Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Investigation of feature extraction algorithms and techniques for hyperspectral images.

Doctor of Philosophy (Computer Engineering). University of KwaZulu-Natal. Durban, 2017.Hyperspectral images (HSIs) are remote-sensed images that are characterized by very high spatial and spectral dimensions and nd applications, for example, in land cover classi cation, urban planning and management, security and food processing. Unlike conventional three bands RGB images, their high dimensional data space creates a challenge for traditional image processing techniques which are usually based on the assumption that there exists su cient training samples in order to increase the likelihood of high classi cation accuracy. However, the high cost and di culty of obtaining ground truth of hyperspectral data sets makes this assumption unrealistic and necessitates the introduction of alternative methods for their processing. Several techniques have been developed in the exploration of the rich spectral and spatial information in HSIs. Speci cally, feature extraction (FE) techniques are introduced in the processing of HSIs as a necessary step before classi cation. They are aimed at transforming the high dimensional data of the HSI into one of a lower dimension while retaining as much spatial and/or spectral information as possible. In this research, we develop semi-supervised FE techniques which combine features of supervised and unsupervised techniques into a single framework for the processing of HSIs. Firstly, we developed a feature extraction algorithm known as Semi-Supervised Linear Embedding (SSLE) for the extraction of features in HSI. The algorithm combines supervised Linear Discriminant Analysis (LDA) and unsupervised Local Linear Embedding (LLE) to enhance class discrimination while also preserving the properties of classes of interest. The technique was developed based on the fact that LDA extracts features from HSIs by discriminating between classes of interest and it can only extract C 1 features provided there are C classes in the image by extracting features that are equivalent to the number of classes in the HSI. Experiments show that the SSLE algorithm overcomes the limitation of LDA and extracts features that are equivalent to ii iii the number of classes in HSIs. Secondly, a graphical manifold dimension reduction (DR) algorithm known as Graph Clustered Discriminant Analysis (GCDA) is developed. The algorithm is developed to dynamically select labeled samples from the pool of available unlabeled samples in order to complement the few available label samples in HSIs. The selection is achieved by entwining K-means clustering with a semi-supervised manifold discriminant analysis. Using two HSI data sets, experimental results show that GCDA extracts features that are equivalent to the number of classes with high classi cation accuracy when compared with other state-of-the-art techniques. Furthermore, we develop a window-based partitioning approach to preserve the spatial properties of HSIs when their features are being extracted. In this approach, the HSI is partitioned along its spatial dimension into n windows and the covariance matrices of each window are computed. The covariance matrices of the windows are then merged into a single matrix through using the Kalman ltering approach so that the resulting covariance matrix may be used for dimension reduction. Experiments show that the windowing approach achieves high classi cation accuracy and preserves the spatial properties of HSIs. For the proposed feature extraction techniques, Support Vector Machine (SVM) and Neural Networks (NN) classi cation techniques are employed and their performances are compared for these two classi ers. The performances of all proposed FE techniques have also been shown to outperform other state-of-the-art approaches

Optimal Clustering Framework for Hyperspectral Band Selection

Band selection, by choosing a set of representative bands in hyperspectral image (HSI), is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection, and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) An optimal clustering framework (OCF), which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint. 2) A rank on clusters strategy (RCS), which provides an effective criterion to select bands on existing clustering structure. 3) An automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared to some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperform the other methods on various data sets

Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems