Xingchao Jian;Martin Gölz;Feng Ji;Wee Peng Tay;Abdelhak M. Zoubir
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A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing With False Discovery Rate Control
The detection of interesting or anomalous signal behavior using sensor networks plays a key role in many applications. In this work, we model the sensor network as a graph, with each vertex representing a sensor and a signal over time associated with each vertex. The objective is to identify the true state of the signal at each point in the joint spatio-temporal domain. We propose a step-up empirical Bayes multiple hypothesis testing approach to make decisions based on local summary statistics. To this end, we establish consistent estimates of the prior probability of the null hypothesis as well as the probability models under the alternative, which are obtained using a bandlimited generalized graph signal model. Asymptotic control of the false discovery rate is proven. Numerical experiments validate the effectiveness of our approach compared to existing methods.
期刊介绍:
The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.