This article investigates the online identification and data clustering problems for mixed linear regression (MLR) model with two components, including the symmetric MLR, and the asymmetric MLR with the balanced mixture. Two corresponding new online identification algorithms are introduced based on the expectation-maximization and least-squares principles. It is shown that both algorithms will converge to the true parameter set for any nonzero initial value without resorting to the traditional independent and identically distributed data assumptions. The main challenge in our investigation lies in the fact that the gradient of the likelihood function does not have a unique zero, and a key step in our analysis is to establish the stability of the corresponding differential equation in order to apply the celebrated Ljung's ordinary differential equation method. It is also shown that the within-cluster error and the probability that the new data are categorized into the correct cluster are asymptotically the same as those in the case of known parameters. Finally, numerical simulations are provided to verify the effectiveness of our online algorithms.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

http://dx.doi.org/10.1109/TAC.2025.3649290

Author:

Liu, Yujing

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Email address: liuyujing@amss.ac.cn

Liu, Zhixin (corresponding author)

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Email address: lzx@amss.ac.cn

Guo, Lei

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Email address: Lguo@amss.ac.cn