IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 1

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1 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 1 GSEAD: Graphical Scoring Estimation for Hyperspectral Anomaly Detection Rui Zhao, Student Member, IEEE, and Liangpei Zhang, Senior Member, IEEE Abstract Hyperspectral anomaly detection has been the subject of increased attention in the past 20 years. One obvious trend for scholars is seeking an appropriate data description in the hyperspectral anomaly detection domain. However, a specific predetermined data model in a given detector may not be able to fit all the other cases of hyperspectral images. Hence, can we construct a hyperspectral anomaly detector from a data-adaptive analysis perspective that can implement detection processing only with the characteristics of the data itself? In our manuscript, we propose a graphical scoring estimation based anomaly detector (GSEAD) that utilizes graphical data description to achieve a data-adaptive analysis-based anomaly detection procedure. First, potential anomalies are screened out by a predicted connected component graph (pcc-graph). The remaining pixels constitute the robust background dataset. Second, an embedded locality preserving graph (elp-graph) is generated with the robust background dataset in an intrinsic manifold space by locality preserving graph embedding. Finally, a k-nearest neighbor graphical scoring estimation is undertaken to output the detection result. A targetembedded hyperspectral dataset and three real hyperspectral images were utilized to validate the detection performance of the proposed method. The experimental results show that GSEAD achieves superior receiver operating characteristic curves, area under ROC curves values, and background-anomaly separation than some of the other state-of-the-art anomaly detection methods. A sensitivity analysis of the relevant parameters was also undertaken in the experimental analysis. Index Terms Anomaly detection, graphical data description, graph embedding, hyperspectral, k-nn scoring estimation, predicted graph. I. INTRODUCTION SPECTRAL imaging, which is also referred to as hyperspectral imaging, captures the approximately consecutive electromagnetic spectra of ground objects in the field of view in a mass of narrow-interval spectral bands from the hyperspectral sensors [1] [3]. The approximately continuous spectral characteristics of ground-surface materials can be obtained from hyperspectral images because of their high spectral resolution, which is usually less than 10 nm [4], [5]. The reflectance Manuscript received February 26, 2016; revised June 7, 2016 and July 26, 2016; accepted August 15, Manuscript received February 26, 2016; revised July 26, 2016; accepted August 15, This work was supported in part by the National Natural Science Foundation of China under Grant , Grant , Grant U , Grant , and Grant , in part by the Natural Science Foundation of Hubei Province under Grant 2014CFB193, and in part by the Fundamental Research Funds for the Central Universities (Corresponding author: Liangpei Zhang). The authors are with the Remote Sensing Group, State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan , China ( @qq.com; zlp62@ public.wh.hb.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JSTARS spectra of hyperspectral images allow us obtain the features of interest for object identification and classification [6], [7]. Target detection applications benefit from the abundant spectral information in hyperspectral imagery. Target detection is a powerful technique for the identification of objects that are significantly different from the surrounding background [8], [9] or have specific features in the spectral domain [10]. Two types of patterns are mainly explored in hyperspectral target detection: spectral matching detection and automatic target detection. Spectral matching detection, which requires the targets spectra in advance, involves identifying pixels whose spectra exhibit a high degree of correlation to the expected signature [11] [13]. However, in most cases, it is difficult to obtain the precise spectra of ground objects. Absorption and scattering of the atmosphere, the subtle effects of illumination, and the spectral response of the sensor must all be considered when measuring the spectral properties of a material through the atmosphere [14]. Moreover, spectral variability also needs to be addressed in spectral matching detection [15], [16]. The multiplicity of possible spectra associated with the objects of interest and the complications of atmospheric compensation have led to the development and application of automatic target detection, which is also called anomaly detection [17]. Anomaly detection techniques, which do not require any prior spectral information about the targets, are more practical in actual applications. Anomaly detection has been the subject of great interest in hyperspectral imagery processing in the last 20 years [18] [20]. From a data description aspect, recent works can be considered as being engaged in seeking different, effective data descriptions for hyperspectral anomaly detection. For the benchmark Reed Xiaoli anomaly detection algorithm [21], a Gaussian data description is utilized. The mean value vector and covariance matrix are the variables that need to be estimated for the Mahalanobis distance detection metric. This establishes a Gaussian hyperellipsoid with the estimated variates to depict the hyperspectral data and rank the anomalous degree of every pixel. However, real-world hyperspectral images usually contain several types of materials, so the inherent assumption of multivariate Gaussianity in the data is typically not true for hyperspectral imagery. Similarly, kernel RX (KRX) [22] also agrees with the Gaussian hyperellipsoid detection approach, but it takes the nonlinear characteristic and complex mixture property of real hyperspectral images into consideration at the same time. KRX projects hyperspectral data to an arbitrary highdimensional kernel Hilbert data space to obtain an appropriate multivariate Gaussian distribution of the data for hyperspectral anomaly detection. Nevertheless, the appropriate data distribution by this projection requires a specific kernel parameter to IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See standards/publications/rights/index.html for more information.

2 2 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING be chosen, and this choice may not satisfy all conditions of hyperspectral imagery. To exploit the categorical information in hyperspectral imagery, the cluster-based anomaly detector (CBAD) [23] assumes that hyperspectral data within clusters can be modeled as multivariate Gaussian distributions of the mean values and covariance matrices that vary cluster-to-cluster. By the k-means technique, CBAD segments the image data into several clusters; however, not all the segmented clusters will strictly adhere to a multivariate Gaussian distribution. A number of other robust detection methods utilize an iterative background mean vector and covariance matrix estimation strategy, with the purpose of achieving a robust background estimation. Methods such as blocked adaptive computationally efficient outlier nominators (BACON) [24] and the minimum covariance detector [25] likewise attempt to set up a multivariate Gaussian model with pixels that are chosen as background. The chosen background pixels may be able to fit the multivariate Gaussian assumption; however, these chosen background pixels will not accurately represent the complex background characteristics in hyperspectral images. In addition, the subspace-based RX detector (SSRX) [26], acting as a feature extraction-based anomaly detection method, considers that the background is spread over several main directions in the hyperspectral data, which can be projected into a subspace that represents the primary background features by representative eigenvectors of the data covariance matrix. In fact, SSRX makes an assumption that the background and anomaly are spanned by respective projections toward different directions in a linear space, and a subspace model can then be established for the background suppression. Nevertheless, the intricate background characteristics of the multiple materials in hyperspectral imagery make it difficult to precisely recognize the background directions in the data-distributed space. It can, therefore, be concluded that different hyperspectral images may not fit with a specific predetermined data model in a given detector, which has become a bottleneck in the current anomaly detection methods. Hence, in our manuscript, we propose a graphical scoring estimation-based anomaly detector (GSEAD), which is constructed by implementing the detection processing only with the characteristics of the data itself. This hyperspectral anomaly detector achieves a data-adaptive analysis-based anomaly detection procedure by utilizing graphical data description. Graphical data description for data analysis has been applied in many academic domains such as image processing [27], [28], pattern recognition [29], visual analysis [30], etc. It has also been utilized in hyperspectral imagery nonlinear analysis [31] and classification [32] [33]. Graphical data description can allow hyperspectral data presentation and analysis from the data itself, and gives us a way to exploit the inherent structure and distribution in hyperspectral data without the use of a predetermined model. In the proposed GSEAD method, three designed graphs are utilized step-by-step for the hyperspectral anomaly target detection: 1) Predicted connected component graph (pcc-graph). For hyperspectral anomaly detection, hyperspectral images are typically considered as consisting of two components: background and anomaly [8], [17]. Anomaly detection assumes that the background occupies a majority of the image pixels, and the anomaly targets in the hyperspectral image have a very low probability in relative terms. Furthermore, it is also assumed that the spectra of the anomalies have distinct spectral differences with the background [35] [37]. This leads to the phenomenon of the background pixels being gathered into a main distribution and having a higher degree of similarity with each other relative to the anomaly pixels. Moreover, the main distribution of the background is usually difficult to describe with a specific predetermined model because hyperspectral images are acquired in a variety of conditions, and the background is usually clustered with multiple types of land cover. In the proposed approach, we first construct a pcc-graph to roughly predict and separate the robust background and potential anomalies. The pcc-graph is constructed and weighted with the geodesic distance as its similarity metric. The prediction and separation processing is implemented by a maximum component calculation method. 2) Embedded locality preserving graph (elp-graph). Pixels in hyperspectral imagery are usually mixed with various kinds of land cover, and the signals of hyperspectral or airborne sensors often reflect or refract more than once on the ground surface. These phenomena lead to the inherently nonlinear characteristic of hyperspectral data. The nonlinearity mainly stems from the nonlinear nature of the scattering, which can be described with the bidirectional reflectance distribution function [38], [39]. Multiple scattering within a pixel and the heterogeneity of the subpixel constituents [15], [40] also contribute to the nonlinearity in hyperspectral imagery. As a result, the intrinsic data structure in hyperspectral imagery can be covered up due to the phenomenon of hyperspectral nonlinearity. Hence, the intrinsic background structural characteristics cannot be precisely exploited when only using a graph that is constructed from the hyperspectral data in a simple weighted manner. In order to solve this problem and reveal the intrinsic background structural characteristics for anomaly detection, we generate an elp-graph with the robust background dataset in an intrinsic manifold space by locality preserving graph embedding [41]. The elp-graph can retain a high degree of local structural similarity for the robust background and keep credible anomalies in the potential anomaly dataset away from the aggregate background. Meanwhile, pixels with a low anomalous degree will adjoin the robust background. This contributes to an admirable separation between anomaly targets and background. 3) A k-nearest neighbor (k-nn) graphical scoring estimation is undertaken for the detection scoring. A k-nn adjacency graph is constructed to estimate the accumulated detection score on the basis of the elp-graph for every pixel. The three step-by-step graphical analyses utilized in GSEAD come from a data-adaptive analysis perspective, and are constructed without the use of any specific predetermined model.

3 ZHAO AND ZHANG: GSEAD: GRAPHICAL SCORING ESTIMATION FOR HYPERSPECTRAL ANOMALY DETECTION 3 The remainder of this paper is organized as follows. In Section II, we introduce the graphical data-driven analyses in the proposed GSEAD method in detail. The experimental results are reported in Section III, along with a description of the experimental datasets, the detection results and analysis, and a discussion. The parameter sensitivity analysis is then presented in Section IV, followed by the conclusion in Section V. II. GRAPHICAL SCORING ESTIMATION-BASED ANOMALY DETECTOR (GSEAD) This section gives a brief introduction to graph construction processing, as well as demonstrating the data-adaptive analyses of the three designed graphs that are utilized step-by-step in GSEAD for hyperspectral anomaly target detection. A. Graph Construction For a given dataset V =[v 1, v 2,..., v s ], s is the dataset size, and a relevant graph G = {V, W} can be constructed with V as its vertex set, where W is an s s similarity matrix of G. Graph construction is a vertex-connection and edge-weighted procedure in that the vertices are connected to each other with edges that should be weighted by a given similarity metric. The similarity matrix W is generated by the given similarity metric. W(i, j) represents the similarity between v i and v j. Graphical analysis can then be carried out with the constructed graph. The undirected weighted k-nn adjacency graph and a graph weighted with the geodesic distance are used in GSEAD. The specific construction processes are demonstrated in the following. B. Predicted Connected Component Graph (Pcc-Graph) For hyperspectral anomaly detection, we generally consider and discuss hyperspectral image data consisting of two components: background and anomaly. The pcc-graph is constructed to roughly predict these two components. We assume that the hyperspectral data are a p n data matrix X =[x 1, x 2,..., x n ], where p is the number of spectral bands and n is the total number of pixels in the hyperspectral image. The pcc-graph G pcc = {X, W G pcc } is defined as the graph whose vertex set is X. To construct G pcc, the vertices in X need to be connected and weighted with a specific similarity metric for the similarity matrix. In our connected component analysis, the geodesic distance [45] is utilized as the similarity metric for constructing G pcc. This geodesic distance similarity metric is a commonly used method [31], [43]. With the concept of the geodesic distance similarity metric, the distance is measured by tracing the adjacent neighborhood trajectory of the dataset, with the hope of achieving a better representation for the data components. When estimating geodesic distances, the similarity metric in a small, local linear neighborhood is applied with the Euclidean distances. The distances to the vertices outside the local neighborhood of a particular vertex are calculated by linking the shortest paths through the vertices common to more than one neighborhood. For the geodesic distance calculation, all the Euclidean distances r ij between pairs of vertices x i and x j are first calculated. A connected graph of the distances W G pcc (i, j) needs to be determined. Whenever vertices x j lie within a neighborhood defined by a set of the k pcc nearest neighbors X i,kpcc of x i, W G pcc (i, j) =r ij. Otherwise, W G pcc (i, j) is set to. The initial similarity matrix W G pcc is represented as follows: W G pcc initial (i, j) =: r ij, x j X i,kpcc, x j / X i,kpcc. (1) Once the initial G pcc has been initialized in this manner, the remaining estimated distances W G pcc (i, j) outside of the neighborhood are computed with Dijkstra s algorithm [44]. Dijkstra s algorithm is an iterative method which uses a relaxation rule for edges. In each iteration, the choice of which edges are relaxed is controlled by a minimum priority queue [45], [46]. The following update rule (2) is used in Dijkstra s algorithm for all the vertices: ( W G pcc (i, j) = min WG (i, j), W m pcc G pcc (i, k) + W G pcc (k, j) ). (2) This means that for each value m =1, 2,..., n in turn, we replace all of W G pcc (i, j) by min m (W G pcc (i, j), W G pcc (i, k)+ W G pcc (k, j)). When all the vertices have been exhausted, the final values of the similarity matrix W G pcc (i, j) will contain the shortest path distances between all the pairs of vertices in G pcc and will be the best estimate of the geodesic distance W G pcc (i, j) for a particular choice of neighborhood size k pcc. A robust background and potential anomaly separation procedure is then carried out after pcc-graph construction. There will be two kinds of components in the pcc-graph: intensively connected and nonconnected. In the pcc-graph, some vertices can be isolated from the vertex set when some blocks of vertices are disconnected from the main distribution. This is because the geodesic distances of these pixels remain infinite values at the termination of the geodesic distance estimation. These vertices which are nonconnected components are considered to be potential anomalies. The main distribution, which is the intensively connected component, is considered to be the robust background pixels. This separation processing is a label assigning procedure with a maximum component calculation method. We set the label set as χ =[l 1,l 2,..., l n ] T with respect to X =[x 1, x 2,..., x n ]. A label assigning function f : X χ should then be established between χ and X. To establish the label assigning function f : X χ, we focus on the rows of the similarity matrix W T G pcc =[w T G pcc,1, wt G pcc,2,..., wt G pcc,n ]. w G pcc,i is the similarity vector of pixel x i with the other pixels. As previously mentioned, pixel x i, which is disconnected from the main distribution, will have some infinite entries in the similarity vector w i. The label assigning function is actually then a calculation index for x i to show whether or not there are infinite entries in w i. Hence, the label assigning function is established as follows: l i = f (x i )=: 0, W G pcc (i, j) j. (3) 1, otherwise

4 4 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING Fig. 1. Robust background and potential anomaly separation with the pcc-graph. Then, if l i is assigned to 0, pixel x i is sorted as robust background. Otherwise, l i is assigned to 1, and pixel x i is sorted as potential anomaly. A graphical example that utilizes a simple vertex set to represent the hyperspectral image data is shown in Fig. 1 to demonstrate this separation procedure. In this example, the neighborhood size k pcc is chosen as 2, and then the pcc-graph is constructed with the geodesic distance similarity metric by Dijkstra s algorithm. From the graph construction, we can see that there exists a main intensively connected part of the vertices, which are represented by green triangles. These vertices are connected and gathered together little by little with respect to their neighborhood similarity connection, and form the main distribution in the vertex set. This main distribution represents the most concentrated group in the dataset, which can then be seen as a robust background representation of the hyperspectral image. Conversely, the rest of the nonconnected vertices possess a distinctly different distribution characteristic from the main distribution, and can be considered as potential anomalies. C. Locality Preserving Graph Embedding In the introduction, we mentioned that the phenomenon of hyperspectral nonlinearity can often conceal the intrinsic data structure in hyperspectral imagery. In order to solve this problem, a graph embedding technique is implemented on the robust background dataset to reveal the intrinsic background structural characteristics for anomaly detection. Graph embedding is an important technique [47], [48], which has been widely used in data analysis [43], [49] [53]. In the GSEAD method, a locality preserving graph embedding technique [41] is employed to generate an elp-graph for the hyperspectral imagery. Locality preserving graph embedding builds a graph incorporating the neighborhood information of the dataset. A transformation matrix that embeds the data vertices in the intrinsic lowdimensional manifold space is then computed. This transformation optimally preserves the local neighborhood information. The elp-graph representation can be viewed as a discrete approximation of the continuous embedding that naturally arises from the geometry of the manifold [50]. The locality preserving graph embedding can also be simply applied to any new data vertex to locate it in the intrinsic manifold space, relying on the given data vertices. The locality preserving graph embedding utilized in GSEAD exploits the intrinsic background characteristics of the hyperspectral imagery, and the elp-graph retains a high degree of local structural similarity for the robust background in the intrinsic manifold space and keeps credible anomalies in the potential anomaly dataset away from the aggregate background due to their different intrinsic characteristics. Meanwhile, pixels with highly similar intrinsic background characteristics in the potential anomaly dataset will adjoin the robust background. This contributes to an admirable separation between anomaly targets and background. The locality preserving graph embedding technique for GSEAD is demonstrated in the following. With the pcc-graph, the hyperspectral image data X are separated into two subsets: robust background X b =[x b1, x b2,..., x bn b ] and potential anomalies X t =[x t1, x t2,..., x tn t ], where n b and n t are the number of robust background and potential anomaly pixels, respectively. Note that, after the separation, the robust background is determined as the most concentrated distribution in the hyperspectral dataset. And the potential anomalies are determined as the pixels that are not intensely distributed with the robust background. Due to the fact that there exists many pixels mixed with spectra of different land covers [15], then a mass of pixels would have relatively low spectral similarity with the representative background. Hence, a mass of pixels will not be included in the robust background dataset. Then, the number of potential anomaly pixels will be much more than the number of real anomaly pixels. A k-nn adjacency graph G X b = {X b, W G X b } is then constructed with X b as its vertex set by a specific adjacency size k elp.thek elp nearest neighbors of x bi are defined as X bi,k elp. The similarity matrix W G X b is generated by a heat kernel [50] as follows: x b x i b j 2 W G X b (i, j) =: e 2 σ 2, x bj X bi,k elp. (4) 0, x bj / X bi,k elp The essential task of locality preserving graph embedding is to find a transformation function F : G X b G Y b that transforms G X b to G Y b = {Y b, W G Y b } in an intrinsic low-dimensional manifold space. Note that X b R p, Y b R p, and p is typically much larger than p. The transformation relationship between X b and Y b is established as follows: Y b = A T elpx b (5)

5 ZHAO AND ZHANG: GSEAD: GRAPHICAL SCORING ESTIMATION FOR HYPERSPECTRAL ANOMALY DETECTION 5 where A elp is an n p transformation matrix that needs to be computed for the locality preserving graph embedding. Furthermore, W G Y b should have a maximum similarity representation with W G X b. We define the diagonal matrix D G X b and the Laplacian matrix L G X b of G X b, which are used in the locality preserving graph embedding. D G X b and L G X b are defined as follows: n L G X b = D G X b W G X b, D G X b (i, i) = (i, j). W G X b j=1 (6) The locality preserving graph embedding considers the problem of mapping the weighted graph G X b to a line so that the connected vertices stay as close together as possible. The graphpreserving criterion for choosing a good embedding procedure is to minimize the following objective function: Δ = arg min 1 2 n i=1 j=1 n ybi y bj 2 WG X b (i, j) (7) under appropriate constraints. The objective function with W G X b (i, j) incurs a heavy penalty if neighboring vertices x bi and x bj are embedded far apart. Therefore, minimizing it helps to ensure that if x bi and x bj are close, then y bi and y bj will also be close. The similarity preservation property from the graph-preserving criterion has a twofold explanation. For a larger similarity between vertices x bi and x bj, the distance between y bi and y bj should be smaller to minimize the objective function. Likewise, a smaller similarity between x bi and x bj should lead to a larger distance between y bi and y bj. Substituting (5) and (6) into (7), we obtain a rewritten formulation of the objective function: Δ = arg min 1 n n ybi y bj 2 WG 2 X b (i, j) i=1 j=1 = arg min 1 n n A T 2 elp x bi A T elpx bj 2 WG X b (i, j) i=1 j=1 ( n = arg min A T elpx bi D G X b (i, i) x T b i A elp n i=1 j=1 i=1 n A T elpx bi W G X b (i, j) x T b j A elp ) ) = arg min (A T elpx b (D G X b W G X b X T b A elp ) = arg min (A T elpx b L G X b X T b A elp. (8) Matrix D G X b provides a natural measure of the data vertices. In robust background dataset X b, there still exists intensely distributed regions and less aggregately distributed regions. Based on D G X b, this characteristic can be revealed. If the value of D G X b (i, i) (corresponding to x bi ) is bigger, x bi is located in the less aggregately distributed region. Then, in the manifold space, we want the vertexes which are in the less aggregately distributed region to be a representation with small intensity, to enhance the objective function (7) of locality preserving graph embedding. Therefore, we impose a constraint as follows: Y T b D G X b Y b = I A T elpx b D G X b X T b A elp = I. (9) With this constraint, the vertexes which are in the less aggregately distributed region, whose D G X b (i, i) is bigger, to be a representation with small intensity ( y bi 2 will be suppressed) in the manifold space. Finally, the minimization problem reduces to finding: Δ = arg min A T elp X b D G X b X T b A elp=i (A T elpx b L G X b X T b A elp ).. (10) The transformation matrix A elp that minimizes the objective function is given by the minimum eigenvalue solution to the generalized eigenvalue problem: X b L G X b X T b a elp = λx b D G X b X T b a elp. (11) We then compute the eigenvectors and eigenvalues for the generalized eigenvector problem as (11). We let the column vectors a elp1, a elp2,..., a elpp be the solution of (11), ordered according to the minimum eigenvalues λ 1 < λ 2 <... < λ p. Finally, the elp-graph G elp is an extended graph, which is embedded by A elp on the whole hyperspectral image dataset X as follows: [ ] X Y elp = A T elpx, A elp = a elp1, a elp2,..., a elpp. (12) D. K-NN Graphical Scoring Estimation After the locality preserving graph embedding, we undertake the detection scoring with a k-nn graphical scoring estimation. A variety of functional scoring methods have been exploited in statistical analysis [54], [55]. The scoring function is actually a mapping procedure that maps the test data X to a numerical representation η, which can be seen as a density level for the dataset. In the proposed GSEAD method, we set the scoring function as η gse = f(x). For the elp-graph G lpe obtained in Section II-C, we first need to recalculate its similarity matrix W gse for the vertices connection with a reconstructed k-nn adjacency graph G gse = {Y lpe, W gse } by a specific adjacency size k gse.the k gse nearest neighbors of y lpei are defined as Y lpei,k gse. Here, due to the fact that the embedded dataset Y lpe primarily preserves the local structural similarity of the background statistics, we choose the Euclidean distance as the similarity metric for W gse to increase the weights of the anomaly pixels. W gse is then computed as follows: W gse (i, j) =: (ylpei y lpej ) T ( ylpei y lpej ), ylpej Y lpei,k gse 0, y lpej / Y lpei,k gse. (13) To further heighten the anomalous degree for the anomalies, the scoring function is set as the accumulation of all the weights

6 6 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING Fig. 2. Flowchart of the graphical scoring estimation-based anomaly detector. of y lpei as follows: η gse (i) = = n W gse (i, j) j=1 k gse (ylpei j=1 y lpej ) T ( ylpei y lpej ), ylpej Y lpei,k gse. (14) We substitute (12) into (14), and the scoring function is then represented as follows: η gse (i) =f (y lpei )= j=1 k gse (ylpei j=1 y lpej ) T ( ylpei y lpej ) k gse ( ) T ( ) = f (x i )= A T lpe x i A T lpe x j A T lpe x i A T lpe x j k gse = (x i x j ) T A lpe A T lpe (x i x j ), y lpej Y lpei,k gse j=1 (15) where η gse is then the final detection output. The flowchart of GSEAD is shown in Fig. 2, and the main steps of computing GSEAD are listed in Algorithm 1. III. EXPERIMENTS AND ANALYSES This section refers to a series of verified experiments, and consists of the following parts: 1) Introduction to the datasets. 2) Detection maps obtained by the proposed GSEAD method and a set of state-of-the-art hyperspectral anomaly detection methods for a target-embedded Pushbroom Hyperspectral Imager (PHI) hyperspectral dataset and three real hyperspectral images: Hyperspectral Digital Imagery Collection Experiment (HYDICE) and Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) images over urban areas and a Hyperion image over a rural area. 3) A quantitative comparison with receiver operating characteristic (ROC) curves, area under ROC curve (AUC) values, and background-anomaly separation analyses of the four experimental datasets between the proposed GSEAD method and the set of state-of-the-art hyperspectral anomaly detection methods. 4) Discussion of the experimental results, the computational complexity, and t-test validation of the proposed GSEAD method versus the other state-of-the-art hyperspectral anomaly detection methods. 5) Sensitivity analysis of the relevant parameters. A. Experimental Datasets 1) Target-embedded PHI hyperspectral data: This dataset is composed of a real hyperspectral image with the added spectra of the targets in certain pixels. The image is a PHI image of the Changzhou area, China. A total of 80 bands of the PHI image ( pixels) were utilized, with a spectral range of nm. The spectral resolution of the PHI hyperspectral sensor was 5 nm. The anomaly spectrum was andradite from the ENVI spectral library, and it was embedded into certain pixels with a predetermined percentage. In the experiment, the anomaly signature was embedded into 100 pixels, and the original signature in these pixels was taken as the background, with the percentage reduced accordingly. The 100 pixels were divided into ten groups according to their targets abundances. The 100 targets were placed in ten columns, with each column of ten targets at the same position. The target embedding was implemented with (16). The positions of the targets are shown in Fig. 3(a) and are denoted by the yellow circles. The abundances of the targets are shown in Fig. 3(b) x =(1 λ) p b + λp t (16) where λ is the abundance of the target, and p b and p t are the spectra of the background and anomalies, respectively. 2) Real hyperspectral images. Three real hyperspectral images were utilized in the experiments. The first real hyperspectral dataset was acquired by the HYDICE hyperspectral remote sensor. This real hyperspectral image, which consists of a suburban residential area with an approximately 3 m spatial resolution, is publicly available. This hyperspectral image consists of 210 spectral channels from 0.4 to 2.5 μm. After removing the water

7 ZHAO AND ZHANG: GSEAD: GRAPHICAL SCORING ESTIMATION FOR HYPERSPECTRAL ANOMALY DETECTION 7 Fig. 3. Target-embedded PHI hyperspectral dataset. (a) Target position. (b) Target abundance. absorption bands, 162 bands remained. The scene is cluttered with different land-cover types of parking lot, soil, water, road I, and road II, with ten vehicles regarded as the anomaly targets. The RGB pseudocolor image and reference for the HYDICE data are shown in Fig. 4(a) and (b), respectively. The spectra of the background and anomalies in the real hyperspectral HYDICE image are shown in Fig. 4(c) and (d). The second real hyperspectral image utilized in our experiments was acquired by the AVIRIS hyperspectral remote sensor over the San Diego airport Fig. 4. Real HYDICE hyperspectral image of an urban area. (a) RGB pseudocolor image. (b) Reference. (c) Spectra of the background. (d) Spectra of the anomalies. area, San Diego, CA, USA. This hyperspectral image consists of 224 spectral channels from 0.4 to 2.5 μm. After removing the low-snr and water absorption bands, 189 bands remained. The 22 small aircrafts are regarded as the anomaly targets in this image. The RGB pseudocolor

8 8 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING Fig. 5. Real AVIRIS hyperspectral image of an urban area. (a) RGB pseudocolor image. (b) Reference. (c) Spectra of the background. (d) Spectra of the anomalies. image and reference for the AVIRIS data are shown in Fig. 5(a) and (b), respectively. The spectra of the background and anomalies in the real AVIRIS hyperspectral image are shown in Fig. 5(c) and (d). Note that the real HYDICE and AVIRIS hyperspectral images both cover urban areas, but the spectra of the background land cover in these two images are very different. And there exists a background land-cover of building in the right-up location of the AVIRIS image that has different spectrum from the background land-covers of airpark and shadow. This makes it difficult to implement accurate background estimation and suppression for these two real urban hyperspectral images. In order to further evaluate the proposed method, a third real-world Hyperion hyperspectral image was also utilized. The Hyperion hyperspectral dataset covers a rural area of the State of Indiana, USA, and can be downloaded from the EO-1 satellite image website. The anomalies in this dataset are not easily distinguishable from the background [9]. The Hyperion dataset has 242 spectral channels spanning μm. After removing the low-snr and water absorption bands, 155 bands were retained for our experiment. A subimage with the ground truth of the anomaly targets was utilized. The anomalies were a storage silo and roof, which occupied 17 pixels in the image. The background objects of field, crops, and water made up 94.22% of the image pixels. The anomalies, especially the storage silo s spectrum, were partly correlated with the spectra of the background objects and were not easily distinguishable from the background. The RGB pseudocolor image and reference for the Hyperion data are shown in Fig. 6(a) and (b). The spectra of the background and anomalies are shown in Fig. 6(c) and (d). Fig. 6. Real Hyperion hyperspectral image of a rural area. (a) RGB pseudocolor image. (b) Reference. (c) Spectra of the background. (d) Spectra of the anomalies. B. Detection Results of the Experimental Datasets In the experiments, we evaluated the detection performance of the proposed GSEAD method compared with some of the stateof-the-art hyperspectral anomaly detection methods: RX [21], CBAD [23], SSRX [26], BACON [24], and KRX [22]. The RX detector is a well-known Mahalanobis distance-based anomaly detection algorithm, and CBAD clusters data into appropriate categories to performance Mahalanobis distance-based anomaly detection within every category. The SSRX method is a subspace-based anomaly detector that finds the best subspace according to several maximum eigenvalues of the covariance matrix. BACON is a robust detection technique that aims to find the most appropriate Gaussian-distributed background pixels to compute the mean value vector and covariance matrix for detection. KRX is a nonlinear anomaly detection method that requires a kernel parameter σ to be chosen. The CBAD, SSRX, and KRX detectors all require parameters to be selected, and all of the methods were implemented with the optimum parameter settings in our experiments, with the same configurations as the respective original references. The detection maps obtained by the compared algorithms and the proposed GSEAD method are shown in Figs. 7 10, respectively. The results of these detection maps are analyzed in the following. Color detection maps of the compared methods and the proposed GSEAD method for the target-embedded PHI data are shown in Fig. 7. For the target-embedded PHI dataset, CBAD obtains its best detection performance by clustering the background into only one category. CBAD then degenerates to RX and obtains the same detection map as RX. However, RX and CBAD obtain a poor background suppression and give high false alarm rates. SSRX, which utilizes three eigenvectors for the subspace projection, performs better than RX and CBAD.

9 ZHAO AND ZHANG: GSEAD: GRAPHICAL SCORING ESTIMATION FOR HYPERSPECTRAL ANOMALY DETECTION 9 Fig. 7. Color detection maps obtained by the detection algorithms for the target-embedded PHI data: (a) RX, (b) CBAD, (c) SSRX, (d) BACON, (e) KRX, and (f) GSEAD, respectively. Fig. 10. Color detection maps of the detection algorithms for the real Hyperion hyperspectral image: (a) RX, (b) CBAD, (c) SSRX, (d) BACON, (e) KRX, and (f) GSEAD, respectively. Fig. 8. Color detection maps of the detection algorithms for the real HYDICE hyperspectral image: (a) RX, (b) CBAD, (c) SSRX, (d) BACON, (e) KRX, and (f) GSEAD, respectively. Fig. 9. Color detection maps of the detection algorithms for the real AVIRIS hyperspectral image: (a) RX, (b) CBAD, (c) SSRX, (d) BACON, (e) KRX, and (f) GSEAD, respectively. Nevertheless, SSRX also fails to suppress some types of background land cover. BACON achieves the best detection performance among the compared methods. KRX fails to suppress the background and generates a high false alarm rate. The proposed GSEAD method obtains a better background suppression than all of the compared detection methods and effectively extrudes the anomaly targets, even in the condition of low target abundances. Color detection maps of the compared methods and the proposed GSEAD method with the HYDICE hyperspectral image are shown in Fig. 8. For the real HYDICE hyperspectral dataset, RX and CBAD fail to suppress the background land cover of road II, and they also obtain high false alarm rates. SSRX successfully suppresses the background but leaves out some of the anomaly targets at the same time. BACON obtains a high false alarm rate due to the noise contamination of the background statistics estimation, and it mistakenly regards noise as anomalies. KRX fails to suppress the background land-cover types, except for parking lot. The proposed GSEAD method successfully suppresses most of the background land-cover types and extrudes the anomaly targets. Color detection maps of the compared methods and the proposed GSEAD method with the AVIRIS hyperspectral image are shown in Fig. 9. For the real AVIRIS hyperspectral dataset, RX, CBAD, and BACON fail to extrude the anomalies from the background and generate high false alarm rates. BACON, in particular, mistakenly considers the house (which is one of the background land-cover types) as an anomaly. SSRX and KRX obtain better detection results than RX, CBAD, and BA- CON; they extrude some of the anomalies from the background, but leave out a certain amount of anomalies. GSEAD performs much better than the compared detection methods; it extrudes all of the anomaly targets from the background and suppresses the background to an acceptable level. Color detection maps of the compared methods and the proposed GSEAD method with the real Hyperion hyperspectral image are shown in Fig. 10. For the real Hyperion hyperspectral dataset, RX, CBAD, and BACON fail to suppress the background land cover of field. Moreover, they also fail to control the noise contamination of the background statistics estimation. SSRX successfully suppresses the background but does not extrude most of the anomalies at the same time. KRX fails to suppress most of the background land-cover types. The proposed

10 10 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING GSEAD method suppresses the background to a satisfactory degree, and also extrudes all of the anomaly targets. Note that, from the detection maps of the four experimental images, it can be found that: 1) Although the first few rows of the embedded anomaly targets feature low target abundances, many of these anomalies can still be extruded by the proposed GSEAD method. 2) For the two real urban hyperspectral images acquired by HYDICE and AVIRIS, big differences between the spectra of the background land cover results in difficulty in implementing accurate background estimation and suppression. This also makes the anomaly targets difficult to detect. However, the proposed GSEAD method suppresses the background land cover in these two datasets to a satisfactory level and extrudes the anomaly targets. 3) The anomalies are partly correlated with the spectra of the background objects and are not easily distinguishable from the background in the real Hyperion hyperspectral image of a rural area. Despite this, the proposed GSEAD method successfully highlights the anomalies and distinguishes them from the background. Fig. 11. ROC curves of the proposed GSEAD method and the compared detection methods for the four experimental datasets: (a) target-embedded PHI data, (b) HYDICE, (c) AVIRIS, and (d) Hyperion, respectively. C. Quantitative Comparison and Discussion In order to quantitatively evaluate the detection performance, ROC curves [56] (with the coordinate axis of the false alarm rate at a log scale) are used to compare the different methods. If the ROC curve illustrates that a detection method acquires a higher detection rate than the other methods at the same false alarm rate, this indicates that the detection method outperforms the other methods. Another quantitative index, AUC, is also utilized to evaluate the methods. A detector with a larger area under its ROC curve will obtain a larger AUC value, which means that the detector obtains a better detection performance. A background-anomaly separation analysis is also implemented to evaluate the detection performance. The ROC curves, AUC values, and background-anomaly detection output ranges of the proposed GSEAD method and the compared detection methods are shown in Figs , respectively. Here, it can be seen that the proposed GSEAD method achieves the best ROC curves on all four experimental datasets, as shown in Fig. 11. For the target-embedded PHI data, SSRX achieves a better ROC curve than the other compared detection methods because there are a number of subpixel anomalies in this data, and SSRX generally performs well in detecting subpixel anomalies. Meanwhile, the GSEAD method performs a little better than SSRX on this dataset due to the fact that the GSEAD method exploits the intrinsic background characteristics, and the background is considerably different from the anomalies in this data. For the real HYDICE and Hyperion hyperspectral datasets, the GSEAD method achieves very low false alarm rates when the probability of detection reaches 100%. Although there are very low amounts of anomaly targets in these two datasets, the GSEAD method still successfully extrudes the anomalies. The strength of the GSEAD method for detecting anomaly targets is demonstrated in these two datasets. For the real AVIRIS hyperspectral image, the house Fig. 12. AUC values of the proposed GSEAD method and the compared detection methods for the four experimental datasets: (a) target-embedded PHI data, (b) HYDICE, (c) AVIRIS, and (d) Hyperion, respectively. can be considered as an interferential type of background land cover when detecting the anomaly targets in this image. Despite this, the GSEAD method achieves a high accuracy of detection with low false alarm rates. Furthermore, the proposed GSEAD method achieves the best AUC values, which are much higher than the values of the compared detection methods, on all four experimental datasets, as shown in Fig. 12. The GSEAD method also achieves better background-anomaly separation than the compared detection methods, as shown in Fig. 13. For the target-embedded PHI data and the real HYDICE and Hyperion hyperspectral datasets, the proposed GSEAD method achieves better background-anomaly separation than the compared detection methods. For the real AVIRIS hyperspectral

11 ZHAO AND ZHANG: GSEAD: GRAPHICAL SCORING ESTIMATION FOR HYPERSPECTRAL ANOMALY DETECTION 11 Fig. 14. Evaluation of the effect for pcc-graph in GSEAD method (a) RGB pseudo-color image of the HYDICE dataset. (b) Result map of pcc-grah. TABLE I RUNNING TIMES OF THE ALGORITHMS OBTAINED WITH THE HYPERSPECTRAL DATASETS /seconds (s) RX CBAD SSRX BACON KRX GSEAD Fig. 13. Detection output range of the background and anomaly targets for the proposed GSEAD method and the compared detection methods with the four experimental datasets: (a) target-embedded PHI data, (b) HYDICE, (c) AVIRIS, and (d) Hyperion, respectively. dataset, none of the competing detection methods obtain a good background-anomaly separation, but the GSEAD method separates the background and anomalies very well, achieving a pleasing background-anomaly separation. These quantitative results indicate that GSEAD can achieve very good background suppression for anomaly detection. In the following, we discuss the experiments with the four hyperspectral datasets. Through the previously described experimental results, it can be seen that the proposed GSEAD method obtains better detection performances than the compared state-of-the-art methods. For the case of subpixel anomalies, the proposed GSEAD method also performs well in extruding the anomaly targets from the background. Moreover, for both the urban areas with various different background landcover spectra and the rural area with the anomalies spectra correlated with the background spectra, the proposed GSEAD method successfully suppresses the background to an acceptable level and extrudes the anomalies. With the graphical analyses, we can conclude that GSEAD can achieve a stable and very pleasing detection performance. Here, we furthermore give a discussion of the effect for the pcc-graph in our proposed GSEAD method. We utilize the HY- DICE dataset in our experiment to evaluate the effect of the pcc-graph. Fig. 14(b) illustrates the result map of pcc-graph in GSEAD method for the HYDICE dataset. The white region represents the robust background and the black region represents the potential anomalies. And the potential anomalies occupy onefourth of the pixels in the HYDICE dataset. It can be seen that, with the pcc-graph, a mass of pixels that are low spectrally similar with the representative background are not included in the robust background. Meanwhile, these pixels which are mainly edge, noise and undefined objects are determined as potential anomalies. PHI HYDICE AVIRIS Hyperion A discussion of the computational complexity of the proposed GSEAD method is also provided. The computational complexity of GSEAD consists of three parts. The first part is the construction of the similarity matrix W G pcc for Dijkstra s algorithm. The complexity of this part is O(p kpcc), 2 where k pcc is the neighborhood size of the pcc-graph and p is the number of hyperspectral bands. The second part is the construction of the Laplacian matrix L G X b for the robust background dataset and solving the eigendecomposition problem X b L G X b X T b a elp = λx b D G X b X T b a elp. The complexity of this part is O(p kelp 2 + n3 b ), where k elp is the neighborhood size of the elp-graph and n b is the number of the robust background pixels. The third part is the construction of the similarity matrix W G gse for the graphical scoring estimation. The complexity of this part is O(p kgse), 2 where k gse is the neighborhood size of k-nn graphical scoring estimation. Therefore, the entire computational complexity of GSEAD is O(p (kpcc 2 + kelp 2 + k2 gse)+n 3 b ). GSEAD is efficient because k pcc, k elp, and k gse are all small numbers, p is usually around two hundred, and n b is usually far more less than the pixel number of the whole image dataset. Note that, the computational complexity analysis is just an approximated version, but not a detailed analysis. The computational costs of the proposed GSEAD method and the compared algorithms are shown in Table I. All of the algorithms and experiments were implemented in MATLAB software (2013a version) on a personal computer with an Intel(R) Core(TM) i GHz central processing unit, 8.0 GB of RAM, and 64-bit Windows 7. It can be seen that the proposed GSEAD method has a slightly higher computational cost than RX and SSRX, but it has a significantly lower computational cost than BACON and KRX. GSEAD also has a comparable computational cost to CBAD, and it beats BACON and KRX. The time cost is an important factor for the practical application

12 12 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING TABLE II WIN/TIE/LOSS EVALUATIONS OF THE PROPOSED GSEAD METHOD VERSUS THESTATE-OF-THE-ART DETECTIONMETHODSBASED ON PAIREDt-TESTS AT A 95% SIGNIFICANCE LEVEL Dataset PHI HYDICE AVIRIS Hyperion Summary for the method comparison RX 1/0/0 1/0/0 1/0/0 1/0/0 4/0/0 CBAD 1/0/0 1/0/0 1/0/0 1/0/0 4/0/0 SSRX 1/0/0 1/0/0 1/0/0 1/0/0 4/0/0 BACON 1/0/0 1/0/0 1/0/0 1/0/0 4/0/0 KRX 0/0/1 1/0/0 1/0/0 1/0/0 3/0/1 Summary for the dataset comparison 4/0/1 5/0/0 5/0/0 5/0/0 19/0/1 of an anomaly detector, so accelerating the proposed GSEAD method will be our future research focus. We also implemented win/tie/loss evaluations of the different methods based on paired t-tests at a 95% significance level, as shown in Table II. The t-test is a powerful statistical significance test, which has been widely utilized in comparing classifiers with multiple datasets [57], [58]. The t-test compares two detection results and reveals whether or not there is a significant statistical difference between the variances of the two detection results. The win/tie/loss approach is an evaluation mechanism for t-tests. If there is no significant difference between the two detection results, we consider the result to be a tie. If there is a significant difference between the two detection results, we then decide which detection result wins and which detection result loses. If one detection result wins, it means that this detection result obtains a less varying distribution for the high detection value range. Then, win means that the detection result is more reasonable and practical than the other. Otherwise, loss means that the detection result is less reasonable and practical. From Table II, we can see that the proposed GSEAD method obtains more reasonable and practical detection results than the other compared methods for most of the experimental datasets utilized in our experiments. D. Parameter Sensitivity Analysis The parameter analyses for the proposed GSEAD method were undertaken with the real HYDICE, AVIRIS, and Hyperion hyperspectral datasets. When implementing the analyses of one or more parameters in GSEAD, the other parameters were set to the values that achieve the best detection performance. The analyses for the neighborhood size k pcc of the pcc-graph for the proposed GSEAD method on the HYDICE, AVIRIS, and Hyperion datasets are shown in Fig. 15. Several different pcc-graph neighborhood sizes for the real HYDICE hyperspectral dataset are shown in Fig. 15(a) and (b), respectively. Fig. 15(c) and (d) show the ROC curves and AUC values with different pcc-graph neighborhood sizes for the real AVIRIS hyperspectral dataset. Fig. 15(e) and (f) show the ROC curves and AUC values with different pcc-graph neighborhood sizes for the real Hyperion hyperspectral dataset. Here, it can be Fig. 15. Analyses of different values of neighborhood size k pcc for the pccgraph. (a) (b): ROC curves and AUC values for the HYDICE hyperspectral dataset. (c) (d): ROC curves and AUC values for the AVIRIS hyperspectral dataset. (e) (f): ROC curves and AUC values for the Hyperion hyperspectral dataset. seen that when k pcc is larger than 3, GSEAD obtains a clearly reduced detection precision for the HYDICE dataset. Meanwhile, when k pcc =8, GSEAD obtains a considerably higher detection precision for the Hyperion dataset. This derives from the fact that the pcc-graph should be constructed with a specific range of neighborhood size. When the size of anomalies is small in the hyperspectral image, such as in HY- DICE and Hyperion dataset, the size of anomalies is one or two pixels, k pcc is mainly related to the number of image pixels. Combining with the dataset volumes of the HYDICE and Hyperion images, the empirical conclusion for choosing k pcc is that a pcc-graph neighborhood size of < k pcc n < generally achieves a good detection precision, where n is the pixel number of the hyperspectral images. Furthermore, when k pcc =7, GSEAD obtains a considerably higher detection precision for the AVIRIS dataset. Note that, the size of anomalies in the AVIRIS dataset is a little larger (5 pixels). This furthermore refines the empirical conclusion that the value of k pcc is also related to the size of anomalies. And the empirical conclusion is that the value of k pcc should be chosen as < s t k pcc n < , where s t is the size of anomalies in the hyperspectral image. Meanwhile, in the overview of the ROC performance in both Fig. 15(a), (c), and (e), it can be seen that the proposed GSEAD method achieves stable ROC

13 ZHAO AND ZHANG: GSEAD: GRAPHICAL SCORING ESTIMATION FOR HYPERSPECTRAL ANOMALY DETECTION 13 Fig. 17. Analyses of different values of neighborhood size k gse for the k-nn scoring estimation. (a) (b): ROC curves and AUC values for the HYDICE hyperspectral dataset. (c) (d): ROC curves and AUC values for the AVIRIS hyperspectral dataset. (e) (f): ROC curves and AUC values for the Hyperion hyperspectral dataset. Fig. 16. Analyses with AUC values for the neighborhood size k elp and the number of transformation vectors for the locality preserving graph embedding: (a) HYDICE dataset, and (b) Hyperion dataset. curve performances with all these different neighborhood sizes of pcc-graph. This proves that k pcc is not a very sensitive parameter and does not greatly affect the detection performance. The analyses with AUC values for the neighborhood size k elp and the number of transformation vectors for the locality preserving graph embedding on the HYDICE and Hyperion datasets are shown in Fig. 16(a) and (b), respectively. From Fig. 16, it can be seen that with transformation vectors, GSEAD obtains satisfactory detection performances with AUC values of more than 0.99 for both the HYDICE and Hyperion datasets. With more than 20 or less than ten transformation vectors, the detection performance of GSEAD clearly decreases. This is due to the fact that the intrinsic background characteristics are usually spanned by a specific number of transformation vectors. Too few transformation vectors will not properly reveal the intrinsic background characteristics, and too many transformation vectors will overly represent the intrinsic background characteristics. The empirical range of the transformation vector number for practical usage is 10 20, based on the aforementioned analysis. On the other hand, from Fig. 16, it can be seen that the neighborhood size k elp of the locality preserving graph embedding does not have a great effect on the detection precision. As with the HYDICE and Hyperion datasets, a neighborhood size for the locality preserving graph embedding in the range of 3 10 can achieve an acceptable detection performance. The analyses for the neighborhood size k gse of the k-nn scoring estimation for the proposed GSEAD method on the HY- DICE, AVIRIS, and Hyperion datasets are shown in Fig. 17. Several different neighborhood sizes of k-nn scoring estimation for the real HYDICE hyperspectral dataset are shown in Fig. 17(a) and (b), respectively. Fig. 17(c) and (d) show the ROC curves and AUC values with different neighborhood sizes of k-nn scoring estimation for the real AVIRIS hyperspectral dataset. Fig. 17(e) and (f) show the ROC curves and AUC values with different neighborhood sizes of k-nn scoring estimation for the real Hyperion hyperspectral dataset. When k gse =3, GSEAD achieves the best detection performance on the HYDICE dataset. When k gse =17, GSEAD achieves the best detection performance on the AVIRIS dataset. When k gse =4, GSEAD achieves the best detection performance on the Hyperion dataset. The empirical conclusion for choosing k gse is that the optimized neighborhood

14 14 IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING size for the k-nn scoring estimation is related to the size of anomalies. When the size of anomalies is small, such as in the HYDICE and Hyperion datasets, the neighborhood size for the k-nn scoring estimation needs to be small (k gse < 5). Oppositely, when the size of anomalies is large, such as in the AVIRIS dataset, the neighborhood size for the k-nn scoring estimation needs to be a little larger (10 <k gse < 20). Meanwhile, in the overview of the ROC performance in Fig. 17(a), (c), and (e), it can be seen that the proposed GSEAD method achieves stable ROC curve performances with all these different neighborhood sizes of k-nn scoring estimation. This proves that k gse is not a very sensitive parameter and does not greatly affect the detection performance. From the aforementioned analyses, it can be concluded that the proposed GSEAD method is not very sensitive to the neighborhood size parameters, i.e., k pcc, k elp, and k gse. However, the number of transformation vectors for the locality preserving graph embedding should be empirically chosen within a specific range. Furthermore, k pcc and k gse values are both related to the size of anomalies in the hyperspectral image. When the size of anomalies is small (one or two pixels), the most appropriate value of k pcc is mainly related to the number of image pixels. IV. CONCLUSION Almost all of the current anomaly detection algorithms exploit specific predetermined models to implement background estimation for hyperspectral anomaly detection. However, this paper has provided a fresh point of view by constructing a hyperspectral anomaly detector from a data-adaptive analysis perspective. The proposed method implements detection processing only with the characteristics of the data itself. With the purpose of exploring data-adaptive analysis for hyperspectral anomaly detection, the graphical description of hyperspectral imagery has been intensively investigated in our study. Analyses with three different graph constructions methods provide ways for the proposed GSEAD to effectively reveal the robust background characteristics, the intrinsic background characteristics, and the background-anomaly differences step-by-step. The proposed method can determine the characteristics of the background land-cover types in a hyperspectral image relative to the anomaly targets, which ensures the maximum separation between background and anomalies. Extensive experiments with a variety of hyperspectral image datasets confirm that the proposed anomaly detection algorithm outperforms the other state-of-the-art anomaly detection methods. REFERENCES [1] S. Rajendran, Hyperspectral Remote Sensing and Spectral Signature Applications. New Delhi, India: New India Publishing, [2] J. 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Syst., 2010, pp Rui Zhao (S 15) received the B.S. degree in photogrammetry and remote sensing from Wuhan University, Wuhan, China, in 2012, where he is currently working toward the Ph.D. degree at the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing. His research interests include hyperspectral image processing and machine learning. Liangpei Zhang (M 06 SM 08) received the B.S. degree in physics from Hunan Normal University, Changsha, China, in 1982, the M.S. degree in optics from the Xi an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi an, China, in 1988, and the Ph.D. degree in photogrammetry and remote sensing from Wuhan University, Wuhan, China, in He is currently the Head of the Remote Sensing Division, State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan, China. He is also a Chang-Jiang Scholar Chair Professor appointed by the Ministry of Education of China. He is currently a Principal Scientist for the China State Key Basic Research Project ( ) appointed by the Ministry of National Science and Technology of China to lead the remote sensing program in China. He has more than 500 research papers and five books. He is the holder of 15 patents. His research interests include hyperspectral remote sensing, high-resolution remote sensing, image processing, and artificial intelligence. Dr. Zhang is the Founding Chair of IEEE Geoscience and Remote Sensing Society Wuhan Chapter. He received the Best Reviewer awards from IEEE GRSS for his service to IEEE JOURNAL OF SELECTED TOPICS IN EARTH OBSERVATIONS AND APPLIED REMOTE SENSING (JSTARS) in 2012 and IEEE GEOSCIENCE AND REMOTE SENSING LETTERS (GRSL) in He was the General Chair for the 4th IEEE GRSS Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing and the Guest Editor of JSTARS. His research teams won the top three prizes of the IEEE GRSS 2014 Data Fusion Contest, and his students have been selected as the winners or finalists of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS) student paper contest in recent years. He is a Fellow of the Institution of Engineering and Technology, Executive Member (Board of Governor) of the China national committee of international geosphere biosphere programme, Executive Member of the China Society of Image and Graphics, etc. He received of the 2010 Best Paper Boeing award and the 2013 Best Paper ERDAS Award from the American Society of Photogrammetry and Remote Sensing (ASPRS). He regularly serves as a Co-Chair of the series SPIE conferences on multispectral image processing and pattern recognition, conference on Asia remote sensing, and many other conferences. He edits several conference proceedings, issues, and geoinformatics symposiums. He also serves as an Associate Editor of the International Journal of Ambient Computing and Intelligence, International Journal of Image and Graphics, International Journal of Digital Multimedia Broadcasting, Journal of Geo-spatial Information Science, andjournal of Remote Sensing, andthe guest editor of Journal of Applied Remote Sensing and Journal of Sensors.He is currently serving as an Associate Editor of the IEEE TRANSACTIONS ON GEO- SCIENCE AND REMOTE SENSING.