200 mixture components. Each component is a Gaussian distribution with $\sigma=1.0$ and $\mu$ on a square of size $70 \times 70$. The means are placed at least $2.5 \sigma$ apart from each other. The dataset contains 50 samples per mixture component.

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          **opt.**                                                                                                                                                                                                                                                                                     
         **method**                      **avg $\pm$ std**                                         **best**                                          **avg $\pm$ std**                                         **best**                                          **avg $\pm$ std**                                        **best**
          hard-EM     ${  \mbox{$\medmuskip=0mu\displaystyle1.9e5 \pm 2e5$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle7.0e4$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle5.8e5 \pm 3e5$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle2.2e5$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle5.3e3 \pm 9e3$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle1.5$}}$
          [G-MM]{}    ${  \mbox{$\medmuskip=0mu\displaystyle9.7e3 \pm 1e4$}}$    ${  \mbox{$\medmuskip=0mu\displaystyle1.5$}}$     ${  \mbox{$\medmuskip=0mu\displaystyle2.0e4 \pm 0$}}$    ${  \mbox{$\medmuskip=0mu\displaystyle2.0e4$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle4.5e3 \pm 8e3$}}$   ${  \mbox{$\medmuskip=0mu\displaystyle1.5$}}$
          hard-EM                         $1.69 \pm 0.03$                                           $1.21$                                           $52.61 \pm 47.06$                                          $4.00$                                            $1.55 \pm 0.17$                                          $1.10$  
          [G-MM]{}                        $1.43 \pm 0.15$                                           $1.10$                                            $1.21 \pm 0.05$                                           $1.10$                                            $1.45 \pm 0.14$                                          $1.10$
          hard-EM                         $1929 \pm 429$                                            $1293$                                           $44453 \pm 88341$                                          $3026$                                             $1237 \pm 92$                                           $1117$
          [G-MM]{}                         $1465 \pm 43$                                            $1246$                                             $1470 \pm 8$                                             $1444$                                             $1162 \pm 95$                                           $1067$
          hard-EM                         $2.25 \pm 0.10$                                           $2.07$                                           $11.20 \pm 0.63$                                           $9.77$                                            $2.12 \pm 0.07$                                          $1.99$
          [G-MM]{}                        $2.04 \pm 0.09$                                           $1.90$                                            $1.85 \pm 0.02$                                           $1.80$                                            $1.98 \pm 0.06$                                          $1.89$
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We compare results from three different initializations: **forgy** selects $k$ training 