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Journal articles on the topic 'Sparsity Problem'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Yang, Wei, Lili Pan, and Jinhui Wan. "Smoothing gradient descent algorithm for the composite sparse optimization." AIMS Mathematics 9, no. 12 (2024): 33401–22. http://dx.doi.org/10.3934/math.20241594.

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<p>Composite sparsity generalizes the standard sparsity that considers the sparsity on a linear transformation of the variables. In this paper, we study the composite sparse optimization problem consisting of minimizing the sum of a nondifferentiable loss function and the $ {\mathcal{\ell}_0} $ penalty term of a matrix times the coefficient vector. First, we consider an exact continuous relaxation problem with a capped-$ {\mathcal{\ell}_1} $ penalty that has the same optimal solution as the primal problem. Specifically, we propose the lifted stationary point of the relaxation problem and

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Li, Haiyang, Jigen Peng, and Shigang Yue. "The Sparsity of Underdetermined Linear System vialpMinimization for0." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/584712.

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The sparsity problems have attracted a great deal of attention in recent years, which aim to find the sparsest solution of a representation or an equation. In the paper, we mainly study the sparsity of underdetermined linear system vialpminimization for0<p<1. We show, for a given underdetermined linear system of equationsAm×nX=b, that although it is not certain that the problem(Pp)(i.e.,minXXppsubject toAX=b, where0<p<1) generates sparser solutions as the value ofpdecreases and especially the problem(Pp)generates sparser solutions than the problem(P1)(i.e.,minXX1subject toAX=b), th

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McCormick, S. Thomas, and S. Frank Chang. "The Weighted Sparsity Problem: Complexity and Algorithms." SIAM Journal on Discrete Mathematics 6, no. 1 (1993): 57–69. http://dx.doi.org/10.1137/0406005.

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O'Brien, Thomas S., and Stuart R. Taylor. "The Problem of Sparsity in Education Provision." Urban Studies 25, no. 6 (1988): 520–26. http://dx.doi.org/10.1080/00420988820080681.

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Ren, Xiaozhen, and Yuying Jiang. "Spatial Domain Terahertz Image Reconstruction Based on Dual Sparsity Constraints." Sensors 21, no. 12 (2021): 4116. http://dx.doi.org/10.3390/s21124116.

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Terahertz time domain spectroscopy imaging systems suffer from the problems of long image acquisition time and massive data processing. Reducing the sampling rate will lead to the degradation of the imaging reconstruction quality. To solve this issue, a novel terahertz imaging model, named the dual sparsity constraints terahertz image reconstruction model (DSC-THz), is proposed in this paper. DSC-THz fuses the sparsity constraints of the terahertz image in wavelet and gradient domains into the terahertz image reconstruction model. Differing from the conventional wavelet transform, we introduce

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Dell’Aversano, Angela, Giovanni Leone, and Raffaele Solimene. "Comparing Two Approaches for Point-Like Scatterer Detection." International Journal of Antennas and Propagation 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/139235.

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Many inverse scattering problems concern the detection and localisation of point-like scatterers which are sparsely enclosed within a prescribed investigation domain. Therefore, it looks like a good option to tackle the problem by applying reconstruction methods that are properly tailored for such a type of scatterers or that naturally enforce sparsity in the reconstructions. Accordingly, in this paper we compare the time reversal-MUSIC and the compressed sensing. The study develops through numerical examples and focuses on the role of noise in data and mutual coupling between the scatterers.

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畅, 含笑. "The Solution of Sparsity-Constrained Split Feasibility Problem." Advances in Applied Mathematics 05, no. 02 (2016): 269–75. http://dx.doi.org/10.12677/aam.2016.52034.

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Wang, Guanglei, and Hassan Hijazi. "Exploiting sparsity for the min k-partition problem." Mathematical Programming Computation 12, no. 1 (2019): 109–30. http://dx.doi.org/10.1007/s12532-019-00165-3.

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Xue, Andy Yuan, Jianzhong Qi, Xing Xie, Rui Zhang, Jin Huang, and Yuan Li. "Solving the data sparsity problem in destination prediction." VLDB Journal 24, no. 2 (2014): 219–43. http://dx.doi.org/10.1007/s00778-014-0369-7.

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PLONKA, GERLIND, and JIANWEI MA. "CURVELET-WAVELET REGULARIZED SPLIT BREGMAN ITERATION FOR COMPRESSED SENSING." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (2011): 79–110. http://dx.doi.org/10.1142/s0219691311003955.

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Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon–Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity c

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Wang, Pu. "An Ontology-Based Collaborative Filtering Personalized Recommendation." Applied Mechanics and Materials 267 (December 2012): 79–82. http://dx.doi.org/10.4028/www.scientific.net/amm.267.79.

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Recommender systems have been successfully used to tackle the problem of information overload, where users of products have too many choices and overwhelming amount of information about each choice. Personalization is widely used in various fields to provide users with more suitable and personalized service. Many e-commerce web sites such as online shop retailers make use of recommendation systems. In order to make recommendations to a user, collaborative filtering is an important personalized recommendation technique applied widely in E-commerce. The collaborative approach faces the hard issu

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Gholami, Ali. "Residual statics estimation by sparsity maximization." GEOPHYSICS 78, no. 1 (2013): V11—V19. http://dx.doi.org/10.1190/geo2012-0035.1.

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Residual statics estimation in complex areas is one of the main challenging problems in seismic data processing. It is well known that the result of this processing step has a profound effect on the quality of final reconstructed image. A novel method is presented to compensate for surface-consistent residual static corrections based on sparsity maximization, which has proved to be a powerful tool in the analysis and processing of signals and related problems. The method is based on the hypothesis that residual static time shift represents itself by noise-like features in the Fourier or curvel

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Pan, Weike, Evan Xiang, Nathan Liu, and Qiang Yang. "Transfer Learning in Collaborative Filtering for Sparsity Reduction." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (2010): 230–35. http://dx.doi.org/10.1609/aaai.v24i1.7578.

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Data sparsity is a major problem for collaborative filtering (CF) techniques in recommender systems, especially for new users and items. We observe that, while our target data are sparse for CF systems, related and relatively dense auxiliary data may already exist in some other more mature application domains. In this paper, we address the data sparsity problem in a target domain by transferring knowledge about both users and items from auxiliary data sources. We observe that in different domains the user feedbacks are often heterogeneous such as ratings vs. clicks. Our solution is to integrat

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Li, Xinqi, Jun Wang, and Sam Kwong. "A Discrete-Time Neurodynamic Approach to Sparsity-Constrained Nonnegative Matrix Factorization." Neural Computation 32, no. 8 (2020): 1531–62. http://dx.doi.org/10.1162/neco_a_01294.

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Sparsity is a desirable property in many nonnegative matrix factorization (NMF) applications. Although some level of sparseness of NMF solutions can be achieved by using regularization, the resulting sparsity depends highly on the regularization parameter to be valued in an ad hoc way. In this letter we formulate sparse NMF as a mixed-integer optimization problem with sparsity as binary constraints. A discrete-time projection neural network is developed for solving the formulated problem. Sufficient conditions for its stability and convergence are analytically characterized by using Lyapunov's

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Zeng, Fanfan, Hongwei Du, Jiaquan Jin, Jinzhang Xu, and Bensheng Qiu. "Compressed Sensing MRI via Extended Anisotropic and Isotropic Total Variation." Journal of Medical Imaging and Health Informatics 9, no. 6 (2019): 1066–75. http://dx.doi.org/10.1166/jmihi.2019.2702.

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Compressed sensing (CS) is a technique to reconstruct images from undersampling data, reducing the scanning time of magnetic resonance imaging (MRI). It utilizes the sparsity of images in some transform domains. Total variation (TV) has been applied to enforce sparsity. However, traditional TV based on the l1-norm is not the most direct way to induce sparsity, and it cannot offer a sufficiently sparse representation. Since the lp-norm (0< p < 1) promotes the sparsity better than that of the l1-norm, we propose two extended TV algorithms based on the lp-norm: anisotropic and isotropic tot

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Zhao, Liquan, Yunfeng Hu, and Yulong Liu. "Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation." Electronics 8, no. 2 (2019): 165. http://dx.doi.org/10.3390/electronics8020165.

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The stochastic gradient matching pursuit algorithm requires the sparsity of the signal as prior information. However, this prior information is unknown in practical applications, which restricts the practical applications of the algorithm to some extent. An improved method was proposed to overcome this problem. First, a pre-evaluation strategy was used to evaluate the sparsity of the signal and the estimated sparsity was used as the initial sparsity. Second, if the number of columns of the candidate atomic matrix was smaller than that of the rows, the least square solution of the signal was ca

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Si, Wei-Jian, Qiang Liu, and Zhi-An Deng. "Adaptive Reconstruction Algorithm Based on Compressed Sensing Broadband Receiver." Wireless Communications and Mobile Computing 2021 (January 15, 2021): 1–12. http://dx.doi.org/10.1155/2021/6673235.

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Existing greedy reconstruction algorithms require signal sparsity, and the remaining sparsity adaptive algorithms can be reconstructed but cannot achieve accurate sparsity estimation. To address this problem, a blind sparsity reconstruction algorithm is proposed in this paper, which is applied to compressed sensing radar receiver system. The proposed algorithm can realize the estimation of signal sparsity and channel position estimation, which mainly consists of two parts. The first part is to use fast search based on dichotomy search, which is based on the high probability reconstruction of g

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Yu, Jiangni, Lixiang Li, and Yixian Yang. "Topology Identification of Coupling Map Lattice under Sparsity Condition." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/303454.

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Coupling map lattice is an efficient mathematical model for studying complex systems. This paper studies the topology identification of coupled map lattice (CML) under the sparsity condition. We convert the identification problem into the problem of solving the underdetermined linear equations. Thel1norm method is used to solve the underdetermined equations. The requirement of data characters and sampling times are discussed in detail. We find that the high entropy and small coupling coefficient data are suitable for the identification. When the measurement time is more than 2.86 times sparsit

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Zahedi, A., and M. H. Kahaei. "Frequency Estimation of Irregularly Sampled Data Using a Sparsity Constrained Weighted Least-Squares Approach." Engineering, Technology & Applied Science Research 3, no. 1 (2013): 368–72. http://dx.doi.org/10.48084/etasr.187.

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In this paper, a new method for frequency estimation of irregularly sampled data is proposed. In comparison with the previous sparsity-based methods where the sparsity constraint is applied to a least-squares fitting problem, the proposed method is based on a sparsity constrained weighted least-squares problem. The resulting problem is solved in an iterative manner, allowing the usage of the solution obtained at each iteration to determine the weights of the least-squares fitting term at the next iteration. Such an appropriate weighting of the least-squares fitting term enhances the performanc

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Wan, Xinyue, Bofeng Zhang, Guobing Zou, and Furong Chang. "Sparse Data Recommendation by Fusing Continuous Imputation Denoising Autoencoder and Neural Matrix Factorization." Applied Sciences 9, no. 1 (2018): 54. http://dx.doi.org/10.3390/app9010054.

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In recent years, although deep neural networks have yielded immense success in solving various recognition and classification problems, the exploration of deep neural networks in recommender systems has received relatively less attention. Meanwhile, the inherent sparsity of data is still a challenging problem for deep neural networks. In this paper, firstly, we propose a new CIDAE (Continuous Imputation Denoising Autoencoder) model based on the Denoising Autoencoder to alleviate the problem of data sparsity. CIDAE performs regular continuous imputation on the missing parts of the original data

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Choi, Keunho, Yongmoo Suh, and Donghee Yoo. "Extended Collaborative Filtering Technique for Mitigating the Sparsity Problem." International Journal of Computers Communications & Control 11, no. 5 (2016): 631. http://dx.doi.org/10.15837/ijccc.2016.5.2152.

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Many online shopping malls have implemented personalized recommendation systems to improve customer retention in the age of high competition and information overload. Sellers make use of these recommendation systems to survive high competition and buyers utilize them to find proper product information for their own needs. However, transaction data of most online shopping malls prevent us from using collaborative filtering (CF) technique to recommend products, for the following two reasons: 1) explicit rating information is rarely available in the transaction data; 2) the sparsity problem usual

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Jabr, R. A. "Exploiting Sparsity in SDP Relaxations of the OPF Problem." IEEE Transactions on Power Systems 27, no. 2 (2012): 1138–39. http://dx.doi.org/10.1109/tpwrs.2011.2170772.

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Wang, Shaohe, Rui Han, Ping Qian, and Chen Li. "Generalized Non-Convex Non-Smooth Group-Sparse Residual Prior for Image Denoising." Electronics 14, no. 2 (2025): 353. https://doi.org/10.3390/electronics14020353.

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Image denoising is a classic yet challenging problem in low-level image processing. Traditional image denoising approaches using convex regularized prior (e.g., L1-norm) often bring bias problems. To address this issue, a novel prior model based on a family of non-convex functions and group sparsity residual (GSC) prior constraint for image denoising is studied. We propose a generalized non-convex GSC prior model for the image denoising problem. We first utilize the group-sparse representation (GSR) before exploiting image prior information. Specifically, to further improve the image denoising

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Khoshsokhan, S., R. Rajabi, and H. Zayyani. "DISTRIBUTED UNMIXING OF HYPERSPECTRAL DATAWITH SPARSITY CONSTRAINT." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W4 (September 26, 2017): 145–50. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w4-145-2017.

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Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm,

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Wu, Yan, Aoming Liu, Zhiwu Huang, Siwei Zhang, and Luc Van Gool. "Neural Architecture Search as Sparse Supernet." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (2021): 10379–87. http://dx.doi.org/10.1609/aaai.v35i12.17243.

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This paper aims at enlarging the problem of Neural Architecture Search (NAS) from Single-Path and Multi-Path Search to automated Mixed-Path Search. In particular, we model the NAS problem as a sparse supernet using a new continuous architecture representation with a mixture of sparsity constraints. The sparse supernet enables us to automatically achieve sparsely-mixed paths upon a compact set of nodes. To optimize the proposed sparse supernet, we exploit a hierarchical accelerated proximal gradient algorithm within a bi-level optimization framework. Extensive experiments on Convolutional Neura

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Junxi, Yang, Zongshui Wang, and Chong Chen. "GCN-MF: A graph convolutional network based on matrix factorization for recommendation." Innovation & Technology Advances 2, no. 1 (2024): 14–26. http://dx.doi.org/10.61187/ita.v2i1.30.

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With the increasing development of information technology and the rise of big data, the Internet has entered the era of information overload. While users enjoy the convenience brought by big data to their daily lives, they also face more and more information filtering and selection problems. In this context, recommendation systems have emerged, and existing recommendation systems cannot effectively deal with the problem of data sparsity. Therefore, this paper proposes a graph convolutional network based on matrix factorization for recommendation. The embedding layer uses matrix factorization i

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Zhu, Junxian, Canhong Wen, Jin Zhu, Heping Zhang, and Xueqin Wang. "A polynomial algorithm for best-subset selection problem." Proceedings of the National Academy of Sciences 117, no. 52 (2020): 33117–23. http://dx.doi.org/10.1073/pnas.2014241117.

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Best-subset selection aims to find a small subset of predictors, so that the resulting linear model is expected to have the most desirable prediction accuracy. It is not only important and imperative in regression analysis but also has far-reaching applications in every facet of research, including computer science and medicine. We introduce a polynomial algorithm, which, under mild conditions, solves the problem. This algorithm exploits the idea of sequencing and splicing to reach a stable solution in finite steps when the sparsity level of the model is fixed but unknown. We define an informa

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Guo, Jingfeng, Chao Zheng, Shanshan Li, Yutong Jia, and Bin Liu. "BiInfGCN: Bilateral Information Augmentation of Graph Convolutional Networks for Recommendation." Mathematics 10, no. 17 (2022): 3042. http://dx.doi.org/10.3390/math10173042.

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The current graph-neural-network-based recommendation algorithm fully considers the interaction between users and items. It achieves better recommendation results, but due to a large amount of data, the interaction between users and items still suffers from the problem of data sparsity. To address this problem, we propose a method to alleviate the data sparsity problem by retaining user–item interactions while fully exploiting the association relationships between items and using side-information enhancement. We constructed a “twin-tower” model by combining a user–item training model and an it

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Wang, Qi, Pengcheng Zhang, Jianming Wang, et al. "Patch-based sparse reconstruction for electrical impedance tomography." Sensor Review 37, no. 3 (2017): 257–69. http://dx.doi.org/10.1108/sr-07-2016-0126.

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Purpose Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Image reconstruction for EIT is a nonlinear problem. A generalized inverse operator is usually ill-posed and ill-conditioned. Therefore, the solutions for EIT are not unique and highly sensitive to the measurement noise. Design/methodology/approach This paper develops a novel image reconstruction algorithm for EIT based on patch-based sparse representation. The sparsifying dictionary opti

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Zhu, Hong, Li-Zhi Liao, and Michael K. Ng. "Multi-Instance Dimensionality Reduction via Sparsity and Orthogonality." Neural Computation 30, no. 12 (2018): 3281–308. http://dx.doi.org/10.1162/neco_a_01140.

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We study a multi-instance (MI) learning dimensionality-reduction algorithm through sparsity and orthogonality, which is especially useful for high-dimensional MI data sets. We develop a novel algorithm to handle both sparsity and orthogonality constraints that existing methods do not handle well simultaneously. Our main idea is to formulate an optimization problem where the sparse term appears in the objective function and the orthogonality term is formed as a constraint. The resulting optimization problem can be solved by using approximate augmented Lagrangian iterations as the outer loop and

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Yuan, Jinfeng, and Li Li. "Recommendation Based on Trust Diffusion Model." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/159594.

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Recommender system is emerging as a powerful and popular tool for online information relevant to a given user. The traditional recommendation system suffers from the cold start problem and the data sparsity problem. Many methods have been proposed to solve these problems, but few can achieve satisfactory efficiency. In this paper, we present a method which combines the trust diffusion (DiffTrust) algorithm and the probabilistic matrix factorization (PMF). DiffTrust is first used to study the possible diffusions of trust between various users. It is able to make use of the implicit relationship

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Wen, Ying, Le Zhang, and Lili Hou. "Discriminant Sparsity Preserving Analysis for Face Recognition." International Journal of Pattern Recognition and Artificial Intelligence 30, no. 02 (2016): 1656003. http://dx.doi.org/10.1142/s0218001416560036.

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Sparse subspace learning has drawn more and more attentions recently, however, most of them are unsupervised and unsuitable for classification tasks. In this paper, a new discriminant sparsity preserving analysis (DSPA) method by integrating sparse reconstructive weighting into Fisher criterion is proposed for face recognition. We first get sparsity preserving space spanned by the eigenvectors of sparsity preserving projections (SPP). Then, the optimal projection can be obtained by solving an eigenvalue and eigenvector problem of the between-class scatter matrix in sparsity preserving space. T

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Tong, Guowei, Shi Liu, and Sha Liu. "Computationally efficient image reconstruction algorithm for electrical capacitance tomography." Transactions of the Institute of Measurement and Control 41, no. 3 (2018): 631–46. http://dx.doi.org/10.1177/0142331218763013.

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The electrical capacitance tomography (ECT) is a visualization measurement method and can reconstruct the spatial permittivity distribution information in a measurement domain based on given capacitance values, in which the effectiveness of the image reconstruction algorithm plays a vital role in real-world engineering applications. Unlike common imaging methods, within the framework of the Tikhonov regularization methodology and the transform-domain sparsity method, a new cost function encapsulating the wavelet-based sparsity constraint is proposed to model the ECT imaging problem. An iterati

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Li, Zhixian. "Exploring the Path of Innovative Development of Traditional Culture under Big Data." Computational Intelligence and Neuroscience 2022 (August 29, 2022): 1–10. http://dx.doi.org/10.1155/2022/7715851.

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Chinese traditional culture is the treasure of our cultural field. In the new era, it is of great significance to give traditional culture a new life and vitality. The term “big data” is hotly debated all over the world, while the development of big data is gradually occupying all aspects of the society that people are compatible with society. It is an imperative initiative to build a cultural data system by making use of big data technology, and cultural big data can make Chinese traditional culture release more vitality. This paper analyzes the new characteristics of traditional culture deve

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Su, Xiaolong, Zhen Liu, Tianpeng Liu, Bo Peng, Xin Chen, and Xiang Li. "A Sparse Representation Method for Coherent Sources Angle Estimation with Uniform Circular Array." International Journal of Antennas and Propagation 2019 (October 13, 2019): 1–9. http://dx.doi.org/10.1155/2019/3849791.

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Coherent source localization is a common problem in signal processing. In this paper, a sparse representation method is considered to deal with two-dimensional (2D) direction of arrival (DOA) estimation for coherent sources with a uniform circular array (UCA). Considering that objective function requires sparsity in the spatial dimension but does not require sparsity in time, singular value decomposition (SVD) is employed to reduce computational complexity and ℓ2 norm is utilized to renew objective function. After the new objective function is constructed to evaluate residual and sparsity, a s

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Dong, Danling, and Libo Wu. "Implementation of English “Online and Offline” Hybrid Teaching Recommendation Platform Based on Reinforcement Learning." Security and Communication Networks 2021 (September 30, 2021): 1–10. http://dx.doi.org/10.1155/2021/4875330.

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At present, there is a serious disconnect between online teaching and offline teaching in English MOOC large-scale hybrid teaching recommendation platform, which is mainly due to the problems of cold start and matrix sparsity in the recommendation algorithm, and it is difficult to fully tap the user's interest characteristics because it only considers the user's rating but neglects the user's personalized evaluation. In order to solve the above problems, this paper proposes to use reinforcement learning thought and user evaluation factors to realize the online and offline hybrid English teachi

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Zang, Tingpeng, Guangrui Wen, and Zhifen Zhang. "Robust Estimation of the Unbalance of Rotor Systems Based on Sparsity Control of the Residual Model." Shock and Vibration 2018 (August 14, 2018): 1–8. http://dx.doi.org/10.1155/2018/6508695.

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The vibration signals of rotating machinery are frequently disturbed by background noise and external disturbances because of the equipment’s particular working environment. Thus, robustness has become one of the most important problems in identifying the unbalance of rotor systems. Based on the observation that external disturbance of the unbalance response often displays sparsity compared with measured vibration data, we present a new robust method for identifying the unbalance of rotor systems based on model residual sparsity control. The residual model is composed of two parts: one part ta

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Jiang, Jiang, Xi Chen, and Hai Tao Gan. "Feature Extraction for Kernel Minimum Squared Error by Sparsity Shrinkage." Applied Mechanics and Materials 536-537 (April 2014): 450–53. http://dx.doi.org/10.4028/www.scientific.net/amm.536-537.450.

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In this paper, a sparsity based model is proposed for feature selection in kernel minimum squared error (KMSE). By imposing a sparsity shrinkage term, we formulate the procedure of subset selection as an optimization problem. With the chosen small portion of training examples, the computational burden of feature extraction is largely alleviated. Experimental results conducted on several benchmark datasets indicate the effectivity and efficiency of our method.

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Menkin, A. V. "Development of a Music Recommender System Based on Content Metadata Processing." Vestnik NSU. Series: Information Technologies 17, no. 3 (2019): 43–60. http://dx.doi.org/10.25205/1818-7900-2019-17-3-43-60.

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Music recommender systems (MRS) help users of music streaming services to find interesting music in the music catalogs. The sparsity problem is an essential problem of MRS research. It refers to the fact that user usually rates only a tiny part of items. As a result, MRS often has not enough data to make a recommendation. To solve the sparsity problem, in this paper, a new approach that uses related items’ ratings is proposed. Hybrid MRS based on this approach is described. It uses tracks, albums, artists, genres normalized ratings along with information about relations between items of differ

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Casas, Eduardo, Christopher Ryll, and Fredi Tröltzsch. "Sparse Optimal Control of the Schlögl and FitzHugh–Nagumo Systems." Computational Methods in Applied Mathematics 13, no. 4 (2013): 415–42. http://dx.doi.org/10.1515/cmam-2013-0016.

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Abstract. We investigate the problem of sparse optimal controls for the so-called Schlögl model and the FitzHugh–Nagumo system. In these reaction–diffusion equations, traveling wave fronts occur that can be controlled in different ways. The L1-norm of the distributed control is included in the objective functional so that optimal controls exhibit effects of sparsity. We prove the differentiability of the control-to-state mapping for both dynamical systems, show the well-posedness of the optimal control problems and derive first-order necessary optimality conditions. Based on them, the sparsity

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Kieu, Hai Dang, Hongchuan Yu, Zhuorong Li, and Jian Jun Zhang. "Locally weighted PCA regression to recover missing markers in human motion data." PLOS ONE 17, no. 8 (2022): e0272407. http://dx.doi.org/10.1371/journal.pone.0272407.

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“Missing markers problem”, that is, missing markers during a motion capture session, has been raised for many years in Motion Capture field. We propose the locally weighted principal component analysis (PCA) regression method to deal with this challenge. The main merit is to introduce the sparsity of observation datasets through the multivariate tapering approach into traditional least square methods and develop it into a new kind of least square methods with the sparsity constraints. To the best of our knowledge, it is the first least square method with the sparsity constraints. Our experimen

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Ozkan, Ece, Valery Vishnevsky, and Orcun Goksel. "Inverse Problem of Ultrasound Beamforming With Sparsity Constraints and Regularization." IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 65, no. 3 (2018): 356–65. http://dx.doi.org/10.1109/tuffc.2017.2757880.

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Winters, D. W., B. D. Van Veen, and S. C. Hagness. "A Sparsity Regularization Approach to the Electromagnetic Inverse Scattering Problem." IEEE Transactions on Antennas and Propagation 58, no. 1 (2010): 145–54. http://dx.doi.org/10.1109/tap.2009.2035997.

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Zhang, Song, Cong Li, Li Ma, and Qi Li. "Alleviating the sparsity problem of collaborative filtering using rough set." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 32, no. 2 (2013): 516–30. http://dx.doi.org/10.1108/03321641311296918.

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Han, Ningning, and Zhanjie Song. "Bayesian multiple measurement vector problem with spatial structured sparsity patterns." Digital Signal Processing 75 (April 2018): 184–201. http://dx.doi.org/10.1016/j.dsp.2018.01.015.

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Yu, Chengyuan, and Linpeng Huang. "CluCF: a clustering CF algorithm to address data sparsity problem." Service Oriented Computing and Applications 11, no. 1 (2016): 33–45. http://dx.doi.org/10.1007/s11761-016-0191-8.

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Shanmuga Sundari, P., and M. Subaji. "Integrating Sentiment Analysis on Hybrid Collaborative Filtering Method in a Big Data Environment." International Journal of Information Technology & Decision Making 19, no. 02 (2020): 385–412. http://dx.doi.org/10.1142/s0219622020500108.

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Most of the traditional recommendation systems are based on user ratings. Here, users provide the ratings towards the product after use or experiencing it. Accordingly, the user item transactional database is constructed for recommendation. The rating based collaborative filtering method is well known method for recommendation system. This system leads to data sparsity problem as the user is unaware of other similar items. Web cataloguing service such as tags plays a significant role to analyse the user’s perception towards a particular product. Some system use tags as additional resource to r

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Schneider, Christopher, and Gerd Wachsmuth. "Regularization and discretization error estimates for optimal control of ODEs with group sparsity." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 2 (2018): 811–34. http://dx.doi.org/10.1051/cocv/2017049.

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It is well known that optimal control problems with L1-control costs produce sparse solutions, i.e., the optimal control is zero on whole intervals. In this paper, we study a general class of convex linear-quadratic optimal control problems with a sparsity functional that promotes a so-called group sparsity structure of the optimal controls. In this case, the components of the control function take the value of zero on parts of the time interval, simultaneously. These problems are both theoretically interesting and practically relevant. After obtaining results about the structure of the optima

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Liu, Li Min, Peng Xiang Zhang, Le Lin, and Zhi Wei Xu. "Research of Data Sparsity Based on Collaborative Filtering Algorithm." Applied Mechanics and Materials 462-463 (November 2013): 856–60. http://dx.doi.org/10.4028/www.scientific.net/amm.462-463.856.

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During the traditional collaborative filtering recommendation algorithm be impacted by itself data sparseness problem. It can not provide accurate recommendation result. In this paper, Using traditional collaborative filtering algorithm and the concept of similar level, take advantage of the idea of data populating to solve sparsity problem, then using the Weighted Slope One algorithm to recommend calculating. Experimental results show that the improved algorithm solved the problem of the recommendation results of low accuracy because of the sparse scoring matrix, and it improved the algorithm

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Han, Jie, Songlin Zhang, Shouzhu Zheng, Minghua Wang, Haiyong Ding, and Qingyun Yan. "Bias Analysis and Correction for Ill-Posed Inversion Problem with Sparsity Regularization Based on L1 Norm for Azimuth Super-Resolution of Radar Forward-Looking Imaging." Remote Sensing 14, no. 22 (2022): 5792. http://dx.doi.org/10.3390/rs14225792.

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The sparsity regularization based on the L1 norm can significantly stabilize the solution of the ill-posed sparsity inversion problem, e.g., azimuth super-resolution of radar forward-looking imaging, which can effectively suppress the noise and reduce the blurry effect of the convolution kernel. In practice, the total variation (TV) and TV-sparsity (TVS) regularizations based on the L1 norm are widely adopted in solving the ill-posed problem. Generally, however, the existence of bias is ignored, which is incomplete in theory. This paper places emphasis on analyzing the partially biased propert

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