基于图谱理论和非负矩阵分解的图像分类
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摘要
随着科学技术的不断发展,在我们的现实生活中出现了大量的数字图像,对这些数字图像进行处理是一门非常重要的学科。而图像分类作为数字图像处理的一个重要方面,近年来受到越来越多的关注。
图像分类的主要过程包括获取图像的基本信息、图像的特征提取、对样本进行学习和训练以及最后的分类判别。在图像分类的过程中,对图像的特征提取是否有效以及分类器的选择是否优化,直接影响图像的分类结果。本文将图谱理论和非负矩阵理论结合起来,并通过选取几种常用的分类器对不同图像进行分类。其主要研究内容和成果如下：
(1)提出了一种基于图的Laplace矩阵和非负矩阵分解的图像分类方法。该分类方法主要是利用图的Laplace矩阵可以代表图像的基本结构信息。对不同的图像先提取其特征点,再对提取得到的特征点构造图的Laplace矩阵,将构造的矩阵分别进行奇异值分解(Singular Value Decomposition, SVD))和非,负矩阵分解(Non-negative Matrix Factorization, NMF)后得到图像的特征向量,最后再将特征向量输入到径向基函数(Radial Basis Function, RBF)神经网络分类器中,对图像进行分类。对模拟图像和真实图像进行了多组实验,结果证明了基于图的Laplace矩阵和非负矩阵分解的图像分类方法与基于图的Laplace矩阵和奇异值分解的图像分类方法相比,准确性更好。
(2)提出了一种基于图的递增权函数的邻接矩阵和非负矩阵分解的图像分类方法。先由图像中提取的特征点构造基于递增权函数的邻接矩阵,再对其进行非负矩阵分解,将分解后得到的特征向量作为概率神经网络(Probabilistic Neural Network, PNN)分类器的输入,实现对图像的分类。通过多组模拟图像实验和真实图像实验的结果比较,验证了使用该算法对图像进行分类,能够获得较高的分类识别率。
(3)提出了一种基于图的高斯核函数的Laplace矩阵和非负矩阵分解的图像分类方法。对图像的特征点构造基于图的高斯核函数的Laplace矩阵,并对该矩阵分别进行非负矩阵、局部非负矩阵(Local Non-negative MatricesFactorization, LNMF)和稀疏非负矩阵分解(Sparse Non-negative Matrices Factorization, SNMF),将分解得到的特征向量输入到概率神经网络分类器中对图像进行分类。通过多组模拟图像和真实图像的实验结果来比较各种算法的优劣。
With the development of science and technology, there appear a large number of digital images in our real life, how to deal with these digital images is a very important subject. And as an important aspect of the digital image processing, the image classification is also get more and more attention.
The main processes of image classification include getting the basic information, extracting the feature of image, learning and training the sample, and finally giving the classification and discrimination. In the process of image classification,the image features extraction and the optimal classifier selecting affect the image classification results directly. This thesis will combine graph theory and nonnegative matrices theory,and use several common classifiers for different images classification. The main research contents and results are as follows:
First of all, an algorithm of image classification is proposed, which is based on graph Laplace matrix and nonnegative matrices factorization of image classification method. The classification method is mainly depend on the graph Laplace matrix can representing the basic structure of image information. First,extracted the feature points from different images,and use these feature points to construct the graph Laplace matrix, then get the image characteristics vector from the matrix constructed respectively singular value decomposition and non-negative matrix factorization. At last, put the characteristics vector into RBF (Radial Basis Function) neural network classifier to classify images. Simulated images and real images of the results of multiple groups based on the graph of Laplace matrix and nonnegative matrices factorization is better than image classification method based on graph with Laplace matrix and singular value decomposition method.
Secondly,the adjacency matrix of graph based on the increasing weighting function combined with the method of non-negative matrix factorization is applied to the image classification.. First, the character points can be distilled from different images. Then, these points will be used to construct the adjacency matrix of the increasing weighting function, and the eigenvector of the image can be obtained by the non-negative matrix factorization of the adjacency matrix. Finally, the eigenvector will be put into PNN(Probabilistic Neural Network)classifier to accomplish the image classification. Several groups of experiment are presented between simulating images and real images. The results show that the method presented in this paper is feasible and accurate.
Finally,proposed a image classification method based on graph Laplace matrix of gaussian kernel and non-negative matrix factorization.The feature points of image based on the structure of gaussian kernel function diagram of the matrix, and respectively use nonnegative matrices,local nonnegative matrices and sparse nonnegative matrices factorization to the matrix,and put the decomposed eigenvector of PNN classifier into the image classification.Compare the different algorithm evaluate through multiple sets of simulated images and real images of experimental results.
图像分类的主要过程包括获取图像的基本信息、图像的特征提取、对样本进行学习和训练以及最后的分类判别。在图像分类的过程中,对图像的特征提取是否有效以及分类器的选择是否优化,直接影响图像的分类结果。本文将图谱理论和非负矩阵理论结合起来,并通过选取几种常用的分类器对不同图像进行分类。其主要研究内容和成果如下：
(1)提出了一种基于图的Laplace矩阵和非负矩阵分解的图像分类方法。该分类方法主要是利用图的Laplace矩阵可以代表图像的基本结构信息。对不同的图像先提取其特征点,再对提取得到的特征点构造图的Laplace矩阵,将构造的矩阵分别进行奇异值分解(Singular Value Decomposition, SVD))和非,负矩阵分解(Non-negative Matrix Factorization, NMF)后得到图像的特征向量,最后再将特征向量输入到径向基函数(Radial Basis Function, RBF)神经网络分类器中,对图像进行分类。对模拟图像和真实图像进行了多组实验,结果证明了基于图的Laplace矩阵和非负矩阵分解的图像分类方法与基于图的Laplace矩阵和奇异值分解的图像分类方法相比,准确性更好。
(2)提出了一种基于图的递增权函数的邻接矩阵和非负矩阵分解的图像分类方法。先由图像中提取的特征点构造基于递增权函数的邻接矩阵,再对其进行非负矩阵分解,将分解后得到的特征向量作为概率神经网络(Probabilistic Neural Network, PNN)分类器的输入,实现对图像的分类。通过多组模拟图像实验和真实图像实验的结果比较,验证了使用该算法对图像进行分类,能够获得较高的分类识别率。
(3)提出了一种基于图的高斯核函数的Laplace矩阵和非负矩阵分解的图像分类方法。对图像的特征点构造基于图的高斯核函数的Laplace矩阵,并对该矩阵分别进行非负矩阵、局部非负矩阵(Local Non-negative MatricesFactorization, LNMF)和稀疏非负矩阵分解(Sparse Non-negative Matrices Factorization, SNMF),将分解得到的特征向量输入到概率神经网络分类器中对图像进行分类。通过多组模拟图像和真实图像的实验结果来比较各种算法的优劣。
With the development of science and technology, there appear a large number of digital images in our real life, how to deal with these digital images is a very important subject. And as an important aspect of the digital image processing, the image classification is also get more and more attention.
The main processes of image classification include getting the basic information, extracting the feature of image, learning and training the sample, and finally giving the classification and discrimination. In the process of image classification,the image features extraction and the optimal classifier selecting affect the image classification results directly. This thesis will combine graph theory and nonnegative matrices theory,and use several common classifiers for different images classification. The main research contents and results are as follows:
First of all, an algorithm of image classification is proposed, which is based on graph Laplace matrix and nonnegative matrices factorization of image classification method. The classification method is mainly depend on the graph Laplace matrix can representing the basic structure of image information. First,extracted the feature points from different images,and use these feature points to construct the graph Laplace matrix, then get the image characteristics vector from the matrix constructed respectively singular value decomposition and non-negative matrix factorization. At last, put the characteristics vector into RBF (Radial Basis Function) neural network classifier to classify images. Simulated images and real images of the results of multiple groups based on the graph of Laplace matrix and nonnegative matrices factorization is better than image classification method based on graph with Laplace matrix and singular value decomposition method.
Secondly,the adjacency matrix of graph based on the increasing weighting function combined with the method of non-negative matrix factorization is applied to the image classification.. First, the character points can be distilled from different images. Then, these points will be used to construct the adjacency matrix of the increasing weighting function, and the eigenvector of the image can be obtained by the non-negative matrix factorization of the adjacency matrix. Finally, the eigenvector will be put into PNN(Probabilistic Neural Network)classifier to accomplish the image classification. Several groups of experiment are presented between simulating images and real images. The results show that the method presented in this paper is feasible and accurate.
Finally,proposed a image classification method based on graph Laplace matrix of gaussian kernel and non-negative matrix factorization.The feature points of image based on the structure of gaussian kernel function diagram of the matrix, and respectively use nonnegative matrices,local nonnegative matrices and sparse nonnegative matrices factorization to the matrix,and put the decomposed eigenvector of PNN classifier into the image classification.Compare the different algorithm evaluate through multiple sets of simulated images and real images of experimental results.
引文
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[3]邱潇钰,张化祥.基于核的最小距离分类法的参数选择方法[J].计算机工程,2008,34(5)：188-190.
[4]Wang Zhou,Bovik A C,Sheikh H R.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13 (4):600-612.
[5]Friedman N,Geiger D,Goldsmfidt M.Bayesian Network Classifiers[J].Mach ine Learning,1997(29):131-163.
[6]Amir Ahmad,Lipika Dey. A k-mean clustering algorithm for mixed numeric and categorical data[J]. Data & Knowledge Engineering,2007,63(2):503-527.
[7]张文君,顾行发,陈良富等.基于均值-标准差的K均值初始聚类中心选取算法[J].遥感学报,2006,10(5)：715-721.
[8]支晓斌,范九伦.基于模糊Fisher准则的自适应降维模糊聚类算法[J].电子与信息学报,2009,31(11)：2653-2658.
[9]杜长海,吉根林.模糊聚类的最大树法在文本分类中的应用研究[J].计算机科学,2005,32(7)：213-216.
[10]义崇政,花向红,龚子桢等.基于ISODATA的点云分割算法实现[J].测绘信息与工程.2010,35(2)：31-33.
[11]E. Huckel. Quantentheoretische Beitrage zum Benzolproblem [D]. Z. Phys.1931, 70:204-286.
[12]D.Cvetkovic,Graphs and their spectra [D].Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz.1971,354:1-50.
[13]F.R.K.Chung.Spectral graph theory[M].Philadelphia:Regional Conference Series In Mathematics,1997:138-146.
[14]D.Cvetkovic,P.Rowlinson,S.Simic.Eigenspace of Graphs [M].Cambridge: Cambridge University Press,1997.
[15]N.L.Biggs.Algebraic Graph Theory[M].Cambridge:Cambridge University Press, 1974.
[16]赵晓颖,张先迪.图和线图的邻接谱及拉普拉斯谱的关系[J].现代电子技术,2008,31(10)：123-126.
[17]M.Fiedler.Algebraic connectivity of graphs[J]Czechoslovak Math.J,1973,23(98): 298-305.
[18]B.Mohar.The Laplacian spectrum of graphs [J].in:Graph Theory, Combinatorics, and Applications,1991,2:871-898.
[19]H.G.Barrow,R.M.Burstall,Subgraph isomorphism,matching relational structures and maximal cliques[J].Information Processing Letters.1976,4(4):83-84.
[20]M.Fischler,R.Elschlager,The representation and matching of pictorical structures [J],IEEE Trans.Comput.1973,22(1):67-92.
[21]S.Umeyama,An eigendecomposition approach to weighted graph matching problems[J].Transactions on Pattern Analysis and Machine Intelligence.1988,10 (5):695-703.
[22]L.S.Shapiro,J.M.Brady,Feature-based correspondence—an eigenvector approach [J], Image and Vision Computing.1992,10(5):283-288.
[23]B.Luo, R.C. Wilson, E.R. Hancock, Graph Spectral Approach for Learning View Structure[C].In the Proceedings of 16th International Conference on Pattern Recognition(ICPR2002):785-788.
[24]陶文兵,金海.一种新的基于图谱理论的图像阈值分割方法.计算机学报[J].2007.30(1)：110-118.
[25]张江,王年,梁栋等.基于Laplace谱的图像分类.计算机技术与发展[J].2008,18(5)：73-78.
[26]Daniel D.Lee,H.Sebastian Seung.Learning the parts of objects by non-negative matrix factorization[J].Nature,1999,401(6755):788-791.
[27]Daniel D.Lee,H.Sebastian Seung.Algorithms for non-negative matrix factorization.Advances in neural information processing system[J].2001,(13):556-562.
[28]Patrik O.Hoyer.Nonnegative matrix factorization with sparseness constraints [J].2004,5:1457-1469.
[29]Cichocki A,Zdunek R,Amari A.New Algorithms for Non-Negative Matrix Factorization in Applications to Blind Source Separation[C].Acounstics,Speech and Signal Processing,2006.
[30]Smaragdis P,Brown J C.Non-negative matrix factorization for polyphonic music transcription[C]. Applications of Signal Processing to Audio and Acoustics,2003:177-180.
[31]Machae W.Berry,Murray Browne.Algorithms and applications for approximate nonnegative matrix factorization[J]. Computational statistics&data analysis. 2007,5(21):1-31.
[32]Mohammadreza Ghaderpanah,A hamza.A Nonnegative Matrix Factorization Scheme for Digital Image Watermarking[C]International Conference on Multimedia and Expo.2006,1573-1576.
[33]候媛彬,杜京义,汪梅.神经网络[M].西安：西安电子科技大学出版社.2007,8.
[34]谷延锋.基于核方法的高光谱图像分类和目标检测技术研究[D].哈尔滨：哈尔滨工业大学,2005.
[35]S.Tong,D. Koller. Support vector machine active learning with applications to text classification[J]. Journal of Machine Learning Research,2002,2:45-66.
[36]Csurka QDance C R,Fan L,et al. Visual categorization with bags of key points[C].Meylan:Proceedings of the ECCV workshop on Statistical learning in Computer Visio,2004:59-74.
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