Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks

Jacek Lebiedź; Piotr Cofta; Cezary Orłowski

doi:10.3390/s21186211

Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks

Sensors ◽

10.3390/s21186211 ◽

2021 ◽

Vol 21 (18) ◽

pp. 6211

Author(s):

Jacek Lebiedź ◽

Piotr Cofta ◽

Cezary Orłowski

Keyword(s):

Social Networks ◽

Sensor Networks ◽

Sensor Network ◽

Analytical Approach ◽

Mathematical Proof ◽

Moving Average ◽

Rigorous Proof ◽

Stable Conditions ◽

Weighted Moving Average ◽

Previous Step

Uncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof. Therefore the question remains, whether under stable conditions, in realistic situations found in IoT networks, this algorithm indeed converges. This paper demonstrates proof of the eventual convergence of the EWMA algorithm. The proof consists of two steps: it models the sensor network as the UOG (Uniform Opinion Graph) that enables the analytical approach to the problem, and then offers the mathematical proof of eventual convergence, using formalizations identified in the previous step. The paper demonstrates that the EWMA algorithm converges under all realistic conditions.

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Change point detection in social networks using a multivariate exponentially weighted moving average chart

Journal of Information Science ◽

10.1177/0165551519863351 ◽

2019 ◽

Vol 46 (6) ◽

pp. 790-809

Author(s):

Ali Salmasnia ◽

Mohammadreza Mohabbati ◽

Mohammadreza Namdar

Keyword(s):

Social Networks ◽

Control Chart ◽

Change Point ◽

Moving Average ◽

Change Point Detection ◽

Network Density ◽

Exponentially Weighted Moving Average ◽

The Social ◽

Point Detection ◽

Weighted Moving Average

Although the significant role of social networks in communications between individuals has attracted researchers’ attention to the social networks, only few authors investigated social network monitoring in their studies. Most of the existing studies in this context suffer from the following three main drawbacks: (1) using the case-based network attributes such as person experiences and departments instead of the main attributes such as network density and centrality attributes, (2) monitoring the social attributes separately with the assumption that they are independent of each other and (3) ignoring detection of real time of change in the network. To overcome the above-mentioned disadvantages, this research develops a statistical method for monitoring the connections among actors in the social networks with the four most important network attributes consisting of (1) network density, (2) degree centrality, (3) betweenness centrality and (4) closeness centrality. To this end, a multivariate exponentially weighted moving average (MEWMA) control chart is used for simultaneous monitoring of these four correlated attributes. Furthermore, since the control chart usually does not alert a signal in the exact time of change due to type II error, this study presents a change point detection method to reduce cost and time required for diagnosing the control chart signal. Eventually, the efficiency of the proposed approach in comparison with the existing methods is evaluated through a simulation procedure. The results indicate that the suggested method has better performance than the univariate approach in detecting change point.

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