基于非平滑非负矩阵分解语音增强

针对非负矩阵分解稀疏性不够,通过引入平滑矩阵调节字典矩阵和系数矩阵的稀疏性,提出基于非平滑非负矩阵分解语音增强算法。算法通过语音和噪声的先验字典学习构造联合字典矩阵;然后通过非平滑非负矩阵分解更新带噪语音在联合字典矩阵下的投影系数实现语音增强;同时通过滑动窗口法实时更新先验噪声字典。仿真结果表明,该算法相对非负矩阵分解语音增强算法和MMSE算法具有更好的抑制噪声能力。     

基于图正则化和稀疏约束的半监督非负矩阵分解

非负矩阵分解是在矩阵非负约束下的分解算法。为了提高识别率,提出了一种基于稀疏约束和图正则化的半监督非负矩阵分解方法。该方法对样本数据进行低维非负分解时,既保持数据的几何结构,又利用已知样本的标签信息进行半监督学习,而且对基矩阵施加稀疏性约束,最后将它们整合于单个目标函数中。构造了一个有效的更新算法,并且在理论上证明了该算法的收敛性。在多个人脸数据库上的仿真结果表明,相对于NMF、GNMF、CNMF等算法,GCNMFS具有更好的聚类精度和稀疏性。     

采用稀疏和平滑双约束的增量正交映射非负矩阵分解目标跟踪

针对目标跟踪在遮挡和尺度变化等复杂背景下跟踪性能下降问题,联合稀疏约束、时间平滑约束以及增量投影非负矩阵分解,提出一种在线目标跟踪算法.首先利用非负矩阵分解学习一个基于部分表示的子空间,在此基础上添加稀疏约束提高处理遮挡能力,添加时间平滑约束提高算法的稳定性;然后用增量方式完成子空间的在线更新,减少算法计算量、提高外观模型更新效率;最后在粒子滤波框架下,以重构误差为基础改进了观测似然函数,将具有最大后验概率的候选目标作为目标在当前帧的图像区域.实验结果表明,在各种含有遮挡和尺度变化的视频中,该算法可以更稳定地跟踪目标.     

稀疏正则非负矩阵分解的语音增强算法

对于非负矩阵分解的语音增强算法在不同环境噪声的鲁棒性问题,提出一种稀疏正则非负矩阵分解（SRNMF）的语音增强算法。该算法不仅考虑到数据处理时的噪声影响,而且对系数矩阵进行了稀疏约束,使其分解出的数据具有较好的语音特征。该算法首先在对语音和噪声的幅度谱先验字典矩阵学习的基础上,构建联合字典矩阵,然后更新带噪语音幅度谱在联合字典矩阵下的系数矩阵,最后重构原始纯净语音,实现语音增强。实验结果表明,在非平稳噪声和低信噪比（小于0 dB）条件下,该算法较好地削弱了噪声的变化对算法性能的影响,不仅有较高的信源失真率（SDR）,提高了1~1.5个数量级,而且运算速度也有一定程度的提高,使得基于非负矩阵分解的语音增强算法更实用。     

稀疏约束图正则非负矩阵分解

非负矩阵分解(NMF)是在矩阵非负约束下的一种局部特征提取算法。为了提高识别率,提出了稀疏约束图正则非负矩阵分解方法。该方法不仅考虑数据的几何信息,而且对系数矩阵进行稀疏约束,并将它们整合于单个目标函数中。构造了一个有效的乘积更新算法,并且在理论上证明了该算法的收敛性。在ORL和MIT-CBCL人脸数据库上的实验表明了该算法的有效性。     

L1范数约束正交子空间非负矩阵分解

针对非负矩阵分解（NMF）相对稀疏或局部化描述原数据时导致的稀疏能力和程度比较弱的问题,提出了L1范数约束正交子空间非负矩阵分解方法.通过将L1范数约束引入到正交子空间非负矩阵分解的目标函数中,提升了分解结果的稀疏性.同时给出累乘迭代规则.在UCI、ORL和Yale三个数据库上进行的实验结果表明,该算法在聚类效果以及稀疏表达方面优于其他算法.     

线性投影非负矩阵分解方法及应用

针对线性投影结构非负矩阵分解迭代方法比较复杂的问题,提出了一种线性投影非负矩阵分解方法.从投影和线性变换角度出发,将Frobenius范数作为目标函数,利用泰勒展开式,严格导出基矩阵和线性变换矩阵的迭代算法,并证明了算法的收敛性.实验结果表明:该算法是收敛的;相对于非负矩阵分解等方法,该方法的基矩阵具有更好的正交性和稀疏性;人脸识别结果说明该方法具有较高的识别率.线性投影非负矩阵分解方法是有效的.     

基于图正则化和稀疏约束的增量型非负矩阵分解

非负矩阵分解(Nonnegative Matrix Factorization,NMF)不仅可以很好地描述数据而且分解后的矩阵具有直观的物理意义。为了提高算法的有效性和识别率,提出了一种更为合理的算法——基于图正则化和稀疏约束的增量型非负矩阵分解(Graph Regularized and Incremental Nonnegative Matrix Factorization with Sparseness Constraints,GINMFSC)。该算法既保持了数据的几何结构,又充分利用上一步的分解结果进行增量学习,而且对系数矩阵施加了稀疏性约束,最后将它们整合于单个目标函数中,构造了一个有效的更新算法。在多个数据库上的仿真结果表明,相对于NMF,GNMF,INMF,IGNMF等算法,GINMFSC算法在降低运算时间的同时,还具有更好的聚类精度和稀疏性。     

用于超分辨率重建的同构过完备字典学习方法

构造合适的过完备字典是基于稀疏表示的超分辨率重建中的关键问题之一。在最大似然估计准则下,建立基于混合高斯的同构过完备字典学习模型。模型采用加权的l2范数来刻画分解残差,由分解残差设计权值矩阵,并且将同构的双字典学习问题转化为单字典的学习。采用稀疏编码和字典更新的交替迭代策略完成目标函数的求解,由内点法进行稀疏编码,采用拉格朗日对偶法完成字典更新。最后将学习得到的字典用于超分辨率重建实验,并与其他方法进行比较。实验结果验证了该模型和算法的有效性。     

ADMM稀疏非负矩阵分解语音增强算法

提出一种基于交替方向乘子法的（Alternating Direction Method of Multipliers,ADMM）稀疏非负矩阵分解语音增强算法,该算法既能克服经典非负矩阵分解（Nonnegative Matrix Factorization,NMF）语音增强算法存在收敛速度慢、易陷入局部最优等问题,也能发挥ADMM分解矩阵具有的强稀疏性。算法分为训练和增强两个阶段：训练时,采用基于ADMM非负矩阵分解算法对噪声频谱进行训练,提取噪声字典,保存其作为增强阶段的先验信息;增强时,通过稀疏非负矩阵分解算法,从带噪语音频谱中对语音字典和语音编码进行估计,重构原始干净的语音,实现语音增强。实验表明,该算法速度更快,增强后语音的失真更小,尤其在瞬时噪声环境下效果显著。     

Sparse representation for robust abnormality detection in crowded scenes

In crowded scenes, the extracted low-level features, such as optical flow or spatio-temporal interest point, are inevitably noisy and uncertainty. In this paper, we propose a fully unsupervised non-negative sparse coding based approach for abnormality event detection in crowded scenes, which is specifically tailored to cope with feature noisy and uncertainty. The abnormality of query sample is decided by the sparse reconstruction cost from an atomically learned event dictionary, which forms a sparse coding bases. In our algorithm, we formulate the task of dictionary learning as a non-negative matrix factorization (NMF) problem with a sparsity constraint. We take the robust Earth Mover's Distance (EMD), instead of traditional Euclidean distance, as distance metric reconstruction cost function. To reduce the computation complexity of EMD, an approximate EMD, namely wavelet EMD, is introduced and well combined into our approach, without losing performance. In addition, the combination of wavelet EMD with our approach guarantees the convexity of optimization in dictionary learning. To handle both local abnormality detection (LAD) and global abnormality detection, we adopt two different types of spatio-temporal basis. Experiments conducted on four public available datasets demonstrate the promising performance of our work against the state-of-the-art methods.     

应用稀疏约束的非负正则矩阵学习算法

针对非负矩阵分解后的数据稀疏性较低,训练样本偏多导致运算规模持续增大的普遍现象,本文提出基于稀疏约束的非负正则矩阵学习算法,本文算法是在样本几何结构信息条件上执行非负矩阵分解操作,并且与学习算法结合,不仅能够有效保持样本局部结构,还能够充分利用前期分解结果参加迭代运算,从而达到降低运算时间目的. 本文实验表明与其他算法比较来说,本文方法在ORL人脸数据库上最多节省时间14.84 s,在COIL20数据集上为136.1 s;而在分解后数据的稀疏性上,本文方法在ORL人脸数据库上的稀疏度提高0.0691,在COIL20数据集上为0.0587. 实验结果表明了算法有效性.     

基于Fisher判别分析的增量式非负矩阵分解算法

增量式非负矩阵分解算法是基于子空间降维技术的无监督增量学习方法.文中将Fisher判别分析思想引入增量式非负矩阵分解中,提出基于Fisher判别分析的增量式非负矩阵分解算法.首先,利用初始样本训练的先验信息,通过索引矩阵对新增系数矩阵进行初始化赋值.然后,将增量式非负矩阵分解算法的目标函数改进为批量式的增量学习算法,在此基础上施加类间散度最大和类内散度最小的约束.最后,采用乘性迭代的方法计算分解后的因子矩阵.在ORL、Yale B和PIE等3个不同规模人脸数据库上的实验验证文中算法的有效性.     

双层非负矩阵分解的分形图像压缩算法

分形图像压缩作为一种基于结构的图像压缩技术,在许多图像处理中得到了应用.但是分形图像压缩的编码阶段非常耗时,且重建图像的质量效果不佳.针对这些问题,提出了一种基于双层非负矩阵分解的分形图像压缩编码算法.在传统的非负矩阵分解理论上,将投影非负矩阵分解与L3/2范数约束相结合,可以在较短的时间内提取具有代表性的图像特征.算...     

非负子空间聚类指导下的非负矩阵分解

非负矩阵分解作为一种有效的数据表示方法被广泛应用于模式识别和机器学习领域。为了得到原始数据紧致有效的低维数据表示,无监督非负矩阵分解方法在特征降维的过程中通常需要同时发掘数据内部隐含的几何结构信息。通过合理建模数据样本间的相似性关系而构建的相似度图,通常被用来捕获数据样本的空间分布结构信息。子空间聚类可以有效发掘数据内部的子空间结构信息,其获得的自表达系数矩阵可用于构建相似度图。该文提出了一种非负子空间聚类算法来发掘数据的子空间结构信息,同时利用该信息指导非负矩阵分解,从而得到原始数据有效的非负低维表示。同时,该文还提出了一种有效的迭代求解方法来求解非负子空间聚类问题。在两个图像数据集上的聚类实验结果表明,利用数据的子空间结构信息可以有效改善非负矩阵分解的性能。     

A sparse kernel algorithm for online time series data prediction

Kernel based methods have been widely applied for signal analysis and processing. In this paper, we propose a sparse kernel based algorithm for online time series prediction. In classical kernel methods, the kernel function number is very large which makes them of a high computational cost and only applicable for off-line or batch learning. In online learning settings, the learning system is updated when each training sample is obtained and it requires a higher computational speed. To make the kernel methods suitable for online learning, we propose a sparsification method based on the Hessian matrix of the system loss function to continuously examine the significance of the new training sample in order to select a sparse dictionary (support vector set). The Hessian matrix is equivalent to the correlation matrix of sample inputs in the kernel weight updating using the recursive least square (RLS) algorithm. This makes the algorithm able to be easily implemented with an affordable computational cost for real-time applications. Experimental results show the ability of the proposed algorithm for both real-world and artificial time series data forecasting and prediction.     

Robust non-negative matrix factorization via joint sparse and graph regularization for transfer learning

In real-world applications, we often have to deal with some high-dimensional, sparse, noisy, and non-independent identically distributed data. In this paper, we aim to handle this kind of complex data in a transfer learning framework, and propose a robust non-negative matrix factorization via joint sparse and graph regularization model for transfer learning. First, we employ robust non-negative matrix factorization via sparse regularization model (RSNMF) to handle source domain data and then learn a meaningful matrix, which contains much common information between source domain and target domain data. Second, we treat this learned matrix as a bridge and transfer it to target domain. Target domain data are reconstructed by our robust non-negative matrix factorization via joint sparse and graph regularization model (RSGNMF). Third, we employ feature selection technique on new sparse represented target data. Fourth, we provide novel efficient iterative algorithms for RSNMF model and RSGNMF model and also give rigorous convergence and correctness analysis separately. Finally, experimental results on both text and image data sets demonstrate that our REGTL model outperforms existing start-of-art methods.     

A sparse neighborhood preserving non-negative tensor factorization algorithm for facial expression recognition

In this paper, a novel sparse neighborhood preserving non-negative tensor factorization (SNPNTF) algorithm is proposed for facial expression recognition. It is derived from non-negative tensor factorization (NTF), and it works in the rank-one tensor space. A sparse constraint is adopted into the objective function, which takes the optimization step in the direction of the negative gradient, and then projects onto the sparse constrained space. To consider the spatial neighborhood structure and the class-based discriminant information, a neighborhood preserving constraint is adopted based on the manifold learning and graph preserving theory. The Laplacian graph which encodes the spatial information in the face samples and the penalty graph which considers the pre-defined class information are considered in this constraint. By using it, the obtained parts-based representations of SNPNTF vary smoothly along the geodesics of the data manifold and they are more discriminant for recognition. SNPNTF is a quadratic convex function in the tensor space, and it could converge to the optimal solution. The gradient descent method is used for the optimization of SNPNTF to ensure the convergence property. Experiments are conducted on the JAFFE database, the Cohn–Kanade database and the AR database. The results demonstrate that SNPNTF provides effective facial representations and achieves better recognition performance, compared with non-negative matrix factorization, NTF and some variant algorithms. Also, the convergence property of SNPNTF is well guaranteed.     

A group interest-based collaborative filtering algorithm for multimedia information

This paper proposes a collaborative filtering algorithm based on user group interest. A novel co-clustering method (BalClust) and various weighted non-negative matrix factorization algorithms are used in the proposed method. The BalClust method is used to divide the raw rating matrix into clusters, which are smaller than the original matrix. Then, the balance factor is introduced to consider the user weight and the item-based CF (collaborative filtering). To predict the rating of the unknown items in the cluster, the non-negative matrix factorization algorithm was used. The proposed method achieves higher predicting accuracy and efficiency on low dimensional and homogeneous sub-matrices, and the method also reduces the computational complexity by combining the user and item-based CF. Based on the proposed method, this paper proposed an incremental learning method to ensure data accuracy and timeliness to overcome the problem brought by data updates. The experimental results show the proposed methods outperformed traditional CF algorithms, and the completion time is reduced.