Hyperspectral Image Classification Based On Low Rank Feature Representation And Divide-and-conquer Multinomial Logistic Regression

With the availability of hardware and data,hyperspectral image?HSI?classification has become an active research area within the remote sensing community.In the past decades,many algorithms have been developed for it,including general algorithms,specific algorithms as well as integrated systems.However,HSI classification also faces many challenges in both algorithm design and system design.Among them,the more prominent ones involve the following issues.The first one is the contradiction between the high dimensionality and relatively few labeled samples of HSI data.It results in statistical difficulties and Hughes issue.The second one is the high space and time complexity in the popular statistical machine learning algorithms,e.g.,multinomial logistic regression?MLR?.What is worse,these algorithms often run out of memory in resource-constrained machines,not to mention real-time calculation.In practical remote sensing systems,the real-time performance is one of the most important considerations.Regarding to the above issues,this dissertation includes the following studies.Firstly,inspired by the HSI characteristics and the correlation between samples,a weighted low rank representation?WLRR?based dimension reduction algorithm coupling with a skinny dictionary is proposed.It aims to improve the estimation of scatter matrices in linear discriminant analysis?LDA?and especially solve the performance degradation issue in small-sample-size scenario.Based on the traditional low rank representation?LRR?,a local weighted regularization is introduced to preserve the local structure of HSI.It is solved by an iterative algorithm based on augmented Lagrange multiplier.Besides,a discriminant dictionary generated by empirical mode decomposition?EMD?is proposed as well.The organic combination makes WLRR not only contain local structure and global structure,but also contain rich discriminant information.Experimental results on several popular HSI data sets show that WLRR yields significant dimension reduction and classification performance improvement when compared to other existing ones.Secondly,a weighted low rank graph discriminant analysis algorithm?WLGDA?is proposed for HSI classification.It is based on the general framework of graph embedding?GE?and the proposed WLRR.It aims to construct a weighted undirected graph such that the structure information of HSI can be preserved as much as possible.Furthermore,by introducing the label information,a discriminant analysis version is developed for it.Experimental results on several popular HSI data sets validate its effectiveness.Thirdly,a maximum correntropy criterion based low rank preserving projection?MCC-LRPP?is proposed for HSI dimension reduction.It employs maximum correntropy criterion?MCC?to model the reconstruction error in LRR.Unlike l₂ or Frobenius related norms,MCC is anisotropy and can better suppress spectral band specific noise separately.The resulting correntropy graph is capable to preserve the band difference to a large extent.Through identical deformation,it can be solved in a row weighted regularization form.On this basis,GE is utilized to seek the projection subspace.Besides,it is extended to a discriminant analysis by introducing label information.Experimental results demonstrate its effectiveness.Finally,to reduce the space and time complexity of MLR,two divide-and-conquer models are proposed for it under both the Gaussian density regularization and Laplacian graph regularization.The bottleneck of traditional MLR is a large linear system which often brings about heavy computation burdens in real applications.By utilizing the symmetric structure of the Hessian matrix of the log likelihood function,MLR is converted into a series of smaller equivalent sub problems with closed solutions under both scenarios.In addition,two complete proofs of their equivalence to the original problems are given.In these divide-and-conquer versions,memory usage is reduced by O?c²/2?and O?c?respectively.Experiments on several popular HSI data sets show that the proposed algorithms can provide one to two orders of magnitude speedups.