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Probabilistic mixture models such as Gaussian mixture models (GMM) are used to resolve point set registration problems in image processing and computer vision fields. For pair-wise point set registration , one point set is regarded as the centroids of mixture models, and the other point set is regarded as data points (observations).
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.
Model-based clustering [1] bases this 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 ...
A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models (Technical Report TR-97-021). International Computer Science Institute. includes a simplified derivation of the EM equations for Gaussian Mixtures and Gaussian Mixture Hidden Markov Models.
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The foundational theory of graph cuts was first applied in computer vision in the seminal paper by Greig, Porteous and Seheult [3] of Durham University.Allan Seheult and Bruce Porteous were members of Durham's lauded statistics group of the time, led by Julian Besag and Peter Green, with the optimisation expert Margaret Greig notable as the first ever female member of staff of the Durham ...
Types of generative models are: Gaussian mixture model (and other types of mixture model) Hidden Markov model; Probabilistic context-free grammar; Bayesian network (e.g. Naive bayes, Autoregressive model) Averaged one-dependence estimators; Latent Dirichlet allocation; Boltzmann machine (e.g. Restricted Boltzmann machine, Deep belief network)
For instance, mixtures of Gaussian process experts, where the number of required experts must be inferred from the data. [8] [9] As draws from a Dirichlet process are discrete, an important use is as a prior probability in infinite mixture models. In this case, is the parametric set of component distributions. The generative process is ...