Density Peak Semi-Tied Covariance Matrices for Gaussian Mixture Models

People widely use Gaussian mixture models (GMM) in data mining and knowledge discovery. The flexibly tied GMM can solve the memory, computational load, and data shortage problems caused by increasing the number of Gaussian components. However, sharing a full-rank matrix for all Gaussian components in a flexibly tied GMM cannot express the data structure. For example, when facing complex data, Gaussian components that share several full-rank matrices have stronger fitting capabilities. Motivated by this problem, this paper proposes an adaptive semi-tied GMM (ASemi-tied GMM). (1) Adaptive grouping of Gaussian components based on defining a similarity measure for the covariance matrix of the Gaussian components and realizing the adaptive semi-tied covariance of GMM by sharing the semi-tied transformation of the covariance within the group. (2) For ASemi-tied GMM, the Grouped Fast Newton Minimum Residual (G-FNMR) algorithm is proposed to estimate the parameters of this model. This paper validates the proposed ASemi-tied GMM on synthetic and real datasets, and experimental results show that its performance in log-likelihood and clustering is better than algorithms such as flexibly tied GMM.