Research On Unsupervised Hyperspectral Band Selection Based On Vector Subspace Projection

Hyperspectral images contain hundreds of bands with a fine resolution,e.g.,less than 0.01 um,which makes it possible to reduce the overlap between classes and therefore enhance the potential to discriminate subtle spectral differences.Hyperspectral remote sensing has been widely used in environmental monitoring,agricultural production prediction,urban monitoring,military object detection and so on.However,the high dimensionality of the data set also brings several challenges for image processing,such as heavy computational and storage burden,high information redundancy and the Hughes Phenomenon.Therefore,to process data effectively,dimensionality reduction(DR)is important and necessary.Band selection(BS)is one of the most commonly-used DR techniques,it reduces the feature space by selecting a subset form the original feature set and can preserve the physical information of the original data,thus it is widely studied.Considering that the prior information of classes is ofen unavailable,it is necessary to develop unsupervised BS techniques.In this study,based on Maximum Ellipsoid Volume(MEV)or maximizing information and minimizing redundancy of selected bands,we research on the relationship among bands by appliying the vector subspace projection(VSP)technique and propose a series of effective unsupervised BS methods,which can be summarized as follows:(1)We propose several novel Maximum Ellipsoid Volume(MEV)based methods for hyperspectral band selection.The MEV method considers the band subset with the maximum ellipsoid volume as the best combination.Based on this point,through combining MEV with the Sequential Forward Search(SFS)algorithm,which is one of greedy algorithms,the MEV-SFS BS method is proposed.The MEV-SFS method avoids the huge computational burden caused by the exhausitive search and makes it possible that the MEV BS method can be used for hyperspectral images.In addition,we apply the triangular factorization(TF)technique to improve the efficiency of the MEV-SFS method and further propose an eqauivalent algorithom,named the MEV-TF algorithm.In applications,the MEV-TF algorithm can find the desired bands from the hyperspectral data in a quite short time.Although the MEV method is a geometry-based method,it is closely related with the vector subspace projection(VSP).In the following portions,an equivalent algorithm of the MEV-SFS algorithm would be derived from the perspective of VSP,thus this portion is the basis of the remaining portions.(2)We develop the orthogonal-projection-based band selection(OPBS)method,in which a subtle relationship between the MEV-SFS and OPBS methods is found and thus some theoretical explanations for the mechanism of the MEV based BS methods can be given.Although the OPBS algorithm still takes MEV as the theoretical basis,it can be proved that both the MEV-SFS and OPBS methods resort to finding the band that has both the maximum information and the minimum redundancy in each round of lookup.Based on this discovery,OPBS is further extended as a BS framework,which provides a new perspective for designing novel and effective selection criteria.(3)The analysis of the mechanism of OPBS indicates that it is reasonable to measure the information and redundancy of bands resepectively and then combine the two metrics as one selection criterion for estimating the importance of bands.We further develop this idea and propose the representativeness-and-redundancy-based BS methods.It is a BS framework and we have given several implementations by using the vector subspace projection(VSP)and other techniques.These BS algorithms can select the bands that are informative for classification and have satisfactory computational efficiencies,moreover,they also show good robustness to noisy bands.(4)We research on the nonlinear BS methods based on VSP.All the previously proposed VSP-based BS methods,including OPBS and most of the representativeness and-redundancy-based BS methods,are linear methods.The kernel trick is used for introducing the nonlinear relationship during BS and thus the nonlinear versions of these BS methods are obtained.The nonlinear versions of algorithms complement the theoretical system of the BS methods based on VSP,and they also extend the application scenarios;thus,the nonlinear BS methods have good theoretical values.