Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization for Hyperspectral Image Classification

Low-Rank and Sparse Representation(LRSR)method has gained popularity in Hyperspectral Image(HSI)processing.However,existing LRSR models rarely exploited spectral-spatial classification of HSI.In this paper,we proposed a novel Low-Rank and Sparse Representation with Adaptive Neighborhood Regularization(LRSR-ANR)method for HSI classification.In the proposed method,we first represent the hyperspectral data via LRSR since it combines both sparsity and low-rankness to maintain global and local data structures simultaneously.The LRSR is optimized by using a mixed Gauss-Seidel and Jacobian Alternating Direction Method of Multipliers(M-ADMM),which converges faster than ADMM.Then to incorporate the spatial information,an ANR scheme is designed by combining Euclidean and Cosine distance metrics to reduce the mixed pixels within a neighborhood.Lastly,the predicted labels are determined by jointly considering the homogeneous pixels in the classification rule of the minimum reconstruction error.Experimental results based on three popular hyperspectral images demonstrate that the proposed method outperforms other related methods in terms of classification accuracy and generalization performance.

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.

Low-Rank Sparse Representation with Pre-Learned Dictionaries and Side Information for Singing Voice Separation

At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorithm called Low-rank, Sparse Representation with pre-learned dictionaries and side Information (LSRi). The algorithm incorporates both the vocal and instrumental spectrograms as sparse matrix and low-rank matrix, meanwhile combines pre-learning dictionary and the reconstructed voice spectrogram form the annotation. Evaluations on the iKala dataset show that the proposed methods are effective and efficient for singing voice separation.

Extraction method of typical IEQ spatial distributions based on low-rank sparse representation and multi-step clustering

Indoor environment quality(IEQ)is one of the most concerned building performances during the operation stage.The non-uniform spatial distribution of various IEQ parameters in large-scale public buildings has been demonstrated to be an essential factor affecting occupant comfort and building energy consumption.Currently,IEQ sensors have been widely employed in buildings to monitor thermal,visual,acoustic and air quality.However,there is a lack of effective methods for exploring the typical spatial distribution of indoor environmental quality parameters,which is crucial for assessing and controlling non-uniform indoor environments.In this study,a novel clustering method for extracting IEQ spatial distribution patterns is proposed.Firstly,representation vectors reflecting IEQ distributions in the concerned space are generated based on the low-rank sparse representation.Secondly,a multi-step clustering method,which addressed the problems of the“curse of dimensionality”,is designed to obtain typical IEQ distribution patterns of the entire indoor space.The proposed method was applied to the analysis of indoor thermal environment in Beijing Daxing international airport terminal.As a result,four typical temperature spatial distribution patterns of the terminal were extracted from a four-month monitoring,which had been validated for their good representativeness.These typical patterns revealed typical environmental issues in the terminal,such as long-term localized overheating and temperature increases due to a sudden influx of people.The extracted typical IEQ spatial distribution patterns could assist building operators in effectively assessing the uneven distribution of IEQ space under current environmental conditions,facilitating targeted environmental improvements,optimization of thermal comfort levels,and application of energy-saving measures.

Weighted Sparse Image Classification Based on Low Rank Representation

The conventional sparse representation-based image classification usually codes the samples independently,which will ignore the correlation information existed in the data.Hence,if we can explore the correlation information hidden in the data,the classification result will be improved significantly.To this end,in this paper,a novel weighted supervised spare coding method is proposed to address the image classification problem.The proposed method firstly explores the structural information sufficiently hidden in the data based on the low rank representation.And then,it introduced the extracted structural information to a novel weighted sparse representation model to code the samples in a supervised way.Experimental results show that the proposed method is superiority to many conventional image classification methods.

Truncated sparse approximation property and truncated q-norm minimization

This paper considers approximately sparse signal and low-rank matrix’s recovery via truncated norm minimization minx∥xT∥q and minX∥XT∥Sq from noisy measurements.We first introduce truncated sparse approximation property,a more general robust null space property,and establish the stable recovery of signals and matrices under the truncated sparse approximation property.We also explore the relationship between the restricted isometry property and truncated sparse approximation property.And we also prove that if a measurement matrix A or linear map A satisfies truncated sparse approximation property of order k,then the first inequality in restricted isometry property of order k and of order 2k can hold for certain different constantsδk andδ2k,respectively.Last,we show that ifδs(k+|T^c|)<√(s-1)/s for some s≥4/3,then measurement matrix A and linear map A satisfy truncated sparse approximation property of order k.It should be pointed out that when Tc=Ф,our conclusion implies that sparse approximation property of order k is weaker than restricted isometry property of order sk.

Nonlocally Centralized Simultaneous Sparse Coding

The concept of structured sparse coding noise is introduced to exploit the spatial correlations and nonlocal constraint of the local structure. Then the model of nonlocally centralized simultaneous sparse coding(NCSSC)is proposed for reconstructing the original image, and an algorithm is proposed to transform the simultaneous sparse coding into reweighted low-rank approximation. Experimental results on image denoisng, deblurring and super-resolution demonstrate the advantage of the proposed NC-SSC method over the state-of-the-art image restoration methods.

Sparse and Low-Rank Covariance Matrix Estimation

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices.We first benefit from a convex optimization which develops l1-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property.For the proposed estimator,we then prove that with high probability,the Frobenius norm of the estimation rate can be of order O(√((slgg p)/n))under a mild case,where s and p denote the number of nonzero entries and the dimension of the population covariance,respectively and n notes the sample capacity.Finally,an efficient alternating direction method of multipliers with global convergence is proposed to tackle this problem,and merits of the approach are also illustrated by practicing numerical simulations.

Convex Relaxation Algorithm for a Structured Simultaneous Low-Rank and Sparse Recovery Problem

This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=0.For this class of NP-hard problems,we propose a convex relaxation algorithm by applying the accelerated proximal gradient method to a convex relaxation model,which is yielded by the smoothed nuclear norm and the weighted l1-norm regularized least squares problem.A theoretical guarantee is provided by establishing the error bounds of the iterates to the true solution under mild restricted strong convexity conditions.To the best of our knowledge,this work is the first one to characterize the error bound of the iterates of the algorithm to the true solution.Finally,numerical results are reported for some random test problems and synthetic data in subspace clustering to verify the efficiency of the proposed convex relaxation algorithm.

基于稀疏超完备表示的目标检测算法

基于视觉超完备机制的图像稀疏表示是一种新的图像表征方法。针对目标检测问题,提出了一种基于视觉稀疏超完备表示的计算模型,实现了非结构化场景中的目标检测。该方法首先基于能量模型和评分匹配(score matching)方法建立稀疏超完备计算模型,进而设计了基于神经元响应以及动态阈值策略的目标检测算法,最后通过多类型交通图像验证算法有效性。结果表明,该方法与计算机视觉方法比较具有较高的准确率,能够利用少样本实现大交通流量中目标的检测。

基于低秩稀疏评分的非监督特征选择

在处理高维数据过程中,特征选择是一个非常重要的数据降维步骤。低秩表示模型具有揭示数据全局结构信息的能力和一定的鉴别能力。稀疏表示模型能够利用较少的连接关系揭示数据的本质结构信息。在低秩表示模型的基础上引入稀疏约束项,构建一种低秩稀疏表示模型学习数据间的低秩稀疏相似度矩阵;基于该矩阵提出一种低秩稀疏评分机制用于非监督特征选择。在不同数据库上将选择后的特征进行聚类和分类实验,同传统特征选择算法进行比较。实验结果表明了低秩特征选择算法的有效性。

结合评分比例因子及项目属性的协同过滤算法

针对传统的协同过滤算法存在用户评分矩阵稀疏及未考虑项目属性之间关系的问题,提出了结合评分比例因子及项目属性的协同过滤算法。首先利用评分矩阵得出项目之间的共同与非共同评分用户数量比矩阵,以此增加项目共同评分用户的影响度,减少用户—项目评分矩阵的稀疏性对项目相似度计算带来的误差;然后对项目属性量化得出其对项目相似度的影响权重,提高项目相似度计算的准确性,根据以上两点提出了一种结合评分比例因子及项目属性权重作为项目相似度权重的算法。实验结果表明,该算法在召回率和准确率上相比现有的方法分别提高了5.1%和4.7%,适用于电商类网站的个性化推荐。

基于组合优化理论的协同过滤推荐算法

针对传统推荐系统中的协同过滤推荐算法无法解决数据间的高度稀疏问题,采用余弦相似性度量运算的物品相似性误差较高,导致系统推荐质量降低,提出基于局部组合优化的协同过滤推荐算法,其改进了物品间相似性的运算,为了解决数据稀疏性问题,选择目标的近邻对象时利用局部优化方法选择推荐群,降低了预测的误差,确保误差值收敛到某固定值,并采用基于内容的方法调整协同过滤预测存在的异常预测结果。实验结果表明,所提算法抑制了数据稀疏性的不利影响,提高了协同过滤预测评分的准确度。

考试评分缺失数据的概化理论分析

考试评分缺失数据较为常见,如何有效利用现有数据进行统计分析是个关键性问题。在考试评分中,题目与评分者对试卷得分的影响不容忽视。根据概化理论原理,按考试评分规则推导出含有缺失数据双侧面交叉设计(p×i×r)方差分量估计公式,用Matlab7.0软件模拟多组缺失数据,验证此公式的有效性。结果发现:(1)推导出的公式较为可靠,估计缺失数据的方差分量偏差相对较小,即便数据缺失率达到50%以上,公式仍能对方差分量进行较为准确地估计;(2)题目数量对概化理论缺失数据方差分量的估计影响最大,评分者次之,当题目数量和评价者数量分别为6和5时,公式能够趋于稳定地估计;(3)学生数量对各方差分量的估计影响较小,无论是小规模考试还是大规模考试,概化理论估计缺失数据的多个方差分量结果相差不大。

不同波型电针治疗恢复期周围性面瘫疗效观察

目的观察不同频率电针治疗恢复期周围性面瘫的临床疗效。方法将94例恢复期周围性面瘫患者随机分为治疗1组22例、治疗2组25例、治疗3组23例和对照组24例。各组取穴相同,治疗1组采用连续波电针,治疗2组采用疏密波电针,治疗3组采用断续波电针,对照组采用单纯针刺。隔日治疗1次,5次为1个疗程。观察各组治疗前及治疗1、3个月后Sunnybrook面神经评分变化情况,并比较各组临床疗效。结果治疗1组、治疗2组、治疗3组的总有效率分别为86.4%、88.0%、82.6%,对照组为62.5%,各治疗组总有效率与对照组比较,差异均具有统计学意义(P<0.05);各治疗组组间总有效率比较,差异均无统计学意义(P>0.05)。各治疗组治疗1、3个月后Sunnybrook评分与同组治疗前比较,差异均具有统计学意义(P<0.05);各治疗组治疗1、3个月后Sunnybrook评分与对照组比较,差异均具有统计学意义(P<0.05)。治疗3组治疗1个月后Sunnybrook评分与治疗1组和治疗2组比较,差异均具有统计学意义(P<0.05)。结论不同电针治疗恢复期周围性面瘫均具有显著的临床疗效,且断续波在恢复期早期对面肌功能恢复更有优势。

融合用户偏好和物品相似度的概率矩阵分解推荐算法

传统的概率矩阵分解算法虽然较好的解决了推荐系统中的用户数据稀疏性问题,但是没有同时考虑到用户之间的关系及物品之间的关系,导致用户物品评分预测准确性仍然不高.本文利用用户物品评分数据及物品信息提出了融合用户偏好和物品相似度的概率矩阵分解推荐算法UPIS-PMF(Probability Matrix Factorization Recommendation Algorithm Combining User Preferences and Item Similarity).首先根据用户评分数据计算用户之间的偏好相似度,得到用户相似度矩阵,再利用物品标签关联度数据和物品流行度数据计算物品相似度,得到物品相似度矩阵,最后将用户相似度矩阵,物品相似度矩阵及用户物品评分矩阵融入概率矩阵分解模型中进行评分预测,Movielens数据集中的实验表明该算法在评分预测准确性方面优于传统的推荐算法,同时也说明了在概率矩阵分解模型中融合用户信息或者物品信息均可以提高评分预测的准确性.

基于用户行为序列的概率矩阵分解推荐算法

传统的概率矩阵分解在推荐算法中取得了一定的效果,但是仍然面临数据稀疏性问题,并且对数据的利用效率不高,不能根据已有数据准确计算用户(物品)之间的关系,评分预测准确性仍然有待提高.本文利用用户对物品的评分序列信息充分挖掘用户(物品)之间的相似度关系,提出了基于用户行为序列的概率矩阵分解推荐算法UBS-PMF(Probability Matrix Factorization Recommendation Algorithm Based on User Behavior Sequence).首先根据用户对物品的评分序列和物品标签信息计算用户对标签的评分序列,即为用户的偏好转移序列,根据该序列可以计算出用户之间的相似度矩阵,同时,用户对物品的评分序列也隐藏着物品之间的关系,利用多个用户对物品的评分序列可以得到物品相似度矩阵,将所得用户(物品)相似度矩阵融入概率矩阵分解模型中进行评分预测,Movielens数据集中的实验表明该算法具有显著的效果,在评分预测准确性方面优于传统的推荐算法.