An efficient ECM algorithm for maximum likelihood estimation in mixtures of t-factor analyzers

• Published in: Computational statistics Vol. 28; no. 2; pp. 751 - 769
• Main Authors: Wang, Wan-Lun, Lin, Tsung-I
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2013; Springer Nature B.V
• Subjects: Accommodation; Algorithms; Approximation; Clustering; Computational mathematics; Convergence; Data compression; Economic Theory/Quantitative Economics/Mathematical Methods; Electrochemical machining; Mathematical models; Mathematics and Statistics; Maximization; Maximum likelihood estimation; Maximum likelihood method; Missing data; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Studies; Theorems; Maximum likelihood estimation; ECM algorithm; MFA; AECM algorithm; EM algorithm; MtFA
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-012-0327-z

Mixture of t factor analyzers (MtFA) have been shown to be a sound model-based tool for robust clustering of high-dimensional data. This approach, which is deemed to be one of natural parametric extensions with respect to normal-theory models, allows for accommodation of potential noise components, atypical observations or data with longer-than-normal tails. In this paper, we propose an efficient expectation conditional maximization (ECM) algorithm for fast maximum likelihood estimation of MtFA. The proposed algorithm inherits all appealing properties of the ordinary EM algorithm such as its stability and monotonicity, but has a faster convergence rate since its CM steps are governed by a much smaller fraction of missing information. Numerical experiments based on simulated and real data show that the new procedure outperforms the commonly used EM and AECM algorithms substantially in most of the situations, regardless of how the convergence speed is assessed by the computing time or number of iterations.