论文标题
在图表上的低级别以及时空数据中的暂时平滑稀疏分解以进行异常检测
Low-rank on Graphs plus Temporally Smooth Sparse Decomposition for Anomaly Detection in Spatiotemporal Data
论文作者
论文摘要
时空数据中的异常检测是在多种应用中遇到的一个具有挑战性的问题，包括高光谱成像，视频监视和城市交通监测。现有的异常检测方法最适合序列数据中的点异常，无法处理时空数据中出现的时间和空间依赖性。近年来，已经提出了基于张量的方法来解决此问题。这些方法依赖于常规的张量分解模型，而不是考虑到异常的结构，而是被监督或半监督。我们引入了一种无监督的基于张量的异常检测方法，该方法考虑了异常的稀疏和时间连续性。特别是，异常检测问题被提出为鲁棒的低位 +稀疏张量分解，并具有正则化项，可最大程度地减少稀疏部分的时间变化，因此提取的异常在时间上是持久的。我们还通过图最小化近似秩最小化，以降低优化算法的复杂性。最终的优化问题是凸，可扩展的，并且证明与缺少的数据和噪声相关。对合成和实际时空城市交通数据进行了评估，并与基线方法进行了评估。
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance, and urban traffic monitoring. Existing anomaly detection methods are most suited for point anomalies in sequence data and cannot deal with temporal and spatial dependencies that arise in spatiotemporal data. In recent years, tensor-based methods have been proposed for anomaly detection to address this problem. These methods rely on conventional tensor decomposition models, not taking the structure of the anomalies into account, and are supervised or semi-supervised. We introduce an unsupervised tensor-based anomaly detection method that takes the sparse and temporally continuous nature of anomalies into account. In particular, the anomaly detection problem is formulated as a robust lowrank + sparse tensor decomposition with a regularization term that minimizes the temporal variation of the sparse part, so that the extracted anomalies are temporally persistent. We also approximate rank minimization with graph total variation minimization to reduce the complexity of the optimization algorithm. The resulting optimization problem is convex, scalable, and is shown to be robust against missing data and noise. The proposed framework is evaluated on both synthetic and real spatiotemporal urban traffic data and compared with baseline methods.
