Research On Constrained Nonnegative Matrix Factorization Algorithm And Its Applications

In recent years,with the rapid development of "Internet of Things”,"Cloud Computing","Big Data" and "Mobile Internet",the ways of acquiring data are varied and the data we obtained is becoming more and more.However,in many real-world applications,the data is high-dimensional,complicated,and usually contains large amounts of redundant information.Facing the growing huge amounts of data,how to efficiently extract useful information,is a very challenging problem.As one of the most important pattern recognition and machine learning technologies,nonnegative matrix factorization can effectively represent the high-dimensional data in the low dimensional subspace.Due to its effectiveness and practicability,nonnegative matrix factorization has been widely applied in image recognition,text mining,remote sensing analysis,and multi-view clustering,etc.The main idea of NMF is to find two non-negative matrices whose product provides a good approximation to the original data matrix.Due to the non-negative constraint,NMF has shown well"parts-based" representation ability in the structural and sparse data alalysis tasks,such as face recognition and text clustering.In recent decades,NMF has attracted a lot of attentations and has been extensively studied.To solve the NMF problem,we usually adopt the interactive optimization method.Under the iterative framework,different constraints can be added into the factorization process to avoid being stuck in the bad local optimum.Meanwhile,different priori information can be incorporated into the iterative framework,which helps to enhance the final factorization performance.From the perspective of definition,development process and the specific application data,exisiting constrained NMF methods can be divided into three stages:basic NMF,extented NMF and multi-view NMF.Due to the complexity of scenes,the influence of uncertain noise and the less explored priori information,the factorization results of the methods belonging to the three stages should be improved,and the results of the quantitative performance evaluation of these methods need to be enhanced.To achieve this goal,this paper proposes several novel constrained NMF methods based on studying many state-of-the-art NMF methods.Then,based on a practical engineering application,the constrained NMF is applied to detect the pavement crack,which is the main road distress.Generally,the main contributions of this thesis are as follows:(1)A semi-supervised nonnegative matrix factorization algorithm based on discriminative constraint embedding(DSNMF)is proposed for semi-supervised feature extraction.In order to fully utilize the label information,DSNMF considers both implicit and explicit embeddings of label information based on the graph regularized nonnegative matrix factorization(GNMF).The local discriminative manifold constraint and the global label mapping constraint are simultaneously considered,which effectively enhance the discrimination.Compared with several state-of-the-art unsupervised and semi-supervised NMF methods,the factorization performance by the proposed method is significantly improved and the clustering performance is enhanced.The average AC of the proposed method on ORL,Yale and Cora datasets are up to 0.894,0.653 and 0.666,respectively.(2)A local and global regularized concept factorization(LGCF)algorithm is proposed for data representation.In order to consider both the local and global structure information in the matrix factorization process,in LGCF,two regularizations(local and global)are incorporated into the CF framework,in which the feature extraction is achieved effectively through the unified iterative process.Specifically,the local and global structures are depicted via a hypergraph and an unsupervised discriminant criterion,respectively.Compared with other manifold constrained CF variants,LGCF can fully discover the latent manifold information,and can achieve better data representation performance.Extensive experiments on PIE,COIL20,MNIST,OUTEX image datasets demonstrate the superiority of the proposed method in terms of clustering accuracy and normalized mutual information.(3)A region sparsity learning based nonnegative matrix factorization(RSLNMF)algorithm is proposed for hyperspectral image unmixing.In RSLNMF,the spectral and spatial information are both considered.First,we construct a sparsity learning model based on small homogeneous region that is obtained via the graph cut algorithm.Then we combine the sparse model with NMF so that the factorization and the sparsity learning can be performed simultaneously.Thus RSLNMF is able to explore the local sparse structure information in the unmixing process.Furthermore,according to the sparse property of abundance,we add an extra L1/2 constraint to improve the unmixing performance.The whole algorithm is optimized in the unified multiplicative iteration framework.On the synthetic dataset,RSLNMF achieves the best SAD and RMSE.On the real JasperRidge and Urban HYDICE hyperspectral datasets,the SAD of the proposed method can reach 0.085 and 0.110,which is superior to several state-of-the-art unmixing methods.The experamental results show that RSLNMF can generate very close abundance map to the reference and the surface distribution can be easily discriminated after unmixing.(4)A double constrained nonnegative matrix factorization(DCNMF)algorithm is proposed for partial multi-view clustering.In order to fullly explore the information,we consider two effective criteria:manifold preserving and clustering similarity,and incorporate the two constraints into NMF.The basic idea of DCNMF is to push clustering solutions of different views from the paired examples towards a common membership matrice,and to maintain the latent geometric structure of the views simultaneously.Thus the information from both the within-view and without-view can be explored,which is helpful to improve the final representation performance of data.Experiments on both synthetic and Texas,Washington,Digit datasets validate the superiority of the proposed method.(5)Traditional pavement crack detection methods detect cracks by using only single type of feature,and can hardly achieve promising results due to the complicated background noises over the pavement surface.In this paper,a novel crack detection method is proposed to fully utilize multiple types of features.First,several kinds of structural information are exploited according to the statistics,shape,and texture of cracks.Then such structural information is incorporated into the objective of matrix factorization as the regularized manifold terms.Finally,factorization metrics and weight coefficients are determined simultaneously in the unified iterative framework.To improve the final detection results,we first use an anisotropy algorithm to enhance the cracks and get the labels of parts of samples,and then further extend a semi-supervised model.Experimental results on a public pavement crack dataset(CrackIT)and a practical highway crack dataset(HN)show that the proposed method is more robust with a good anti-noise performance,and their accuracy,integrity of crack detection are superior to many commonly used traditional methods.Especially when the crack dataset suffered from complex conditions and serious noise interference,the F? of the method is up to 0.878 and thus verify its effectiveness.