An adaptive optimization method for estimating the number of components in a Gaussian mixture model

Regarding the determination of the number of components (M) in a Gaussian mixture model (GMM), this study proposes a novel method for adaptively locating an optimal value of M when using a GMM to fit a given dataset; this method avoids underfitting and overfitting due to an unreasonable manually specified interval. The major contributions of this study are highlighted: (1) An adaptive interval for M (denoted as M is an element of [M-Min(Ada), M-Max(Ada)]) based on two procedures of a novel method, the modified incremental Gaussian mixture model (MIGMM), is determined via an adjustable parameter beta. (2) Considering some typical criteria, the optimal number.. within the obtained adaptive interval [M-Min(Ada), M-Max(Ada)], M-Opt(Ada) , is ultimately determined. Regarding the adaptive interval, extensive experiments with typical synthetic datasets show that [M-Min(Ada) M-Max(Ada)], corresponding to the parameter [beta(Min) = 10(-11), beta(Max) = 10(-2)], is determined. The performance of the M-Opt(Ada) determination based on several typical criteria is evaluated on both synthetic and real-world datasets.