摘要
大多数现有的高维图像、视频数据,一般本身就具有天然的张量结构,或者可以被组织成张量结构。张量结构具有良好的表达能力和计算特性,为此本文在总结和继承前人的研究成果的基础上,对基于张量的相关算法进行了研究,主要研究内容如下：
(1)提出了图像内容相关的支持张量机分类器初始化方法。传统的支持张量机初始化方法以及非负矩阵降维方法均采用随机初始化方式,这种方法的缺点体现在两个方面：一方面,在没有数据的情况下,需要假定其分布,比如高斯分布,均匀分布等,这些分布的参数也很难假定,只能通过对测试数据多次验证的方式来确定；另一方面,采用随机初始化的方式很难捕获到图像本身的特性,所以随机方式会最终影响到分类器的分类结果以及降维结果的有效性。
本文针对这两种随机初始化问题,提出图像内容相关的初始化方法,利用图像内容初始化支持张量机及非负矩阵分解方法。首先将支持张量机所要处理的数据构造成张量形式,对每幅图像,构造三阶图像特征张量,将图像集合构造成四阶张量。其次,提出了一种加权高阶奇异值分解算法对支持张量机进行初始化,该方法结合图谱理论与流形学习算法,利用图像数据集对支持张量机初始化,避免了随机性对分类器的影响。接着,对于子空问降维方法,本文选用非负矩阵分解方法对三阶图像特征张量进行降维,提出了基于二维主成分分析的方法初始化非负矩阵分解方法,充分利用了图像内容相关信息。最后,对输入支持张量机的数据,利用改进的非负矩阵分解算法进行降维,在该降维后的子空间中对支持张量机进行训练,利用该降维方法与改进的支持张量机分类器相结合进行图像分类。实验表明,与其他相关算法相比,本文所提方法分类结果较好。
(2)提出了一种基于图和低秩表示的非负张量分解算法。指出如果在图像处理领域中对图像数据集采用非负矩阵分解方法,需要把每个图像数据拉直成向量形式,在转换过程中会丢失图像数据本身的结构信息,破坏图像的空间几何结构,为了避免这些问题,提出了两种非负张量分解算法的改进方法,并利用这两种子空间降维方法对图像进行分类实验。首先,提出了基于图的非负张量分解算法。在基于图的非负矩阵分解算法的基础上,扩展非负张量分解算法,继续借鉴图谱理论与流形学习算法的优势,把数据集的结构信息引入到非负张量分解算法中。其次,由于构建近邻图对于大数据来说太过耗费时间,计算量过大,提出了一种基于低秩表示的非负张量分解算法。作为压缩感知理论的推广和发展,低秩表示将矩阵的秩作为一种稀疏测度,由于矩阵的秩反映了矩阵的固有特性,所以低秩表示能有效的分析和处理矩阵数据,本文把低秩表示引入到张量模型中,即引入到非负张量分解算法中,进一步扩展非负张量分解算法。实验结果表明,本文所提两种算法与其他相关算法相比,分类结果较好。
(3)提出了一种基于高阶奇异值分解的多级非负低秩稀疏矩阵分解算法。首先对低秩稀疏矩阵分解的计算方法进行了详细介绍。其次,对视频图像序列数据的张量表示及必要性做详细地说明,并对高阶奇异值分解与低秩稀疏矩阵分解的结合方法作出说明,指出视频图像序列数据的排列方式的重要性,以及高阶奇异值分解对数据排序的影响。本文在此基础上,提出了一种高阶奇异值分解下的多级非负低秩稀疏矩阵分解算法,该方法为了确保视频图像序列数据的特征不会被削弱,并实现原视频数据的纯加性描述,引入了非负约束,把数据逐级分解成时间和空问信息。另外,由于该方法是逐级分解方式,所以非负约束尤为重要。二级或更高级分解过程仅针对低秩矩阵,分解结果为稀疏矩阵对应时问信息(运动信息),低秩矩阵对应空间信息(背景信息)。通过对两个视频图像序列进行实验,说明了本文所提方法对提取前景及背景信息均有效。
We know that most of the existing high-dimensional image and video data has a natural tensor structure, or can be organized into a tensor structure. Moreover, the tensor structure representation possesses good presentation skills and calculation features, thus on the basis of summarizing and inheriting the predecessors' research results. This thesis studies the related algorithms based on tensor. The main contents are as follows:
(1) Initialization method has been proposed for support tensor machine classifier. We point out that the disadvantages of the initialization method for the non-negative matrix dimensionality reduction method of traditional support tensor machine via randomization. On one hand, in the absence of the data, it needs an assumption of the data distribution, such as Gaussian distribution, uniform distribution, etc; it is also not easy to estimate the parameters of the distribution only by repeatedly veritification on test data. On the other hand, it is difficult to capture the characteristics of image itself by using the method of random initialization. Therefore, the random way will ultimately affect the classification results of the classifiers and the performances of the dimension reduction results.
In order to address these two problems of random initialization method, this paper put forwards the image content based initialization method and makes use of the image content to initialize the support tensor machine and the non-negative matrix decomposition method. First of all, the raw data is processed by support tensor machine into tensor form. Specifically, each image is represented by a third-order tensor structure, and the collections of images become a fourth-order tensor. Secondly, this paper proposed a weighted higher order singular value decomposition algorithm for support tensor machine initialization. This initialization method combines graph theory with manifold learning algorithm, and initializes the support tensor machine by the image data set to avoid the influence caused by the random initialization. Moreover, in terms of subspace dimension reduction method, this paper adopts the non-negative matrix decomposition method for third-order image characteristics tensor dimensionality reduction, and proposes to initialize the non-negative matrix decomposition method via the two-dimensional principal component analysis method, which makes full use of the correlated information of the collections of image contents. At last, the dimensionality of the input data of support tensor machine is reduced by the method of the improved non-negative matrix decomposition algorithm. After that, support tensor machine has been trained in the subspace and the image classification has been performed by a dimension reduction method with the improved classifier of support tensor machine. Experimental results show that the classification results are better compared with other algorithms.
(2) Non-negative tensor decomposition based on graph and low-rank representation has been proposed. We point out that, in the field of image processing, if the non-negative matrix decomposition method is adopted, each image is required to be straightened into a vector form. In the procedure of conversion, the structural information of the image content is lost and the space geometry structure of image is damaged. In order to avoid these problems, two improvement methods of the non-negative tensor decomposition algorithm have been proposed, and the two subspace dimension reduction methods have been used for image classification. At first, we put forward the new non-negative tensor decomposition algorithm based on graph. Based on the non-negative tensor decomposition algorithm for graph, the non-negative tensor decomposition algorithm has been further expanded. By learning lessons from graph theory and the advantages of manifold learning algorithm, we introduce the structural information of data sets into the non-negative tensor decomposition algorithm. Then, considering the construction of neighborhood graph for big data consuming too much time on the calculation, this paper presents a non-negative tensor decomposition algorithm based on low-rank representation. As the extension and the development of compressed sensing theory, the low-rank representation denotes that the rank of the matrix can be used as a measurement of sparsity. Since the rank of a matrix reflects the inherent property of the matrix, the low-rank analysis can effectively analyze and process the matrix data. This paper introduces the low-rank representation into tensor model, namely to introduce it into non-negative tensor decomposition algorithm and to further expand the non-negative tensor decomposition algorithm. Experimental results show that the classification accuracy of the two algorithms proposed in this paper is better compared to other existing algorithms.
(3) A multistage nonnegative low-rank sparse matrix decomposition algorithm based on high-order singular value decomposition has been proposed. Firstly, the details of the calculation method for the low-rank sparse matrix decomposition algorithm are introduced. Then, the importance of the data arrangement for the image sequence is pointed out, as well as the impact to the data sorting after using high-order singular value decomposition. The method, which is to combine the high-order singular value decomposition and low-rank sparse matrix decomposition, has been introduced. It further manifests that the video image sequence data can be separated by low-rank of tensor representation into foreground and background. Inspired by these, we proposed a higher order singular value decomposition method via a multistage nonnegative low-rank sparse matrix decomposition algorithm. In order to ensure that the characteristics of the video image sequence data are not undermined, and to implement that the pure additive description of the original video data, this method introduces the non-negative constraints and decomposes the data information into time and space information at each step. It is worth mentioning that, because of this gradual decomposition method, the non-negative constraints are particularly of great importance. Secondary or higher decomposition process of low-rank matrix is only for sparse matrix and the decomposition results of the sparse matrix is corresponding to the time information (motion information), and the result of the low-rank matrix is the space information (background information). From the experiments of two image sequences, they show the promising results of the proposed method in this part for extracting the foreground and background information.
引文
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