空域协同自编码器的高光谱异常检测

目的 自编码器作为一种无监督的特征提取算法,可以在无标签的条件下学习到样本的高阶、稠密特征。然而当训练集含噪声或异常时,会迫使自编码器学习这些异常样本的特征,导致性能下降。同时,自编码器应用于高光谱图像处理时,往往会忽略掉空域信息,进一步限制了自编码器的探测性能。针对上述问题,本文提出一种基于空域协同自编码器的高光谱异常检测算法。方法 利用块图模型优良的背景抑制能力从空域角度筛选用于自编码器训练的背景样本集。自编码器采用经预筛选的训练样本集进行网络参数更新,在提升对背景样本表达能力的同时避免异常样本对探测性能的影响。为进一步将空域信息融入探测结果,利用块图模型得到的异常响应构建权重,起到突出目标并抑制背景的作用。结果 实验在3组不同尺寸的高光谱数据集上与5种代表性的高光谱异常检测算法进行比较。本文方法在3组数据集上的AUC(area under the curve)值分别为0.990 4、0.988 8和0.997 0,均高于其他算法。同时,对比了不同的训练集选择策略,与随机选取和使用全部样本进行对比。结果表明,本文基于空域响应的样本筛选方法相较对比方法具有较明显的优势。结论 提出的基...     

粗定位和协同表示的高光谱图像异常检测

目的 由于在军事和民用应用中的重要作用,高光谱遥感影像异常检测在过去的20~30年里一直都是备受关注的研究热点。然而,考虑到异常点往往藏匿于大量的背景像元之中,且只占据很少的数量,给精确检测带来了不小的挑战。针对此问题,基于异常点往往表现在高频的细节区域这一前提,本文提出了一种基于异常点粗定位和协同表示的高光谱遥感影像异常检测算法。方法 对输入的原始高光谱遥感影像进行空间维的降质操作;通过衡量降质后影像与原始影像在空间维的差异,粗略定位可能的异常点位置;将粗定位的异常点位置用于指导像元间的协同表示以重构像元;通过衡量重构像元与原始像元的差异,从而进一步优化异常检测结果。结果 在4个数据集上与6种方法进行了实验对比。对于San Diego数据集,次优算法和本文算法分别取得的AUC （area under curve）值为0.978 6和0.994 0;对于HYDICE （hyperspectral digital image collection equipment）数据集,次优算法和本文算法的AUC值为0.993 6和0.998 5;对于Honghu数据集,次优算法和本文方法的AUC值分别为0.999 2和0.999 3;对Grand Isle数据集而言,尽管本文方法以0.001的差距略低于性能第1的算法,但从目视结果图中可见,本文方法所产生的虚警目标远少于性能第1的算法。结论 本文所提出的粗定位和协同表示的高光谱异常检测算法,综合考虑了高光谱遥感影像的谱间特性,同时还利用了其空间特性以及空间信息的先验分布,从而获得异常检测结果的提升。     

Random selection-based adaptive saliency-weighted RXD anomaly detection for hyperspectral imagery

With recent advances in hyperspectral imaging sensors, subtle and concealed targets that cannot be detected by multispectral imagery can be identified. The most widely used anomaly detection method is based on the Reed–Xiaoli (RX) algorithm. This unsupervised technique is preferable to supervised methods because it requires no a priori information for target detection. However, two major problems limit the performance of the RX detector (RXD). First, the background covariance matrix cannot be properly modelled because the complex background contains anomalous pixels and the images contain noise. Second, most RX-like methods use spectral information provided by data samples but ignore the spatial information of local pixels. Based on this observation, this article extends the concept of the weighted RX to develop a new approach called an adaptive saliency-weighted RXD (ASW-RXD) approach that integrates spectral and spatial image information into an RXD to improve anomaly detection performance at the pixel level. We recast the background covariance matrix and the mean vector of the RX function by multiplying them by a joint weight that in fuses spectral and local spatial information into each pixel. To better estimate the purity of the background, pixels are randomly selected from the image to represent background statistics. Experiments on two hyperspectral images showed that the proposed random selection-based ASW RXD (RSASW-RXD) approach can detect anomalies of various sizes, ranging from a few pixels to the sub-pixel level. It also yielded good performance compared with other benchmark methods.     

A spectral-spatial method based on low-rank and sparse matrix decomposition for hyperspectral anomaly detection

Recently, some methods based on low-rank and sparse matrix decomposition (LRASMD) have been developed to improve the performance of hyperspectral anomaly detection (AD). However, these methods mainly take advantage of the spectral information in hyperspectral imagery (HSI), and ignore the spatial information. This article proposes an LRASMD-based spectral-spatial (LS-SS) method for hyperspectral AD. First, the Go Decomposition (GoDec) algorithm is employed to solve the low-rank background component and the sparse anomaly component. Next, the sparse component is explored to calculate the spectral sparsity divergence index (SDI). Based on spectral SDI, the detection result in the spectral domain and the reliable background points, which are employed as training data to construct the background manifold by linear local tangent space alignment (LLTSA), can also be obtained. Then, based on the background manifold and the transformation matrix, the low-dimensional manifold of the whole data is computed by linear mapping. After that, the kernel collaborative representation detector (KCRD) is used in the low-dimensional manifold of the whole data for the spatial SDI. Finally, SS SDI is computed for the final detection result. The theoretical analysis and experimental results demonstrate that the proposed LS-SS can achieve better performance when compared with the comparison algorithms.     

Fast anomaly detection in hyperspectral images with RX method on heterogeneous clusters

Remotely sensed hyperspectral sensors provide image data containing rich information in both the spatial and the spectral domain, and this information can be used to address detection tasks in many applications. One of the most widely used and successful algorithms for anomaly detection in hyperspectral images is the RX algorithm. Despite its wide acceptance and high computational complexity when applied to real hyperspectral scenes, few approaches have been developed for parallel implementation of this algorithm. In this paper, we evaluate the suitability of using a hybrid parallel implementation with a high-dimensional hyperspectral scene. A general strategy to automatically map parallel hybrid anomaly detection algorithms for hyperspectral image analysis has been developed. Parallel RX has been tested on an heterogeneous cluster using this routine. The considered approach is quantitatively evaluated using hyperspectral data collected by the NASA’s Airborne Visible Infra-Red Imaging Spectrometer system over the World Trade Center in New York, 5 days after the terrorist attacks. The numerical effectiveness of the algorithms is evaluated by means of their capacity to automatically detect the thermal hot spot of fires (anomalies). The speedups achieved show that a cluster of multi-core nodes can highly accelerate the RX algorithm.     

结合孪生网络和像素配对的高光谱图像异常检测

目的 高光谱遥感中,通常利用像素的光谱特征来区分背景地物和异常目标,即通过二者之间的光谱差异来寻找图像中的异常像元。但传统的异常检测算法并未有效挖掘光谱的深层特征,高光谱图像中丰富的光谱信息没有被充分利用。针对这一问题,本文提出结合孪生神经网络和像素配对策略的高光谱图像异常检测方法,利用深度学习技术提取高光谱图像的深层非线性特征,提高异常检测精度。方法 采用像素配对的思想构建训练样本,与原始数据集相比,配对得到的新数据集数量呈指数增长,从而满足深度网络对数据集数量的需求。搭建含有特征提取模块和特征处理模块的孪生网络模型,其中,特征处理模块中的卷积层可以专注于提取像素对之间的差异特征,随后利用新的训练像素对数据集进行训练,并将训练好的分类模型固定参数,迁移至检测过程。用滑动双窗口策略对测试集进行配对处理,将测试像素对数据集送入网络模型,得到每个像素相较于周围背景像素的差异性分数,从而识别测试场景中的异常地物。结果 在异常检测的实验结果中,本文提出的孪生网络模型在San Diego数据集的两幅场景和ABU-Airport数据集的一幅场景上,得到的AUC （area under the curve）值分别为0.993 51、0.981 21和0.984 38,在3个测试集上的表现较传统方法和基于卷积神经网络的异常检测算法具有明显优势。结论 本文方法可以提取输入像素对的深层光谱特征,并根据其特征的差异性,让网络学习到二者的区分度,从而更好地赋予待测像素相对于周围背景的异常分数。本文方法相对于卷积神经网络的异常检测方法可以有效地降低虚警,与传统方法相比能够更加明显地突出异常目标,提高了检测率,同时也具有较强的鲁棒性。     

Hyperspectral anomaly detection based on constrained eigenvalue–eigenvector model

Anomaly detection in a large area using hyperspectral imaging is an important application in real-time remote sensing. Anomaly detectors based on subspace models are suitable for such an anomaly and usually assume the main background subspace and its dimensions are known. These detectors can detect the anomaly for a range of values of the dimension of the subspace. The objective of this paper is to develop an anomaly detector that extends this range of values by assuming main background subspace with an unknown user-specified dimension and by imposing covariance of error to be a diagonal matrix. A pixel from the image is modeled as the sum of a linear combination of the unknown main background subspace and an unknown error. By having more unknown quantities, there are more degrees of freedom to find a better way to fit data to the model. By having a diagonal matrix for the covariance of the error, the error components become uncorrelated. The coefficients of the linear combination are unknown, but are solved by using a maximum likelihood estimation. Experimental results using real hyperspectral images show that the anomaly detector can detect the anomaly for a significantly larger range of values for the dimension of the subspace than conventional anomaly detectors.     

一种改进PCA与IHS融合的高光谱图像异常检测算法

高光谱图像空间分辨率不足容易导致异常检测虚警率过高,针对此提出了一种新的异常检测算法。算法首先利用主成分分析PCA对低分辨率高光谱图像进行主成分提取,然后对所提取的主成分和高分辨率图像分别进行IHS变换,分别得到各自的强度分量。运用IHS变换的可逆性,将高光谱数据新的强度分量与原色度分量H和饱和度分量S进行IHS逆变换,得到空间信息增强的高光谱图像数据,最后使用改进的KwRX算法对空间信息增强的高光谱图像数据进行异常检测。仿真实验表明,与KRX算法、PCA-KRX算法相比,本算法在检测目标像素数和虚警个数上都有较大的改善,说明了本算法的的有效性和可行性。     

基于增强空谱特征网络的空间感知协同表示算法

高光谱图像具有高维度、带间相关性较高、样本数量较少等诸多问题,直接利用表示学习算法对高光谱图像进行分类会导致严重的维数灾难.对于高光谱图像,不是所有的光谱带都可用于特定的分类任务.因此,文中提出基于增强空谱特征网络的空间感知协同表示算法.依据高光谱图像内在的低维流形构建基于空谱特征的分层网络.利用训练的网络对高维数据进...     

结合超像元和子空间投影支持向量机的高光谱图像分类

目的 高光谱图像包含了丰富的空间、光谱和辐射信息,能够用于精细的地物分类,但是要达到较高的分类精度,需要解决高维数据与有限样本之间存在矛盾的问题,并且降低因噪声和混合像元引起的同物异谱的影响。为有效解决上述问题,提出结合超像元和子空间投影支持向量机的高光谱图像分类方法。方法 首先采用简单线性迭代聚类算法将高光谱图像分割成许多无重叠的同质性区域,将每一个区域作为一个超像元,以超像元作为图像分类的最小单元,利用子空间投影算法对超像元构成的图像进行降维处理,在低维特征空间中执行支持向量机分类。本文高光谱图像空谱综合分类模型,对几何特征空间下的超像元分割与光谱特征空间下的子空间投影支持向量机（SVMsub）,采用分割后进行特征融合的处理方式,将像元级别转换为面向对象的超像元级别,实现高光谱图像空谱综合分类。结果 在AVIRIS（airbone visible/infrared imaging spectrometer）获取的Indian Pines数据和Reflective ROSIS（optics system spectrographic imaging system）传感器获取的University of Pavia数据实验中,子空间投影算法比对应的非子空间投影算法的分类精度高,特别是在样本数较少的情况下,分类效果提升明显;利用马尔可夫随机场或超像元融合空间信息的算法比对应的没有融合空间信息的算法的分类精度高;在两组数据均使用少于1%的训练样本情况下,同时融合了超像元和子空间投影的支持向量机算法在两组实验中分类精度均为最高,整体分类精度高出其他相关算法4%左右。结论 利用超像元处理可以有效融合空间信息,降低同物异谱对分类结果的不利影响;采用子空间投影能够将高光谱数据变换到低维空间中,实现有限训练样本条件下的高精度分类;结合超像元和子空间投影支持向量机的算法能够得到较高的高光谱图像分类精度。     

RX architectures for real-time anomaly detection in hyperspectral images

In the field of hyperspectral image processing, anomaly detection (AD) is a deeply investigated task whose goal is to find objects in the image that are anomalous with respect to the background. In many operational scenarios, detection, classification and identification of anomalous spectral pixels have to be performed in real time to quickly furnish information for decision-making. In this framework, many studies concern the design of computationally efficient AD algorithms for hyperspectral images in order to assure real-time or nearly real-time processing. In this work, a sub-class of anomaly detection algorithms is considered, i.e., those algorithms aimed at detecting small rare objects that are anomalous with respect to their local background. Among such techniques, one of the most established is the Reed–Xiaoli (RX) algorithm, which is based on a local Gaussian assumption for background clutter and locally estimates its parameters by means of the pixels inside a window around the pixel under test (PUT). In the literature, the RX decision rule has been employed to develop computationally efficient algorithms tested in real-time systems. Initially, a recursive block-based parameter estimation procedure was adopted that makes the RX processing and the detection performance differ from those of the original RX. More recently, an update strategy has been proposed which relies on a line-by-line processing without altering the RX detection statistic. In this work, the above-mentioned RX real-time oriented techniques have been improved using a linear algebra-based strategy to efficiently update the inverse covariance matrix thus avoiding its computation and inversion for each pixel of the hyperspectral image. The proposed strategy has been deeply discussed pointing out the benefits introduced on the two analyzed architectures in terms of overall number of elementary operations required. The results show the benefits of the new strategy with respect to the original architectures.     

双卷积池化结构的3D-CNN高光谱遥感影像分类方法

目的 高光谱遥感影像数据包含丰富的空间和光谱信息,但由于信号的高维特性、信息冗余、多种不确定性和地表覆盖的同物异谱及同谱异物现象,导致高光谱数据结构呈高度非线性。3D-CNN（3D convolutional neural network）能够利用高光谱遥感影像数据立方体的特性,实现光谱和空间信息融合,提取影像分类中重要的有判别力的特征。为此,提出了基于双卷积池化结构的3D-CNN高光谱遥感影像分类方法。方法 双卷积池化结构包括两个卷积层、两个BN（batch normalization）层和一个池化层,既考虑到高光谱遥感影像标签数据缺乏的问题,也考虑到高光谱影像高维特性和模型深度之间的平衡问题,模型充分利用空谱联合提供的语义信息,有利于提取小样本和高维特性的高光谱影像特征。基于双卷积池化结构的3D-CNN网络将没有经过特征处理的3D遥感影像作为输入数据,产生的深度学习分类器模型以端到端的方式训练,不需要做复杂的预处理,此外模型使用了BN和Dropout等正则化策略以避免过拟合现象。结果 实验对比了SVM（support vector machine）、SAE（stack autoencoder）以及目前主流的CNN方法,该模型在Indian Pines和Pavia University数据集上最高分别取得了99.65%和99.82%的总体分类精度,有效提高了高光谱遥感影像地物分类精度。结论 讨论了双卷积池化结构的数目、正则化策略、高光谱首层卷积的光谱采样步长、卷积核大小、相邻像素块大小和学习率等6个因素对实验结果的影响,本文提出的双卷积池化结构可以根据数据集特点进行组合复用,与其他深度学习模型相比,需要更少的参数,计算效率更高。     

局部梯度轮廓变换的高光谱异常检测

目的 高光谱异常检测由于其重要的应用价值,引起了研究人员的广泛关注,但大部分的检测算法,往往直接利用输入的高光谱遥感影像所携带的光谱信息或者空谱信息进行检测。考虑到由于成像过程的限制,如成像条件的复杂性以及光谱通道众多导致的每个通道光子数量有限等问题,所获取的高光谱遥感影像往往在一定程度上偏离真实场景,而这也制约了异常检测的精度。针对此问题,本文提出了一种局部梯度轮廓变换的高光谱遥感影像异常检测算法。方法 为了在不影响算法性能的基础上减少计算复杂度,首先选取部分可能的异常像元,只对这些局部的异常像元可能位置进行梯度轮廓变换。其次,将变换后的梯度轮廓用于指导原始高光谱遥感影像的空域增强。最后,对增强后的高光谱遥感影像进行检测。通过将局部梯度轮廓用于影像的增强,避免了成像过程中由于细节损失而造成检测精度受限的情况。结果 实验在来自4个数据集的6幅高光谱遥感影像上进行了性能验证。首先利用经典的Global-RX （Reed Xiaoli）检测算法同时检测本文算法增强后的影像和原始影像,分别取得的平均AUC （area under curve）值为0.987 1和0.933 6,本文算法带来了0.053 5的精度提升;同时,通过与其他3种预处理方法进行比较,证明了本文局部梯度轮廓变换方法的有效性;更进一步,利用基于协同表示CRD （collaborative representation-based detector）的检测器对增强后的影像和原始影像分别进行检测,分别取得的平均AUC值为0.990 7和0.977 5,检测结果再次验证了本文算法能够有效提升影像的检测精度;通过对比,实验数据表明本文所采用的局部梯度轮廓变换可减少约37.82%的时间复杂度。结论 本文算法通过将局部的梯度轮廓进行变换并用于指导原始影像的增强过程,使得影像的空间轮廓信息更为锐利,更为接近真实场景,从而获得异常检测结果的提升。     

Feature extraction method based on spectral dimensional edge preservation filtering for hyperspectral image classification

ABSTRACT

A large amount of spectral and spatial information contained in hyperspectral imagery has provided a great opportunity to effectively characterize and identify the surface materials of interest. Feature extraction plays a very important role for hyperspectral data classification, which can reduce noise from the original data and improve the separability of land classes. A novel feature extraction technique based on spectral dimensional edge preserving filter is proposed in this paper. A series of Gaussian filters are applied in the spatial domain of the hyperspectral image to produce the guidance image, then, the edge preserving filter which is guided by the guidance image is adopted and applied in the spectral domain of the hyperspectral data to get the feature. For the feature is produced by filtering in the spectral domain, the spectral curves of the feature are more continues, which avoids the spectral discontinuity problems result from the traditional two-dimensional spatial filter. The guidance image is obtained by filtering the original image in the spatial domain, so, the spatial and the spectral information are integrated together in the following spectral edge preserving filtering process. We carefully adjusted the parameters of the filter and applied it to different real hyperspectral remote sensing images, with the support vector machine, multinomial logistic regression, and random forest serving as the classifier, by comparing with other feature extraction methods presented in recent literature, the results indicate that the proposed methodology always has a great performance in different kinds of cases.     

嵌入式深度神经网络高光谱图像聚类

目的 高光谱图像的高维特性和非线性结构给聚类任务带来了"维数灾难"和线性不可分问题，以往的工作将特征提取过程与聚类过程互相剥离，难以同时优化。为了解决上述问题，提出了一种新的嵌入式深度神经网络模糊C均值聚类方法（EDFCC）。方法 EDFCC算法为了提取更加有效的深层特征，联合优化高光谱图像的特征提取和聚类过程，将模糊C均值聚类算法嵌入至深度自编码器网络中，可以保持两任务联合优化的优势，同时利用深度自编码器网络降维以及逼近任意非线性函数的能力，逐步将原始数据映射到潜在特征空间，提取数据的深层特征。所提方法采用模糊C均值聚类算法约束特征提取过程，学习适用于聚类的高光谱数据深层特征，动态调整聚类指示矩阵。结果 实验结果表明，EDFCC算法在Indian Pines和Pavia University两个高光谱数据集上的聚类精度分别达到了42.95%和60.59%，与当前流行的低秩子空间聚类算法（LRSC）相比分别提高了3%和4%，相比于基于自编码器的数据聚类算法（AEKM）分别提高了2%和3%。结论 EDFCC算法能够从高光谱图像的高维光谱信息中提取更加有效的深层特征，提升聚类精度，并且由于EDFCC算法不需要额外的训练过程，大大提升了聚类效率。     

Hyperspectral anomaly detection using spectral–spatial features based on the human visual system

ABSTRACT

Anomaly detection (AD) is one of the most attracting topics within the recent 10 years in hyperspectral imagery (HSI). The goal of the AD is to label the pixels with significant spectral or spatial differences to their neighbours, as targets. In this paper, we propose a method that uses both spectral and spatial information of HSI based on human visual system (HVS). By inspiring the retina and the visual cortex functionality, the multiscale multiresolution analysis is applied to some principal components of hyperspectral data, to extract features from different spatial levels of the image. Then the global and local relations between features are considered based on inspiring the visual attention mechanism and inferotemporal (IT) part of the visual cortex. The effects of the attention mechanism are implemented using the logarithmic function which well highlights, small variations in pixels’ grey levels in global features. Also, the maximum operation is used over the local features for imitating the function of IT. Finally, the information theory concept is used for generating the final detection map by weighting the global and local detection maps to obtain the final anomaly map. The result of the proposed method is compared with some state-of-the-art methods such as SSRAD, FLD, PCA, RX, KPCA, and AED for two well-known real hyperspectral data which are San Diego airport and Pavia city, and a synthetic hyperspectral data. The results demonstrate that the proposed method effectively improves the AD capabilities, such as enhancement of the detection rate, reducing the false alarm rate and the computation complexity.     

Maximized subspace model for hyperspectral anomaly detection

An important application in remote sensing using hyperspectral imaging system is the detection of anomalies in a large background in real-time. A basic anomaly detector for hyperspectral imagery that performs reasonaly well is the RX detector. In practice, the subspace RX (SSRX) detector which deletes the clutter subspace has been known to perform better than the RX detector. In this paper an anomaly detector that can do better than the SSRX detector without having to delete the clutter subspace is developed. The anomaly detector partials out the effect of the clutter subspace by predicting the background using a linear combination of the clutter subspace. The Mahalanobis distance of the resulting residual is defined as the anomaly detector. The coefficients of the linear combination are chosen to maximize a criterion based on squared correlation. The experimental results are obtained by implementing the anomaly detector as a global anomaly detector in unsupervised mode with background statistics computed from hyperspectral data cubes with wavelengths in the visible and near-infrared range. The results show that the anomaly detector has a better performance than the SSRX detector. In conclusion, the anomaly detector that is based on partialling out can achieve better performance than the conventional anomaly detectors.     

Geostatistical and local cluster analysis of high resolution hyperspectral imagery for detection of anomalies

This paper describes a new methodology to detect small anomalies in high resolution hyperspectral imagery, which involves successively: (1) a multivariate statistical analysis (principal component analysis, PCA) of all spectral bands; (2) a geostatistical filtering of noise and regional background in the first principal components using factorial kriging; and finally (3) the computation of a local indicator of spatial autocorrelation to detect local clusters of high or low reflectance values and anomalies. The approach is illustrated using 1 m resolution data collected in and near northeastern Yellowstone National Park. Ground validation data for tarps and for disturbed soils on mine tailings demonstrate the ability of the filtering procedure to reduce the proportion of false alarms (i.e., pixels wrongly classified as target), and its robustness under low signal to noise ratios. In almost all scenarios, the proposed approach outperforms traditional anomaly detectors (i.e., RX detector which computes the Mahalanobis distance between the vector of spectral values and the vector of global means), and fewer false alarms are obtained when using a novel statistic S₂ (average absolute deviation of p-values from 0.5 through all spectral bands) to summarize information across bands. Image degradation through addition of noise or reduction of spectral resolution tends to blur the detection of anomalies, increasing false alarms, in particular for the identification of the least pure pixels. Results from a mine tailings site demonstrate the approach performs reasonably well for highly complex landscape with multiple targets of various sizes and shapes. By leveraging both spectral and spatial information, the technique requires little or no input from the user, and hence can be readily automated.     

Variable factorization model based on numerical optimization for hyperspectral anomaly detection

The objective of this article is to develop an anomaly detector as an analytical expression for detecting anomalous objects in remote sensing using hyperspectral imaging. Conventional anomaly detectors based on the subspace model have a parameter which is the dimension of the clutter subspace. The range of possible values for this parameter is typically large, resulting in a large number of images of detector output to be analyzed. An anomaly detector with a different parameter is proposed. The pixel of known random variables from a data cube is modeled as a linear transformation of a set of unknown random variables from the clutter subspace plus an error of unknown random variables in which the transformation matrix of constants is also unknown. The dimension of the clutter subspace for each spectral component of the pixel can vary, hence some elements in the transformation matrix are constrained to be zeros. The anomaly detector is the Mahalanobis distance of the resulting residual. The experimental results which are obtained by implementing the anomaly detector as a global anomaly detector in unsupervised mode with background statistics computed from hyperspectral data cubes with wavelengths in the visible and near-infrared range show that the parameter in the anomaly detector has a significantly reduced number of possible values in comparison with conventional anomaly detectors.