Dirichlet Process Mixture Modelling

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DP-Means

Note: The data have been generated by drawing from the following process:
  • \( \mathbf{g} \sim \operatorname{Dir} (\alpha, \ldots, \alpha) \)
  • \( \forall k \in \{1, \ldots, K\} \)
    • \( \theta_k \sim \operatorname{MVNorm} \left( \left(\begin{array}{c} \\ 0 \\ 0 \end{array}\right), \rho \mathbf{I} \right) \)
  • \( \forall i \in \{1, \ldots, n\} \)
    • \( z_i \sim \operatorname{Multinom} \left( \mathbf{g} \right) \)
    • \( x_i \sim \operatorname{MVNorm} \left(\theta_{z_i}, \mathbf{\Sigma} \right)\)
The DP-Means algorithm ('Revisiting k-means : New Algorithms via Bayesian Nonparametrics', Kulis et al), converged in the following number of iterations:

          

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