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Mixture models are used for clustering, ... A Bayesian Gaussian mixture model is commonly extended to fit a vector of unknown parameters (denoted in bold), or ...
Model-based clustering [1] based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not ...
It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem. [2] EM clustering of Old Faithful eruption data. The random initial model (which, due to the different scales of the axes, appears to be two very flat and wide ellipses) is fit to the observed data.
Standard model-based clustering methods include more parsimonious models based on the eigenvalue decomposition of the covariance matrices, that provide a balance between overfitting and fidelity to the data. One prominent method is known as Gaussian mixture models (using the expectation-maximization algorithm).
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
This behavior is important in the general case of a mixture of multiple distribution components. Let X be a mixture of G p-dimensional Gaussian distributions with common covariance. Then for any fixed K less than G, the distortion of a clustering as p goes to infinity is infinite. Intuitively, this means that a clustering of less than the ...
Additionally, the nonparametric nature of this model makes it an ideal candidate for clustering problems where the distinct number of clusters is unknown beforehand. In addition, the Dirichlet process has also been used for developing a mixture of expert models, in the context of supervised learning algorithms (regression or classification ...
A more general class of regression-based multi-fidelity methods are Bayesian approaches, e.g. Bayesian linear regression, [3] Gaussian mixture models, [10] [11] Gaussian processes, [12] auto-regressive Gaussian processes, [2] or Bayesian polynomial chaos expansions. [4]