基于非负矩阵分解的图像表示和分类研究

发布时间：2018-03-10 13:20

本文选题：数据降维　切入点：非负矩阵分解　出处：《辽宁工业大学》2015年硕士论文　论文类型：学位论文

【摘要】：近年来，随着多媒体技术的快速发展，获得高质量的图像变得越来越容易，如何对这些高质量的图像进行表示和分类成为最近的研究热点。一方面，高质量的图像具有高维性，高维性使得图像特征更加丰满；另一方面，高维性却给人们的处理带来了困难，这些利于图像表示的高维数据往往会造成“维度灾难”。所以，在对图像进行分类之前要进行必要的降维表示。目前，数据降维有许多方法，但大多数分解方法的结果中允许负值存在，很显然这些负值在实际问题中没有物理意义。非负矩阵分解方法则是在保证非负值的情况下进行的降维。这种降维方法一方面使得数据得到了降维，数据具有纯加性和一定的稀疏性，纯加性凸显了分解的合理性，稀疏性可以抑制外界对数据特征的影响，具有一定的鲁棒性；另一方面对非负数据进行分解时采用了简单有效的迭代算法，通过不断的学习得到了含有图像局部特征的信息，符合人类认知事物由部分到整体的感知过程。图像表示和分类是模式识别领域内非常重要的课题。在图像分类过程中，对图像特征提取是否合理以及对图像分类所用分类函数是否最优将会直接影响图像的分类结果。本文应用了非负矩阵分解算法的相关理论对图像数据进行降维表示和局部特征提取，进而进行分类。本文针对图像处理领域的内容研究了稀疏约束非负矩阵分解、图正则化非负矩阵分解、标签约束非负矩阵分解等理论。综合这些理论本文提出了三种改进的非负矩阵分解算法，包括基于稀疏约束的半监督非负矩阵分解算法、基于稀疏约束的图正则化半监督非负矩阵分解、基于稀疏和先验约束的有监督非负矩阵分解。在完成图像降维和特征提取后，本文利用K均值进行聚类，而对于监督的非负矩阵分解算法为了使分类效果更好，本文结合了支持向量机理论进行分类。本文在常见的人脸数据集和物体数据集上进行了实验，实验表明本文的算法具有合理性和有效性。
[Abstract]:In recent years, with the rapid development of multimedia technology, it becomes more and more easy to obtain high quality images. How to represent and classify these high quality images has become a research hotspot. On the one hand, high quality images have high dimension. On the other hand, the high dimension makes it difficult for people to deal with it, and the high-dimensional data which is good for image representation will often cause "dimensionality disaster". The necessary dimensionality reduction representation should be made before the image is classified. At present, there are many methods to reduce the dimension of data, but the results of most decomposition methods allow negative values to exist. It is obvious that these negative values have no physical significance in practical problems. The non-negative matrix factorization method is a dimensionality reduction method that guarantees the non-negative values. On the one hand, this dimensionality reduction method results in the reduction of the dimension of the data. Data has pure additivity and certain sparsity, pure additivity highlights the rationality of decomposition, sparsity can restrain the external influence on data characteristics, and it has certain robustness. On the other hand, a simple and effective iterative algorithm is used to decompose the non-negative data. Through continuous learning, the information containing local features of the image is obtained, which accords with the perception process of human cognition from part to whole. Image representation and classification is a very important topic in the field of pattern recognition. Whether the image feature extraction is reasonable or not and whether the classification function used in image classification is optimal will directly affect the image classification results. This paper applies the theory of non-negative matrix decomposition algorithm to reduce the dimension of image data. Display and local feature extraction, In this paper, sparse constrained nonnegative matrix decomposition, graph regularized nonnegative matrix decomposition, and image processing are studied. This paper presents three improved nonnegative matrix factorization algorithms, including semi-supervised nonnegative matrix decomposition algorithm based on sparse constraints. The graph regularized nonnegative matrix decomposition based on sparse constraints and the supervised nonnegative matrix factorization based on sparse and prior constraints. After image reduction and feature extraction, K-means clustering is used in this paper. In order to make the classification effect better, the supervised non-negative matrix decomposition algorithm is combined with the support vector machine theory. Experiments show that the proposed algorithm is reasonable and effective.
【学位授予单位】：辽宁工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TP391.41;O151.21

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