稀疏约束非负矩阵分解方法及其应用研究

发布时间：2018-02-06 07:38

本文关键词： 稀疏约束非负矩阵分解乘性迭代规则正交投影非负矩阵分解交替方向乘子法语音增强目标跟踪　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】："互联网+"时代,信息的数量呈现爆炸式增长,而且信息维度也愈来愈大,如何处理这些海量高维数据是当前科学研究的热点问题之一。基于稀疏约束的非负矩阵分解方法不仅拥有普通非负矩阵分解的非负特性,使得分解结果有直观的物理意义,而且还可以对数据产生稀疏的表示,挖掘数据背后隐含的模式或特征,便于数据的存储和分析。稀疏非负矩阵分解技术已广泛应用于计算机视觉、语音识别、文本聚类、网络安全、生物医学工程等诸多领域,特别是在大规模数据处理任务中具有重要的理论意义和应用价值。本文主要研究带稀疏约束的非负矩阵分解方法,主要的研究内容如下:(1)基于L_(1/2)范数约束的稀疏卷积非负矩阵分解方法在L_q范数约束的基础上,提出一种基于L1/2范数的稀疏约束卷积非负矩阵分解方法,给出了一种基于乘性迭代规则的求解算法,并对收敛性进行分析。该方法利用欧式距离衡量分解误差,使用稀疏性更强的L1/2范数对分解系数进行稀疏约束。基于上述方法,本文还提出了一种基于L1/2稀疏约束卷积非负矩阵分解的单通道语音增强模型。该模型在刻画语音基的帧间相关性和在信号稀疏表示方面具有明显优势。在语音增强过程中,该模型先对噪声进行非负矩阵分解得到噪声基,以此作为先验信息用于含噪语音的稀疏约束卷积非负矩阵分解中,并利用分解后的语音基和相应系数重建干净语音。实验结果表明该方法分解后得到的语音基含有噪声成分更少,相比传统的语音增强方法,该模型重建后语音的可懂度有所提高。(2)正交投影非负矩阵的交替方向乘子分解方法本文提出一种基于交替方向乘子的正交投影非负矩阵分解方法。在普通非负矩阵分解方法中引入基矩阵正交和投影约束后,得到正交投影非负矩阵分解方法。正交约束可减少基向量之间的相关性,从而得到稀疏性更强的基向量。同时,针对基于乘性规则的传统求解算法收敛速度慢等问题,本文提出一种基于交替方向乘子的优化方法,比传统的乘性更新规则收敛更快、更稳定。仿真实验结果表明基于交替方向乘子的求解方法比乘性迭代规则在收敛精度和速度上均有优势,特别是在大规模数据条件下,处理速率明显加快。本文将该方法应用于目标跟踪问题的模板更新中,实验结果表明该方法不仅可以提高跟踪速度,还能得到稀疏性更好的候选模板,有效地处理目标跟踪中模板的噪声问题。
[Abstract]:In the era of "Internet", the quantity of information is increasing explosively, and the dimension of information is becoming larger and larger. How to deal with these massive high-dimensional data is one of the hot issues in current scientific research. The non-negative matrix decomposition method based on sparse constraints not only has the non-negative characteristics of ordinary non-negative matrix decomposition. The decomposition results have intuitive physical significance, but also can produce sparse representation of the data, mining the hidden patterns or characteristics behind the data. Sparse non-negative matrix decomposition technology has been widely used in computer vision, speech recognition, text clustering, network security, biomedical engineering and many other fields. Especially in the large-scale data processing task has important theoretical significance and application value. This paper mainly studies the non-negative matrix decomposition method with sparse constraints. The main research contents are as follows: 1: 1) the sparse convolution nonnegative matrix decomposition method based on L / S 1 / 2) norm constraint is based on the L _ S _ Q norm constraint. A sparse constrained convolution nonnegative matrix decomposition method based on L 1 / 2 norm is proposed, and an algorithm based on multiplicative iterative rules is presented. The method uses Euclidean distance to measure the decomposition error and uses the more sparse L 1 / 2 norm to constrain the decomposition coefficient. This paper also proposes a single channel speech enhancement model based on L 1 / 2 sparse constrained convolution nonnegative matrix factorization. The model has obvious advantages in describing the inter-frame correlation of speech bases and in signal sparse representation. Speech enhancement. The noise base is obtained by non-negative matrix decomposition of noise, which is used as prior information in sparse constrained convolution nonnegative matrix decomposition of noisy speech. The experimental results show that the speech base obtained by this method contains less noise than the traditional speech enhancement method. The intelligibility of the reconstructed speech is improved. In this paper, a method of orthogonal projection nonnegative matrix decomposition based on alternating direction multiplier is proposed. The orthogonal matrix and projection reduction of base matrix are introduced in the ordinary nonnegative matrix decomposition method. Back. The orthogonal projection nonnegative matrix decomposition method is obtained. The orthogonal constraints can reduce the correlation between the basis vectors and obtain more sparse basis vectors. At the same time. In view of the slow convergence speed of the traditional algorithm based on multiplicative rules, this paper proposes an optimization method based on alternating direction multipliers, which converges faster than the traditional multiplicative updating rules. The simulation results show that the method based on alternating direction multiplier has more advantages in convergence accuracy and speed than the multiplicative iterative rule, especially under the condition of large scale data. This method is applied to the template updating of target tracking problem. The experimental results show that this method can not only improve the tracking speed, but also obtain a more sparse candidate template. The problem of template noise in target tracking is effectively dealt with.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21

【相似文献】