TY - JOUR

T1 - Bounded Confidence Gossip Algorithms for Opinion Formation and Data Clustering

AU - Nguyen, Linh Thi Hoai

AU - Wada, Takayuki

AU - Masubuchi, Izumi

AU - Asai, Toru

AU - Fujisaki, Yasumasa

N1 - Funding Information:
This work was supported by JST CREST Grant Number JPMJCR15K2, Japan.
Funding Information:
Manuscript received January 22, 2018; revised January 25, 2018; accepted May 14, 2018. Date of publication June 1, 2018; date of current version February 26, 2019. This work was supported by JST CREST Grant Number JPMJCR15K2, Japan. Recommended by Associate Editor Z. Sun. (Corresponding author: Takayuki Wada.) L. T. H. Nguyen, T. Wada, and Y. Fujisaki are with the Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan (e-mail: nth.linh@ist.osaka-u.ac.jp; t-wada@ist.osaka-u.ac.jp; fujisaki@ist.osaka-u.ac.jp).
Publisher Copyright:
© 1963-2012 IEEE.

PY - 2019/3

Y1 - 2019/3

N2 - 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.

AB - 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.

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U2 - 10.1109/TAC.2018.2843294

DO - 10.1109/TAC.2018.2843294

M3 - Article

AN - SCOPUS:85048015377

VL - 64

SP - 1150

EP - 1155

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 3

M1 - 8370736

ER -