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Machine learning techniques have been widely used in communication systems because of their superior performance. Among them, the classical machine learning algorithm Principal Component Analysis (PCA) aims to estimate the principal subspace of the received signals, and thus is also known as subspace estimation. It is often used in Direction of Arrival (DoA) tasks. Recently, the widespread deployment of networks has motivated researchers to solve the problem of subspace estimation in decentralized settings. An important concern in the design of decentralized algorithms is the communication complexity, because communication consumes much energy, while the sensors in the network are generally energy-limited. Specifically, communication complexity refers to the minimum amount of transmitted variables to obtain an estimate with an error smaller than $\varepsilon$. For existing algorithms, this complexity is $O(\log ^{2}(1/\varepsilon))$. In this paper, we improve this complexity to be $O(\log (1/\varepsilon))$ by designing a new algorithm named Decentralized Subspace Estimation (DSE). Such improvement is achieved by using the gradient tracking technique. We theoretically analyze the influence of the network connectivity and the eigen-gap of the data on communication complexity. In addition, we use DSE to solve the DoA estimation problem. Experiments verify the effectiveness of the algorithm and the correctness of the theoretical result. [ABSTRACT FROM AUTHOR]

Change-Point Detection (CPD) has been researched for a long time in statistical signal processing, and has been widely used in many applications such as monitoring and anomaly detection. When detecting over networks, existing algorithms require sensors to exchange information via transmitting full-precision variables, which requires large bandwidth and consumes a large amount of energy. To address these problems, we explore the idea of quantizing data with low precision without deteriorating the detection performance. Specifically, considering the strong autocorrelation of the transmitted sequence in time domain and the accumulation of quantization error due to the autocorrelation, we design a scheme that combines the differential quantization technique and the error feedback technique. Based on this scheme, we propose a communication-efficient decentralized CPD algorithm named Quantized CUSUM (Q-CUSUM), which only requires small bandwidth and has low energy consumption. We theoretically analyze two commonly-used detection criteria, namely Average Run Length (ARL) and Expected Detection Delay (EDD), and compute their theoretical bounds. It is proved that the detection performance is robust to the quantization error. The proposed quantization scheme can be easily extended to the partial-communication case, where at each time only a subset of sensor pairs are allowed to exchange information. Experiments are implemented on both synthetic and real-world datasets. The results indicate that the proposed quantization scheme can effectively reduce the communication cost without deteriorating the detection performance. [ABSTRACT FROM AUTHOR]

Change-point detection has a long history of research in statistical signal processing and remains a fundamental problem in many real-world applications involving information extraction from streaming data. Exploiting low-dimensional structures (subspace in particular) of high-dimensional signals is another research topic of significance, as it improves not only efficiency in computation, storage, and communication, but also interpretability and understanding of data. In this paper, we formulate the problem of subspace change-point detection, where a stream of high-dimensional data points lie on a low-dimensional subspace that abruptly changes at a certain time instant. Then, we propose a cumulative-sum-based algorithm for the task of detection in this problem setup. From the algorithmic perspective, the proposed method is computationally efficient, as it proceeds in an online and recursive manner, and each iteration involves simple matrix computation; it is also practical and flexible, as it works under mild conditions on the distribution of data points after change point. From the theoretical perspective, we derive rigorous performance bounds of the proposed algorithm in terms of false alarm rate and detection delay. We also conduct extensive numerical experiments on both synthetic and real-world data to validate effectiveness of our algorithm and correctness of theoretical analysis. [ABSTRACT FROM AUTHOR]