different angles, while the selected images by DS3 and K-medoids contain repetitious angles. Figure \[fig:time\_n\_error\] shows the performance of different selection algorithms in terms of normalized projection error and running time. It is evident that our proposed approach finds a better minimizer for Problem defined in equation (\[eq:orig\_sel\]) and is able to do so in orders of magnitude less time.

[0.48]{} ![Performance of different methods for minimizing the main cost function of representative selection in equation (\[eq:orig\_sel\]). (Left) The ratio of projection error using selection algorithms to projection error of random selection for selecting $K$ representatives from each subject, averaged over all the subjects. (Right) Running time of different algorithms versus number of input samples for selection.[]{data-label="fig:time_n_error"}](Figures/PIE_simulation_ratio_cropped.eps "fig:"){width="1\columnwidth"}

[0.48]{} ![Performance of different methods for minimizing the main cost function of representative selection in equation (\[eq:orig\_sel\]). (Left) The ratio of projection error using selection algorithms to projection error of random selection for selecting $K$ representatives from each subject, averaged over all the subjects. (Right) Running time of different algorithms versus number of input samples for selection.[]{data-label="fig:time_n_error"}](Figures/time_multipie_cropped.eps "fig:"){width="1\columnwidth"}

### Representatives To Generate Multi-view Images Using GAN {#sec:reps_multipie_gan}

Next, to investigate the effectiveness of the proposed selection, we use the selected samples to 