Relevant bibliographies by topics / Sparse Low-Rank Representation

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  2. Dissertations / Theses
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Academic literature on the topic 'Sparse Low-Rank Representation'

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Published: 27 January 2024

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Journal articles on the topic "Sparse Low-Rank Representation"

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Hengdong Zhu, Hengdong Zhu, Ting Yang Hengdong Zhu, Yingcang Ma Ting Yang, and Xiaofei Yang Yingcang Ma. "Multi-view Re-weighted Sparse Subspace Clustering with Intact Low-rank Space Learning." 電腦學刊 33, no. 4 (August 2022): 121–31. http://dx.doi.org/10.53106/199115992022083304010.

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<p>In this paper, we propose a new Multi-view Re-weighted Sparse Subspace Clustering with Intact Low-rank Space Learning (ILrS-MRSSC) method, trying to find a sparse representation of the complete space of information. Specifically, this method integrates the complementary information inherent in multiple angles of the data, learns a complete space of potential low-rank representation, and constructs a sparse information matrix to reconstruct the data. The correlation between multi-view learning and subspace clustering is strengthened to the greatest extent, so that the subspace representation is more intuitive and accurate. The optimal solution of the model is solved by the augmented lagrangian multiplier (ALM) method of alternating direction minimal. Experiments on multiple benchmark data sets verify the effec-tiveness of this method.</p> <p>&nbsp;</p>
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Zhao, Jianxi, and Lina Zhao. "Low-rank and sparse matrices fitting algorithm for low-rank representation." Computers & Mathematics with Applications 79, no. 2 (January 2020): 407–25. http://dx.doi.org/10.1016/j.camwa.2019.07.012.

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Kim, Hyuncheol, and Joonki Paik. "Video Summarization using Low-Rank Sparse Representation." IEIE Transactions on Smart Processing & Computing 7, no. 3 (June 30, 2018): 236–44. http://dx.doi.org/10.5573/ieiespc.2018.7.3.236.

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CHENG, Shilei, Song GU, Maoquan YE, and Mei XIE. "Action Recognition Using Low-Rank Sparse Representation." IEICE Transactions on Information and Systems E101.D, no. 3 (2018): 830–34. http://dx.doi.org/10.1587/transinf.2017edl8176.

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Wang, Jun, Daming Shi, Dansong Cheng, Yongqiang Zhang, and Junbin Gao. "LRSR: Low-Rank-Sparse representation for subspace clustering." Neurocomputing 214 (November 2016): 1026–37. http://dx.doi.org/10.1016/j.neucom.2016.07.015.

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Du, Haishun, Xudong Zhang, Qingpu Hu, and Yandong Hou. "Sparse representation-based robust face recognition by graph regularized low-rank sparse representation recovery." Neurocomputing 164 (September 2015): 220–29. http://dx.doi.org/10.1016/j.neucom.2015.02.067.

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Zhang, Xiujun, Chen Xu, Min Li, and Xiaoli Sun. "Sparse and Low-Rank Coupling Image Segmentation Model Via Nonconvex Regularization." International Journal of Pattern Recognition and Artificial Intelligence 29, no. 02 (February 27, 2015): 1555004. http://dx.doi.org/10.1142/s0218001415550046.

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This paper investigates how to boost region-based image segmentation by inheriting the advantages of sparse representation and low-rank representation. A novel image segmentation model, called nonconvex regularization based sparse and low-rank coupling model, is presented for such a purpose. We aim at finding the optimal solution which is provided with sparse and low-rank simultaneously. This is achieved by relaxing sparse representation problem as L1/2 norm minimization other than the L1 norm minimization, while relaxing low-rank representation problem as the S1/2 norm minimization other than the nuclear norm minimization. This coupled model can be solved efficiently through the Augmented Lagrange Multiplier (ALM) method and half-threshold operator. Compared to the other state-of-the-art methods, the new method is better at capturing the global structure of the whole data, the robustness is better and the segmentation accuracy is also competitive. Experiments on two public image segmentation databases well validate the superiority of our method.
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Zheng, Chun-Hou, Yi-Fu Hou, and Jun Zhang. "Improved sparse representation with low-rank representation for robust face recognition." Neurocomputing 198 (July 2016): 114–24. http://dx.doi.org/10.1016/j.neucom.2015.07.146.

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Du, Shiqiang, Yuqing Shi, Guangrong Shan, Weilan Wang, and Yide Ma. "Tensor low-rank sparse representation for tensor subspace learning." Neurocomputing 440 (June 2021): 351–64. http://dx.doi.org/10.1016/j.neucom.2021.02.002.

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Zou, Dongqing, Xiaowu Chen, Guangying Cao, and Xiaogang Wang. "Unsupervised Video Matting via Sparse and Low-Rank Representation." IEEE Transactions on Pattern Analysis and Machine Intelligence 42, no. 6 (June 1, 2020): 1501–14. http://dx.doi.org/10.1109/tpami.2019.2895331.

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Dissertations / Theses on the topic "Sparse Low-Rank Representation"

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Cordolino, Sobral Andrews. "Robust low-rank and sparse decomposition for moving object detection : from matrices to tensors." Thesis, La Rochelle, 2017. http://www.theses.fr/2017LAROS007/document.

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Dans ce manuscrit de thèse, nous introduisons les avancées récentes sur la décomposition en matrices (et tenseurs) de rang faible et parcimonieuse ainsi que les contributions pour faire face aux principaux problèmes dans ce domaine. Nous présentons d’abord un aperçu des méthodes matricielles et tensorielles les plus récentes ainsi que ses applications sur la modélisation d’arrière-plan et la segmentation du premier plan. Ensuite, nous abordons le problème de l’initialisation du modèle de fond comme un processus de reconstruction à partir de données manquantes ou corrompues. Une nouvelle méthodologie est présentée montrant un potentiel intéressant pour l’initialisation de la modélisation du fond dans le cadre de VSI. Par la suite, nous proposons une version « double contrainte » de l’ACP robuste pour améliorer la détection de premier plan en milieu marin dans des applications de vidéo-surveillance automatisées. Nous avons aussi développé deux algorithmes incrémentaux basés sur tenseurs afin d’effectuer une séparation entre le fond et le premier plan à partir de données multidimensionnelles. Ces deux travaux abordent le problème de la décomposition de rang faible et parcimonieuse sur des tenseurs. A la fin, nous présentons un travail particulier réalisé en conjonction avec le Centre de Vision Informatique (CVC) de l’Université Autonome de Barcelone (UAB)
This thesis introduces the recent advances on decomposition into low-rank plus sparse matrices and tensors, as well as the main contributions to face the principal issues in moving object detection. First, we present an overview of the state-of-the-art methods for low-rank and sparse decomposition, as well as their application to background modeling and foreground segmentation tasks. Next, we address the problem of background model initialization as a reconstruction process from missing/corrupted data. A novel methodology is presented showing an attractive potential for background modeling initialization in video surveillance. Subsequently, we propose a double-constrained version of robust principal component analysis to improve the foreground detection in maritime environments for automated video-surveillance applications. The algorithm makes use of double constraints extracted from spatial saliency maps to enhance object foreground detection in dynamic scenes. We also developed two incremental tensor-based algorithms in order to perform background/foreground separation from multidimensional streaming data. These works address the problem of low-rank and sparse decomposition on tensors. Finally, we present a particular work realized in conjunction with the Computer Vision Center (CVC) at Autonomous University of Barcelona (UAB)
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Oreifej, Omar. "Robust Subspace Estimation Using Low-Rank Optimization. Theory and Applications in Scene Reconstruction, Video Denoising, and Activity Recognition." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5684.

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In this dissertation, we discuss the problem of robust linear subspace estimation using low-rank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time. Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories...etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using low-rank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a two-fold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for low-rank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is ill-posed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the state-of-the-art. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using low-rank optimization. Therefore, we propose a data-driven two-stage approach, where the first stage “sparsifies” the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or de-warping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the problem of simultaneous turbulence mitigation and moving object detection. We propose a novel three-term low-rank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and L1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by L1 norm. Second, since the object's motion is linear and intrinsically different than the Gaussian-like turbulence, a Gaussian-based turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the low-rank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in miss-detections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned difficulties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camera-induced and object-induced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results. Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size ... etc. In this extremely challenging task, high-level features have recently shown a promising direction as in [53, 129], where core low-level events referred to as concepts are annotated and modeled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding high-level features are significantly noisy. In order to address this problem, we propose a novel low-rank formulation, which combines the precisely annotated videos used to train the concepts, with the rich high-level features. Our approach finds a new representation for each event, which is not only low-rank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the high-level features by a significant margin.
Ph.D.
Doctorate
Electrical Engineering and Computing
Engineering and Computer Science
Computer Engineering
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Zhang, Yu. "Investigating Key Techniques to Leverage the Functionality of Ground/Wall Penetrating Radar." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/799.

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Ground penetrating radar (GPR) has been extensively utilized as a highly efficient and non-destructive testing method for infrastructure evaluation, such as highway rebar detection, bridge decks inspection, asphalt pavement monitoring, underground pipe leakage detection, railroad ballast assessment, etc. The focus of this dissertation is to investigate the key techniques to tackle with GPR signal processing from three perspectives: (1) Removing or suppressing the radar clutter signal; (2) Detecting the underground target or the region of interest (RoI) in the GPR image; (3) Imaging the underground target to eliminate or alleviate the feature distortion and reconstructing the shape of the target with good fidelity. In the first part of this dissertation, a low-rank and sparse representation based approach is designed to remove the clutter produced by rough ground surface reflection for impulse radar. In the second part, Hilbert Transform and 2-D Renyi entropy based statistical analysis is explored to improve RoI detection efficiency and to reduce the computational cost for more sophisticated data post-processing. In the third part, a back-projection imaging algorithm is designed for both ground-coupled and air-coupled multistatic GPR configurations. Since the refraction phenomenon at the air-ground interface is considered and the spatial offsets between the transceiver antennas are compensated in this algorithm, the data points collected by receiver antennas in time domain can be accurately mapped back to the spatial domain and the targets can be imaged in the scene space under testing. Experimental results validate that the proposed three-stage cascade signal processing methodologies can improve the performance of GPR system.
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Hrbáček, Radek. "Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-220303.

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This thesis deals with the nuclear magnetic resonance field, especially spectroscopy and spectroscopy imaging, sparse signal representation and low-rank approximation approaches. Spectroscopy imaging methods are becoming very popular in clinical praxis, however, long measurement times and low resolution prevent them from their spreading. The goal of this thesis is to improve state of the art methods by using sparse signal representation and low-rank approximation approaches. The compressed sensing technique is demonstrated on the examples of magnetic resonance imaging speedup and hyperspectral imaging data saving. Then, a new spectroscopy imaging scheme based on compressed sensing is proposed. The thesis deals also with the in vivo spectrum quantitation problem by designing the MRSMP algorithm specifically for this purpose.
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Kolbábková, Anežka. "Algoritmy doplňování chybějících dat v audiosignálech." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231131.

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Tato práce se zabývá doplňováním chybějících dat do audio signálů a algoritmy řešícími problém založenými na řídké reprezentaci audio signálu. Práce se zaměřuje na některé algoritmy, které řeší doplňování chybějících dat do audio signálů pomocí řídké reprezentace signálů. Součástí práce je také návrh algoritmu, který používá řídkou reprezentaci signálu a také nízkou hodnost signálu ve spektrogramu audio signálu. Dále práce uvádí implementaci tohoto algoritmu v programu Matlab a jeho vyhodnocení.
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Liu, Zhenjiao. "Incomplete multi-view data clustering with hidden data mining and fusion techniques." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAS011.

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Le regroupement de données multivues incomplètes est un axe de recherche majeur dans le domaines de l'exploration de données et de l'apprentissage automatique. Dans les applications pratiques, nous sommes souvent confrontés à des situations où seule une partie des données modales peut être obtenue ou lorsqu'il y a des valeurs manquantes. La fusion de données est une méthode clef pour l'exploration d'informations multivues incomplètes. Résoudre le problème de l'extraction d'informations multivues incomplètes de manière ciblée, parvenir à une collaboration flexible entre les vues visibles et les vues cachées partagées, et améliorer la robustesse sont des défis. Cette thèse se concentre sur trois aspects : l'exploration de données cachées, la fusion collaborative et l'amélioration de la robustesse du regroupement. Les principales contributions sont les suivantes:1) Exploration de données cachées pour les données multi-vues incomplètes : les algorithmes existants ne peuvent pas utiliser pleinement l'observation des informations dans et entre les vues, ce qui entraîne la perte d'une grande quantité d'informations. Nous proposons donc un nouveau modèle de regroupement multi-vues incomplet IMC-NLT (Incomplete Multi-view Clustering Based on NMF and Low-Rank Tensor Fusion) basé sur la factorisation de matrices non négatives et la fusion de tenseurs de faible rang. IMC-NLT utilise d'abord un tenseur de faible rang pour conserver les caractéristiques des vues avec une dimension unifiée. En utilisant une mesure de cohérence, IMC-NLT capture une représentation cohérente à travers plusieurs vues. Enfin, IMC-NLT intègre plusieurs apprentissages dans un modèle unifié afin que les informations cachées puissent être extraites efficacement à partir de vues incomplètes. Des expériences sur cinq jeux de données ont validé les performances d'IMC-NLT.2) Fusion collaborative pour les données multivues incomplètes : notre approche pour résoudre ce problème est le regroupement multivues incomplet par représentation à faible rang. L'algorithme est basé sur une représentation éparse de faible rang et une représentation de sous-espace, dans laquelle les données manquantes sont complétées en utilisant les données d'une modalité et les données connexes d'autres modalités. Pour améliorer la stabilité des résultats de clustering pour des données multi-vues avec différents degrés de manquants, CCIM-SLR utilise le modèle Γ-norm, qui est une méthode de représentation à faible rang ajustable. CCIM-SLR peut alterner entre l'apprentissage de la vue cachée partagée, la vue visible et les partitions de clusters au sein d'un cadre d'apprentissage collaboratif. Un algorithme itératif avec convergence garantie est utilisé pour optimiser la fonction objective proposée.3) Amélioration de la robustesse du regroupement pour les données multivues incomplètes : nous proposons une fusion de la convolution graphique et des goulots d'étranglement de l'information (apprentissage de la représentation multivues incomplète via le goulot d'étranglement de l'information). Nous introduisons la théorie du goulot d'étranglement de l'information afin de filtrer les données parasites contenant des détails non pertinents et de ne conserver que les éléments les plus pertinents. Nous intégrons les informations sur la structure du graphe basées sur les points d'ancrage dans les informations sur le graphe local. Le modèle intègre des représentations multiples à l'aide de goulets d'étranglement de l'information, réduisant ainsi l'impact des informations redondantes dans les données. Des expériences approfondies sont menées sur plusieurs ensembles de données du monde réel, et les résultats démontrent la supériorité de IMRL-AGI. Plus précisément, IMRL-AGI montre des améliorations significatives dans la précision du clustering et de la classification, même en présence de taux élevés de données manquantes par vue (par exemple, 10,23 % et 24,1% respectivement sur l'ensemble de données ORL)
Incomplete multi-view data clustering is a research direction that attracts attention in the fields of data mining and machine learning. In practical applications, we often face situations where only part of the modal data can be obtained or there are missing values. Data fusion is an important method for incomplete multi-view information mining. Solving incomplete multi-view information mining in a targeted manner, achieving flexible collaboration between visible views and shared hidden views, and improving the robustness have become quite challenging. This thesis focuses on three aspects: hidden data mining, collaborative fusion, and enhancing the robustness of clustering. The main contributions are as follows:1. Hidden data mining for incomplete multi-view data: existing algorithms cannot make full use of the observation of information within and between views, resulting in the loss of a large amount of valuable information, and so we propose a new incomplete multi-view clustering model IMC-NLT (Incomplete Multi-view Clustering Based on NMF and Low-Rank Tensor Fusion) based on non-negative matrix factorization and low-rank tensor fusion. IMC-NLT first uses a low-rank tensor to retain view features with a unified dimension. Using a consistency measure, IMC-NLT captures a consistent representation across multiple views. Finally, IMC-NLT incorporates multiple learning into a unified model such that hidden information can be extracted effectively from incomplete views. We conducted comprehensive experiments on five real-world datasets to validate the performance of IMC-NLT. The overall experimental results demonstrate that the proposed IMC-NLT performs better than several baseline methods, yielding stable and promising results.2. Collaborative fusion for incomplete multi-view data: our approach to address this issue is Incomplete Multi-view Co-Clustering by Sparse Low-Rank Representation (CCIM-SLR). The algorithm is based on sparse low-rank representation and subspace representation, in which jointly missing data is filled using data within a modality and related data from other modalities. To improve the stability of clustering results for multi-view data with different missing degrees, CCIM-SLR uses the Γ-norm model, which is an adjustable low-rank representation method. CCIM-SLR can alternate between learning the shared hidden view, visible view, and cluster partitions within a co-learning framework. An iterative algorithm with guaranteed convergence is used to optimize the proposed objective function. Compared with other baseline models, CCIM-SLR achieved the best performance in the comprehensive experiments on the five benchmark datasets, particularly on those with varying degrees of incompleteness.3. Enhancing the clustering robustness for incomplete multi-view data: we offer a fusion of graph convolution and information bottlenecks (Incomplete Multi-view Representation Learning Through Anchor Graph-based GCN and Information Bottleneck - IMRL-AGI). First, we introduce the information bottleneck theory to filter out the noise data with irrelevant details and retain only the most relevant feature items. Next, we integrate the graph structure information based on anchor points into the local graph information of the state fused into the shared information representation and the information representation learning process of the local specific view, a process that can balance the robustness of the learned features and improve the robustness. Finally, the model integrates multiple representations with the help of information bottlenecks, reducing the impact of redundant information in the data. Extensive experiments are conducted on several real-world datasets, and the results demonstrate the superiority of IMRL-AGI. Specifically, IMRL-AGI shows significant improvements in clustering and classification accuracy, even in the presence of high view missing rates (e.g. 10.23% and 24.1% respectively on the ORL dataset)
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Mangová, Marie. "Komprimované snímání v perfuzním zobrazování pomocí magnetické rezonance." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231150.

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Magnetic resonance perfusion imaging is a today's very promising method for medicine diagnosis. This thesis deals with a sparse representation of signals, low-rank matrix recovery and compressed sensing, which allows overcoming present physical limitations of magnetic resonance perfusion imaging. Several models for reconstruction of measured perfusion data is introduced and numerical methods for their software implementation, which is an important part of the thesis, is mentioned. Proposed models are verified on simulated and real perfusion data from magnetic resonance.
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Weisbecker, Clément. "Improving multifrontal solvers by means of algebraic Block Low-Rank representations." Phd thesis, Toulouse, INPT, 2013. http://oatao.univ-toulouse.fr/10506/1/weisbecker.pdf.

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We consider the solution of large sparse linear systems by means of direct factorization based on a multifrontal approach. Although numerically robust and easy to use (it only needs algebraic information: the input matrix A and a right-hand side b, even if it can also digest preprocessing strategies based on geometric information), direct factorization methods are computationally intensive both in terms of memory and operations, which limits their scope on very large problems (matrices with up to few hundred millions of equations). This work focuses on exploiting low-rank approximations on multifrontal based direct methods to reduce both the memory footprints and the operation count, in sequential and distributed-memory environments, on a wide class of problems. We first survey the low-rank formats which have been previously developed to efficiently represent dense matrices and have been widely used to design fast solutions of partial differential equations, integral equations and eigenvalue problems. These formats are hierarchical (H and Hierarchically Semiseparable matrices are the most common ones) and have been (both theoretically and practically) shown to substantially decrease the memory and operation requirements for linear algebra computations. However, they impose many structural constraints which can limit their scope and efficiency, especially in the context of general purpose multifrontal solvers. We propose a flat format called Block Low-Rank (BLR) based on a natural blocking of the matrices and explain why it provides all the flexibility needed by a general purpose multifrontal solver in terms of numerical pivoting for stability and parallelism. We compare BLR format with other formats and show that BLR does not compromise much the memory and operation improvements achieved through low-rank approximations. A stability study shows that the approximations are well controlled by an explicit numerical parameter called low-rank threshold, which is critical in order to solve the sparse linear system accurately. Details on how Block Low-Rank factorizations can be efficiently implemented within multifrontal solvers are then given. We propose several Block Low-Rank factorization algorithms which allow for different types of gains. The proposed algorithms have been implemented within the MUMPS (MUltifrontal Massively Parallel Solver) solver. We first report experiments on standard partial differential equations based problems to analyse the main features of our BLR algorithms and to show the potential and flexibility of the approach; a comparison with a Hierarchically SemiSeparable code is also given. Then, Block Low-Rank formats are experimented on large (up to a hundred millions of unknowns) and various problems coming from several industrial applications. We finally illustrate the use of our approach as a preconditioning method for the Conjugate Gradient.
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Teng, Luyao. "Research on Joint Sparse Representation Learning Approaches." Thesis, 2019. https://vuir.vu.edu.au/40024/.

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Dimensionality reduction techniques such as feature extraction and feature selection are critical tools employed in artificial intelligence, machine learning and pattern recognitions tasks. Previous studies of dimensionality reduction have three common problems: 1) The conventional techniques are disturbed by noise data. In the context of determining useful features, the noises may have adverse effects on the result. Given that noises are inevitable, it is essential for dimensionality reduction techniques to be robust from noises. 2) The conventional techniques separate the graph learning system apart from informative feature determination. These techniques used to construct a data structure graph first, and keep the graph unchanged to process the feature extraction or feature selection. Hence, the result of feature extraction or feature selection is strongly relying on the graph constructed. 3) The conventional techniques determine data intrinsic structure with less systematic and partial analyzation. They maintain either the data global structure or the data local manifold structure. As a result, it becomes difficult for one technique to achieve great performance in different datasets. We propose three learning models that overcome prementioned problems for various tasks under different learning environment. Specifically, our research outcomes are listing as followings: 1) We propose a novel learning model that joints Sparse Representation (SR) and Locality Preserving Projection (LPP), named Joint Sparse Representation and Locality Preserving Projection for Feature Extraction (JSRLPP), to extract informative features in the context of unsupervised learning environment. JSRLPP processes the feature extraction and data structure learning simultaneously, and is able to capture both the data global and local structure. The sparse matrix in the model operates directly to deal with different types of noises. We conduct comprehensive experiments and confirm that the proposed learning model performs impressive over the state-of-the-art approaches. 2) We propose a novel learning model that joints SR and Data Residual Relationships (DRR), named Unsupervised Feature Selection with Adaptive Residual Preserving (UFSARP), to select informative features in the context of unsupervised learning environment. Such model does not only reduce disturbance of different types of noise, but also effectively enforces similar samples to have similar reconstruction residuals. Besides, the model carries graph construction and feature determination simultaneously. Experimental results show that the proposed framework improves the effect of feature selection. 3) We propose a novel learning model that joints SR and Low-rank Representation (LRR), named Sparse Representation based Classifier with Low-rank Constraint (SRCLC), to extract informative features in the context of supervised learning environment. When processing the model, the Low-rank Constraint (LRC) regularizes both the within-class structure and between-class structure while the sparse matrix works to handle noises and irrelevant features. With extensive experiments, we confirm that SRLRC achieves impressive improvement over other approaches. To sum up, with the purpose of obtaining appropriate feature subset, we propose three novel learning models in the context of supervised learning and unsupervised learning to complete the tasks of feature extraction and feature selection respectively. Comprehensive experimental results on public databases demonstrate that our models are performing superior over the state-of-the-art approaches.
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Books on the topic "Sparse Low-Rank Representation"

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Dai, Qionghai, and Tsinghua University Tsinghua University Press. Multidimensional Signal Processing: Fast Transform, Sparse Representation, Low Rank Analysis. de Gruyter GmbH, Walter, 2027.

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Dai, Qionghai, and Tsinghua University Tsinghua University Press. Multidimensional Signal Processing: Fast Transform, Sparse Representation, Low Rank Analysis. de Gruyter GmbH, Walter, 2027.

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Dai, Qionghai, and Tsinghua University Tsinghua University Press. Multidimensional Signal Processing: Fast Transform, Sparse Representation, Low Rank Analysis. de Gruyter GmbH, Walter, 2027.

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Book chapters on the topic "Sparse Low-Rank Representation"

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Liu, Guangcan, and Shuicheng Yan. "Latent Low-Rank Representation." In Low-Rank and Sparse Modeling for Visual Analysis, 23–38. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12000-3_2.

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Liu, Guangcan, and Shuicheng Yan. "Scalable Low-Rank Representation." In Low-Rank and Sparse Modeling for Visual Analysis, 39–60. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12000-3_3.

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Li, Jingshan, Caikou Chen, Xielian Hou, and Rong Wang. "Laplacian Regularized Non-negative Sparse Low-Rank Representation Classification." In Biometric Recognition, 683–90. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69923-3_73.

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Kang, Peipei, Xiaozhao Fang, Wei Zhang, Shaohua Teng, Lunke Fei, Yong Xu, and Yubao Zheng. "Supervised Group Sparse Representation via Intra-class Low-Rank Constraint." In Biometric Recognition, 206–13. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97909-0_22.

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Xiao, Shijie, Mingkui Tan, and Dong Xu. "Weighted Block-Sparse Low Rank Representation for Face Clustering in Videos." In Computer Vision – ECCV 2014, 123–38. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10599-4_9.

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Wang, Ziqiang, Yingzhi Ouyang, Weidan Zhu, Bin Sun, and Qiang Liu. "Common Subspace Based Low-Rank and Joint Sparse Representation for Multi-view Face Recognition." In Lecture Notes in Computer Science, 145–56. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-34113-8_13.

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Wang, Zhen-Chang, Jin-Xing Liu, Jun-Liang Shang, Ling-Yun Dai, Chun-Hou Zheng, and Juan Wang. "ARGLRR: An Adjusted Random Walk Graph Regularization Sparse Low-Rank Representation Method for Single-Cell RNA-Sequencing Data Clustering." In Bioinformatics Research and Applications, 126–37. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-23198-8_12.

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Dantas, Cássio F., Jérémy E. Cohen, and Rémi Gribonval. "Learning Fast Dictionaries for Sparse Representations Using Low-Rank Tensor Decompositions." In Latent Variable Analysis and Signal Separation, 456–66. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93764-9_42.

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Wang, Yitang, Tau Fu, Tianci Zhang, and Xueguan Song. "A Denoising Method by Low-Rank and Sparse Representations and Its Application in Tunnel Boring Machine." In Lecture Notes in Electrical Engineering, 565–72. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3171-0_46.

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Conference papers on the topic "Sparse Low-Rank Representation"

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Dao, Minh, Yuanming Suo, Sang Peter Chin, and Trac D. Tran. "Structured sparse representation with low-rank interference." In 2014 48th Asilomar Conference on Signals, Systems and Computers. IEEE, 2014. http://dx.doi.org/10.1109/acssc.2014.7094407.

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Li, Jingshan, Caikou Chen, Xielian Hou, Tianchen Dai, and Rong Wang. "Weighted non-negative sparse low-rank representation classification." In 2017 IEEE 2nd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). IEEE, 2017. http://dx.doi.org/10.1109/iaeac.2017.8054398.

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Zhang, Yongqiang, Daming Shi, Junbin Gao, and Dansong Cheng. "Low-Rank-Sparse Subspace Representation for Robust Regression." In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2017. http://dx.doi.org/10.1109/cvpr.2017.317.

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Zou, Dongqing, Xiaowu Chen, Guangying Cao, and Xiaogang Wang. "Video Matting via Sparse and Low-Rank Representation." In 2015 IEEE International Conference on Computer Vision (ICCV). IEEE, 2015. http://dx.doi.org/10.1109/iccv.2015.183.

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Wang, Boyue, Yongli Hu, Junbin Gao, Yanfeng Sun, and Baocai Yin. "Cascaded Low Rank and Sparse Representation on Grassmann Manifolds." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/382.

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Inspired by low rank representation and sparse subspace clustering acquiring success, ones attempt to simultaneously perform low rank and sparse constraints on the affinity matrix to improve the performance. However, it is just a trade-off between these two constraints. In this paper, we propose a novel Cascaded Low Rank and Sparse Representation (CLRSR) method for subspace clustering, which seeks the sparse expression on the former learned low rank latent representation. To make our proposed method suitable to multi-dimension or imageset data, we extend CLRSR onto Grassmann manifolds. An effective solution and its convergence analysis are also provided. The excellent experimental results demonstrate the proposed method is more robust than other state-of-the-art clustering methods on imageset data.
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Li, Jianwei, Xiaowu Chen, Dongqing Zou, Bo Gao, and Wei Teng. "Conformal and Low-Rank Sparse Representation for Image Restoration." In 2015 IEEE International Conference on Computer Vision (ICCV). IEEE, 2015. http://dx.doi.org/10.1109/iccv.2015.35.

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Huang, Libo, Bingo Wing-Kuen Ling, Yan Zeng, and Lu Gan. "Spike Sorting Based On Low-Rank And Sparse Representation." In 2020 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2020. http://dx.doi.org/10.1109/icme46284.2020.9102837.

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Sun, Jing, Zongze Wu, Deyu Zeng, and Zhigang Ren. "A New Representation for Data: Sparse and Low-Rank." In 2018 Chinese Automation Congress (CAC). IEEE, 2018. http://dx.doi.org/10.1109/cac.2018.8623248.

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Li, Tao, Weiwei Wang, Long Xu, and Xiangchu Feng. "Image Denoising Using Low-Rank Dictionary and Sparse Representation." In 2014 Tenth International Conference on Computational Intelligence and Security (CIS). IEEE, 2014. http://dx.doi.org/10.1109/cis.2014.56.

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Zhu, Yanping, Aimin Jiang, Xiaofeng Liu, and Hon Keung Kwan. "Sparse representation and low-rank approximation for sensor signal processing." In 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE). IEEE, 2017. http://dx.doi.org/10.1109/ccece.2017.7946701.

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