# Dirichlet Process Mixture Modelling

Generate Observations

X1 X2
1
0
0
1

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: