core idea of BSUFS is to incorporate $\ell_{2,p}$-norm and $\ell_q$-norm into the classical PCA, which enables our method to select relevant features and filter out irrelevant noises, thereby obtaining discriminative features. Here, the parameters $p$ and $q$ are within the range of $[0, 1)$. Therefore, BSUFS not only constructs a unified framework for bi-sparse optimization, but also includes some existing works as special cases. To solve the resulting non-convex model, we propose an efficient proximal alternating minimization (PAM) algorithm using Stiefel manifold optimization and sparse optimization techniques. In addition, the computational complexity analysis is presented. Extensive numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposed BSUFS. The results reveal the advantages of bi-sparse optimization in feature selection and show its potential for other fields in image processing. Our code is available at https://github.com/xianchaoxiu/BSUFS.

math.OC↗

arXiv2025

Multi-View Clustering Meets Heterogenous Data: A Fusion Regularized Method

Multi-view clustering leverages consistent and complementary information across multiple views to provide more comprehensive insights than single-view analysis. However, the heterogeneity and redundancy of multi-view data pose significant challenges to the existing clustering techniques. To tackle these challenges effectively, this paper proposes a novel multi-view fusion regularized clustering method with adaptive group sparsity, enabling discriminative clustering while capturing informative features. Technically, for heterogeneous multi-view data with mixed-type feature sets, different losses or divergence metrics are considered with a joint fusion penalty to obtain consistent cluster structures. Moreover, the non-convex group sparsity consisting of inter-group sparsity and intra-group sparsity is utilized to eliminate redundant features, thereby enhancing the robustness. Furthermore, we develop an effective alternating direction method of multipliers (ADMM), where all subproblems can be solved in closed form. Extensive numerical experiments on real data validate the superior performance of our presented method in clustering accuracy and feature selection.

math.OC↗

arXiv2025

STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising

Remote sensing image (RSI) denoising is an important topic in the field of remote sensing. Despite the impressive denoising performance of RSI denoising methods, most current deep learning-based approaches function as black boxes and lack integration with physical information models, leading to limited interpretability. Additionally, many methods may struggle with insufficient attention to non-local self-similarity in RSI and require tedious tuning of regularization parameters to achieve optimal performance, particularly in conventional iterative optimization approaches. In this paper, we first propose a novel RSI denoising method named sparse tensor-aided representation network (STAR-Net), which leverages a low-rank prior to effectively capture the non-local self-similarity within RSI. Furthermore, we extend STAR-Net to a sparse variant called STAR-Net-S to deal with the interference caused by non-Gaussian noise in original RSI for the purpose of improving robustness. Different from conventional iterative optimization, we develop an alternating direction method of multipliers (ADMM)-guided deep unrolling network, in which all regularization parameters can be automatically learned, thus inheriting the advantages of both model-based and deep learning-based approaches and successfully addressing the above-mentioned shortcomings. Comprehensive experiments on synthetic and real-world datasets demonstrate that STAR-Net and STAR-Net-S outperform state-of-the-art RSI denoising methods.

cs.CV↗

arXiv2025

Robust Sparse Phase Retrieval: Statistical Guarantee, Optimality Theory and Convergent Algorithm

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a novel robust sparse PR method that covers both real- and complex-valued cases. The core is to leverage the Huber function to measure the loss and adopt the $\ell_{1/2}$-norm regularization to realize feature selection, thereby improving the robustness of PR. In theory, we establish statistical guarantees for such robustness and derive necessary optimality conditions for global minimizers. Particularly, for the complex-valued case, we provide a fixed point inclusion property inspired by Wirtinger derivatives. Furthermore, we develop an efficient optimization algorithm by integrating the gradient descent method into a majorization-minimization (MM) framework. It is rigorously proved that the whole generated sequence is convergent and also has a linear convergence rate under mild conditions, which has not been investigated before. Numerical examples under different types of noise validate the robustness and effectiveness of our proposed method.

math.OC↗

arXiv2025

Bi-Level Unsupervised Feature Selection

Unsupervised feature selection (UFS) is an important task in data engineering. However, most UFS methods construct models from a single perspective and often fail to simultaneously evaluate feature importance and preserve their inherent data structure, thus limiting their performance. To address this challenge, we propose a novel bi-level unsupervised feature selection (BLUFS) method, including a clustering level and a feature level. Specifically, at the clustering level, spectral clustering is used to generate pseudo-labels for representing the data structure, while a continuous linear regression model is developed to learn the projection matrix. At the feature level, the $\ell_{2,0}$-norm constraint is imposed on the projection matrix for more effectively selecting features. To the best of our knowledge, this is the first work to combine a bi-level framework with the $\ell_{2,0}$-norm. To solve the proposed bi-level model, we design an efficient proximal alternating minimization (PAM) algorithm, whose subproblems either have explicit solutions or can be computed by fast solvers. Furthermore, we establish the convergence result and computational complexity. Finally, extensive experiments on two synthetic datasets and eight real datasets demonstrate the superiority of BLUFS in clustering and classification tasks.

cs.LG↗

arXiv2025

Robust Orthogonal NMF with Label Propagation for Image Clustering

Non-negative matrix factorization (NMF) is a popular unsupervised learning approach widely used in image clustering. However, in real-world clustering scenarios, most existing NMF methods are highly sensitive to noise corruption and are unable to effectively leverage limited supervised information. To overcome these drawbacks, we propose a unified non-convex framework with label propagation called robust orthogonal nonnegative matrix factorization (RONMF). This method not only considers the graph Laplacian and label propagation as regularization terms but also introduces a more effective non-convex structure to measure the reconstruction error and imposes orthogonal constraints on the basis matrix to reduce the noise corruption, thereby achieving higher robustness. To solve RONMF, we develop an alternating direction method of multipliers (ADMM)-based optimization algorithm. In particular, all subproblems have closed-form solutions, which ensures its efficiency. Experimental evaluations on eight public image datasets demonstrate that the proposed RONMF outperforms state-of-the-art NMF methods across various standard metrics and shows excellent robustness. The code will be available at https://github.com/slinda-liu.

cs.CV↗

arXiv2025

Tuning-Free Structured Sparse PCA via Deep Unfolding Networks

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and conventional approaches, including grid search and Bayesian optimization, not only bring great computational costs but also exhibit high sensitivity. To address these limitations, we first establish a structured sparse PCA formulation by integrating $\ell_1$-norm and $\ell_{2,1}$-norm to capture the local and global structures, respectively. Building upon the off-the-shelf alternating direction method of multipliers (ADMM) optimization framework, we then design an interpretable deep unfolding network that translates iterative optimization steps into trainable neural architectures. This innovation enables automatic learning of the regularization parameters, effectively bypassing the empirical tuning requirements of conventional methods. Numerical experiments on benchmark datasets validate the advantages of our proposed method over the existing state-of-the-art methods. Our code will be accessible at https://github.com/xianchaoxiu/SPCA-Net.

cs.LG↗

arXiv2025

Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization

Unsupervised feature selection (UFS) is widely applied in machine learning and pattern recognition. However, most of the existing methods only consider a single sparsity, which makes it difficult to select valuable and discriminative feature subsets from the original high-dimensional feature set. In this paper, we propose a new UFS method called DSCOFS via embedding double sparsity constrained optimization into the classical principal component analysis (PCA) framework. Double sparsity refers to using $\ell_{2,0}$-norm and $\ell_0$-norm to simultaneously constrain variables, by adding the sparsity of different types, to achieve the purpose of improving the accuracy of identifying differential features. The core is that $\ell_{2,0}$-norm can remove irrelevant and redundant features, while $\ell_0$-norm can filter out irregular noisy features, thereby complementing $\ell_{2,0}$-norm to improve discrimination. An effective proximal alternating minimization method is proposed to solve the resulting nonconvex nonsmooth model. Theoretically, we rigorously prove that the sequence generated by our method globally converges to a stationary point. Numerical experiments on three synthetic datasets and eight real-world datasets demonstrate the effectiveness, stability, and convergence of the proposed method. In particular, the average clustering accuracy (ACC) and normalized mutual information (NMI) are improved by at least 3.34% and 3.02%, respectively, compared with the state-of-the-art methods. More importantly, two common statistical tests and a new feature similarity metric verify the advantages of double sparsity. All results suggest that our proposed DSCOFS provides a new perspective for feature selection.

math.OC↗

arXiv2024

Revisiting $L_q(0\leq q<1)$ Norm Regularized Optimization

Sparse optimization has seen its advances in recent decades. For scenarios where the true sparsity is unknown, regularization turns out to be a promising solution. Two popular non-convex regularizations are the so-called $L_0$ norm and $L_q$ norm with $q\in(0,1)$, giving rise to extensive research on their induced optimization. However, the majority of these work centered around the main function that is twice continuously differentiable and the best convergence rate for an algorithm solving the optimization with $q\in(0,1)$ is superlinear. This paper explores the $L_q$ norm regularized optimization in a unified way for any $q\in[0,1)$, where the main function has a semismooth gradient. In particular, we establish the first-order and the second-order optimality conditions under mild assumptions and then integrate the proximal operator and semismooth Newton method to develop a proximal semismooth Newton pursuit algorithm. Under the second sufficient condition, the whole sequence generated by the algorithm converges to a unique local minimizer. Moreover, the convergence is superlinear and quadratic if the gradient of the main function is semismooth and strongly semismooth at the local minimizer, respectively. Hence, this paper accomplishes the quadratic rate for an algorithm designed to solve the $L_q$ norm regularization problem for any $q\in(0,1)$. Finally, some numerical experiments have showcased its nice performance when compared with several existing solvers.

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