Latent variable models and factors analysis
Latent variable models and factors analysis
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Mixtures of probabilistic principal component analyzers
Neural Computation
Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood
IEEE Transactions on Pattern Analysis and Machine Intelligence
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Probabilistic characterization and synthesis of complex driven systems
Probabilistic characterization and synthesis of complex driven systems
Parsimonious Gaussian mixture models
Statistics and Computing
Model-based clustering with non-elliptically contoured distributions
Statistics and Computing
Computational Statistics & Data Analysis
Robust mixture modeling using multivariate skew t distributions
Statistics and Computing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Model-based classification via mixtures of multivariate t-distributions
Computational Statistics & Data Analysis
Dimension reduction for model-based clustering
Statistics and Computing
Model-Based Learning Using a Mixture of Mixtures of Gaussian and Uniform Distributions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Model-based clustering via linear cluster-weighted models
Computational Statistics & Data Analysis
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In model-based clustering and classification, the cluster-weighted model is a convenient approach when the random vector of interest is constituted by a response variable $$Y$$ and by a vector $${\varvec{X}}$$ of $$p$$ covariates. However, its applicability may be limited when $$p$$ is high. To overcome this problem, this paper assumes a latent factor structure for $${\varvec{X}}$$ in each mixture component, under Gaussian assumptions. This leads to the cluster-weighted factor analyzers (CWFA) model. By imposing constraints on the variance of $$Y$$ and the covariance matrix of $${\varvec{X}}$$ , a novel family of sixteen CWFA models is introduced for model-based clustering and classification. The alternating expectation-conditional maximization algorithm, for maximum likelihood estimation of the parameters of all models in the family, is described; to initialize the algorithm, a 5-step hierarchical procedure is proposed, which uses the nested structures of the models within the family and thus guarantees the natural ranking among the sixteen likelihoods. Artificial and real data show that these models have very good clustering and classification performance and that the algorithm is able to recover the parameters very well.