Landmark-based large-scale sparse subspace clustering method for hyperspectral images

Sparse subspace clustering (SSC) has achieved the state-of-the-art performance in the clustering of hyperspectral images (HSIs). However, the high computational complexity and sensitivity to noise limit its clustering performance. In this paper, we propose a scalable SSC method for the large-scale HSIs, which significantly accelerates the clustering speed of SSC without sacrificing clustering accuracy. A small landmark dictionary is first generated by applying k-means to the original data, which results in the significant reduction of the number of optimization variables in terms of sparse matrix. In addition, we incorporate spatial regularization based on total variation (TV) and improve this way strongly robustness to noise. A landmark-based spectral clustering method is applied to the obtained sparse matrix, which further improves the clustering speed. Experimental results on two real HSIs demonstrate the effectiveness of the proposed method and the superior performance compared to both traditional SSC-based methods and the related large-scale clustering methods

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

Hyperspectral Data Acquisition and Its Application for Face Recognition

Current face recognition systems are rife with serious challenges in uncontrolled conditions: e.g., unrestrained lighting, pose variations, accessories, etc. Hyperspectral imaging (HI) is typically employed to counter many of those challenges, by incorporating the spectral information within different bands. Although numerous methods based on hyperspectral imaging have been developed for face recognition with promising results, three fundamental challenges remain: 1) low signal to noise ratios and low intensity values in the bands of the hyperspectral image specifically near blue bands; 2) high dimensionality of hyperspectral data; and 3) inter-band misalignment (IBM) correlated with subject motion during data acquisition. This dissertation concentrates mainly on addressing the aforementioned challenges in HI. First, to address low quality of the bands of the hyperspectral image, we utilize a custom light source that has more radiant power at shorter wavelengths and properly adjust camera exposure times corresponding to lower transmittance of the filter and lower radiant power of our light source. Second, the high dimensionality of spectral data imposes limitations on numerical analysis. As such, there is an emerging demand for robust data compression techniques with lows of less relevant information to manage real spectral data. To cope with these challenging problems, we describe a reduced-order data modeling technique based on local proper orthogonal decomposition in order to compute low-dimensional models by projecting high-dimensional clusters onto subspaces spanned by local reduced-order bases. Third, we investigate 11 leading alignment approaches to address IBM correlated with subject motion during data acquisition. To overcome the limitations of the considered alignment approaches, we propose an accurate alignment approach ( A3) by incorporating the strengths of point correspondence and a low-rank model. In addition, we develop two qualitative prediction models to assess the alignment quality of hyperspectral images in determining improved alignment among the conducted alignment approaches. Finally, we show that the proposed alignment approach leads to promising improvement on face recognition performance of a probabilistic linear discriminant analysis approach

K-Deep Simplex: Deep Manifold Learning via Local Dictionaries

We propose K-Deep Simplex (KDS), a unified optimization framework for nonlinear dimensionality reduction that combines the strengths of manifold learning and sparse dictionary learning. Our approach learns local dictionaries that represent a data point with reconstruction coefficients supported on the probability simplex. The dictionaries are learned using algorithm unrolling, an increasingly popular technique for structured deep learning. KDS enjoys tremendous computational advantages over related approaches and is both interpretable and flexible. In particular, KDS is quasilinear in the number of data points with scaling that depends on intrinsic geometric properties of the data. We apply KDS to the unsupervised clustering problem and prove theoretical performance guarantees. Experiments show that the algorithm is highly efficient and performs competitively on synthetic and real data sets.Comment: 14 pages, 6 figure

Characterization and Reduction of Noise in Manifold Representations of Hyperspectral Imagery

A new workflow to produce dimensionality reduced manifold coordinates based on the improvements of landmark Isometric Mapping (ISOMAP) algorithms using local spectral models is proposed. Manifold space from nonlinear dimensionality reduction better addresses the nonlinearity of the hyperspectral data and often has better per- formance comparing to the results of linear methods such as Minimum Noise Fraction (MNF). The dissertation mainly focuses on using adaptive local spectral models to fur- ther improve the performance of ISOMAP algorithms by addressing local noise issues and perform guided landmark selection and nearest neighborhood construction in local spectral subsets. This work could benefit the performance of common hyperspectral image analysis tasks, such as classification, target detection, etc., but also keep the computational burden low. This work is based on and improves the previous ENH- ISOMAP algorithm in various ways. The workflow is based on a unified local spectral subsetting framework. Embedding spaces in local spectral subsets as local noise models are first proposed and used to perform noise estimation, MNF regression and guided landmark selection in a local sense. Passive and active methods are proposed and ver- ified to select landmarks deliberately to ensure local geometric structure coverage and local noise avoidance. Then, a novel local spectral adaptive method is used to construct the k-nearest neighbor graph. Finally, a global MNF transformation in the manifold space is also introduced to further compress the signal dimensions. The workflow is implemented using C++ with multiple implementation optimizations, including using heterogeneous computing platforms that are available in personal computers. The re- sults are presented and evaluated by Jeffries-Matsushita separability metric, as well as the classification accuracy of supervised classifiers. The proposed workflow shows sig- nificant and stable improvements over the dimensionality reduction performance from traditional MNF and ENH-ISOMAP on various hyperspectral datasets. The computa- tional speed of the proposed implementation is also improved

A manifold learning approach to target detection in high-resolution hyperspectral imagery

Imagery collected from airborne platforms and satellites provide an important medium for remotely analyzing the content in a scene. In particular, the ability to detect a specific material within a scene is of high importance to both civilian and defense applications. This may include identifying targets such as vehicles, buildings, or boats. Sensors that process hyperspectral images provide the high-dimensional spectral information necessary to perform such analyses. However, for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m \u3c\u3c d. In the remote sensing community, this has led to a recent increase in the use of manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data; this is particularly true when implementing traditional target detection approaches, and the limitations of these models are well-documented. With manifold learning based approaches, the only assumption is that the data reside on an underlying manifold that can be discretely modeled by a graph. The research presented here focuses on the use of graph theory and manifold learning in hyperspectral imagery. Early work explored various graph-building techniques with application to the background model of the Topological Anomaly Detection (TAD) algorithm, which is a graph theory based approach to anomaly detection. This led towards a focus on target detection, and in the development of a specific graph-based model of the data and subsequent dimensionality reduction using manifold learning. An adaptive graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation; the artificial target manifold helps to guide the separation of the target data from the background data in the new, lower-dimensional manifold coordinates. Then, target detection is performed in the manifold space