One-Class Support Measure Machines for Group Anomaly Detection

arXiv.org Machine Learning

We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish an interesting connection to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.


A Theoretical Investigation of Graph Degree as an Unsupervised Normality Measure

arXiv.org Machine Learning

For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The measure is intuitive given the abnormal samples are usually rare and they are dissimilar to the rest of the data. In order to have an in-depth theoretical understanding, in this manuscript, we investigate the graph degree in spectral graph clustering based and kernel based point of views and draw connections to a recent kernel method for the two sample problem. We show that our analyses guide us to choose fully-connected graphs whose edge weights are calculated via universal kernels. We show that a simple graph degree based unsupervised anomaly detection method with the above properties, achieves higher accuracy compared to other unsupervised anomaly detection methods on average over 10 widely used datasets. We also provide an extensive analysis on the effect of the kernel parameter on the method's accuracy.


One-Class Support Measure Machines for Group Anomaly Detection

arXiv.org Machine Learning

We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish an interesting connection to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.


Detecting Relative Anomaly

arXiv.org Machine Learning

System states that are anomalous from the perspective of a domain expert occur frequently in some anomaly detection problems. The performance of commonly used unsupervised anomaly detection methods may suffer in that setting, because they use frequency as a proxy for anomaly. We propose a novel concept for anomaly detection, called relative anomaly detection. It is tailored to be robust towards anomalies that occur frequently, by taking into account their location relative to the most typical observations. The approaches we develop are computationally feasible even for large data sets, and they allow real-time detection. We illustrate using data sets of potential scraping attempts and Wi-Fi channel utilization, both from Google, Inc.


Adversarial Regression for Detecting Attacks in Cyber-Physical Systems

arXiv.org Artificial Intelligence

Attacks in cyber-physical systems (CPS) which manipulate sensor readings can cause enormous physical damage if undetected. Detection of attacks on sensors is crucial to mitigate this issue. We study supervised regression as a means to detect anomalous sensor readings, where each sensor's measurement is predicted as a function of other sensors. We show that several common learning approaches in this context are still vulnerable to \emph{stealthy attacks}, which carefully modify readings of compromised sensors to cause desired damage while remaining undetected. Next, we model the interaction between the CPS defender and attacker as a Stackelberg game in which the defender chooses detection thresholds, while the attacker deploys a stealthy attack in response. We present a heuristic algorithm for finding an approximately optimal threshold for the defender in this game, and show that it increases system resilience to attacks without significantly increasing the false alarm rate.