Spectral anomaly detection using graph-based filtering for wireless sensor networks

Abstract

This paper introduces a novel spectral anomaly detection method by developing a graph-based filtering framework. In particular, we consider the problem of unsupervised data anomaly detection over wireless sensor networks (WSNs) where sensor measurements are represented as signals on a graph. In our framework, graphs are chosen to capture useful proximity information about measured data. The associated graph-based filters are then employed to project the graph signals on normal and anomaly subspaces, and resulting projections are used in detection of data anomalies. The proposed approach has two main advantages over the standard spectral technique, principal component analysis (PCA). Firstly, graph-based filtering allows us to incorporate structural information known a priori (e.g., distance between sensors) in addition to data. Secondly, it provides localized transformations leading to effective distributed anomaly detection. Our experimental results show that our proposed solution outperforms PCA-based and distributed clustering-based anomaly detection methods in terms of receiver operating characteristics (ROCs).

Graph Signal Processing: Overview, Challenges, and Applications

“…Then, data observations that are similar at neighboring nodes lead naturally to a smooth (low-pass) graph signal. Such a smooth graph signal model makes it possible to detect outliers or abnormal values by highpass filtering and thresholding [51], [155], or to build effective signal reconstruction methods from sparse set of sensor readings, as in [156], [157], [158], which can potentially lead to significant savings in energy resources, bandwidth and latency in sensor network applications.…”

Anomaly Detection in Partially Observed Traffic Networks

“…So, we refer to some survey papers that cover many of the recent techniques in graph based approaches: [32] and [33]. In particular, similar to the low rank approaches for SD networks, there are low rank approaches to graph models such as [34] who assume the inverse covariance matrix of their wireless sensor network data has a graph structure and solve a low rank penalized Gaussian graphical model problem and [35] who impose graph smoothness by a low rank assumption on graph Laplacian of the features of the network. [36] also uses a low rank approach on their KDD intrusion data set, but they directly apply the low rank assumption to the network characteristics of their data.…”

Learning Graphs With Monotone Topology Properties and Multiple Connected Components

“…In this section, we evaluate Algorithm 1 with image data. We use the Brodatz texture images from the USC-SIPI dataset 3 . We take the subset of rotated textures straw*.tiff and partition each image into non-overlapping blocks of size 8 × 8.…”

“…Particularly, in signal processing and machine learning, graphs have been extensively used for modeling high dimensional datasets, where graphs' nodes represent objects of interest and the edges with designated weights encode pairwise relations between them. Applications of such models include transformation [1], filtering [2], [3] and sampling of signals defined on graphs [4], as well as clustering [5], [6], semi-supervised learning [7], dynamical systems [8], [9], and network-oriented data problems [10], [11].…”