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Bounded Confidence Gossip Algorithms for Opinion Formation and Data Clustering

机译：舆论形成和数据聚类的有界置信八卦算法

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摘要

This paper presents a bounded confidence gossip algorithm for describing the process of opinion formation over a communication network. Each agent in the network keeps a time-varying opinion vector (or state), which represents its opinion about a set of matters. A common confidence threshold is set for all of the agents. The states of agents in the network will be updated time by time according to an iterative procedure: At each time, 1) one agent is chosen randomly, then it chooses one of its neighbors on the communication graph to contact with; 2) they exchange their states; and 3) if they have different states and the distance between their states is strictly smaller than the confidence threshold, they update their states as the average of the two. This algorithm converges almost surely to some equilibrium point such that any two adjacent agents either have the same state or have distinct states whose distance is no less than the confidence threshold. This is called the constant confidence threshold algorithm. An increasing confidence threshold algorithm, which repeats the constant confidence threshold algorithm several times with increasing confidence threshold, is also proposed. The algorithm is also convergent almost surely to some equilibrium point. Applicability of the method to clustering problems is shown through numerical examples.
机译：本文提出了一种有界置信八卦算法，用于描述通信网络中意见形成的过程。网络中的每个代理都保留一个时变的观点向量（或状态），该向量代表其对一系列事务的观点。为所有代理设置共同的置信度阈值。网络中代理的状态将根据迭代过程一次次更新：每次：1）随机选择一个代理，然后在通信图上选择其邻居之一进行联系； 2）他们交换自己的状态； 3）如果它们具有不同的状态，并且它们之间的距离严格小于置信度阈值，则将其状态更新为两者的平均值。该算法几乎可以肯定地收敛到某个平衡点，以使任何两个相邻代理具有相同的状态或具有不小于置信度阈值的不同状态。这称为恒定置信度阈值算法。还提出了一种增加置信度阈值算法，该算法随着置信度阈值的增加多次重复恒定置信度阈值算法。该算法也几乎可以肯定地收敛到某个平衡点。通过数值示例说明了该方法对聚类问题的适用性。

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