each class and use this reduced training set for learning. Finding representatives reduces the computation and storage requirements, and can even be used for tasks such as clustering. In the ideal case, if we collect the samples that contain enough information about the distribution of the whole data set, the learning performance would be very close to the performance using all the data.

### Finding Representatives for Multi-PIE Dataset {#subsec:reps_multipie}

[1]{} ![ Selection of 10 representatives out of 520 images of a subject and their corresponding angles. []{data-label="fig:PIE_selection"}](Figures/PIE_selection2.png "fig:"){width="0.8\columnwidth"}

[1]{} ![ Selection of 10 representatives out of 520 images of a subject and their corresponding angles. []{data-label="fig:PIE_selection"}](Figures/angles.pdf "fig:"){width="0.6\columnwidth"}

Here, we present our experimental results on CMU Multi-PIE Face Database [@Gross2010Multi-PIE]. We use 249 subjects from the first session with 13 poses, 20 illuminations, and two expressions. Thus, there are $13\times 20\times 2$ images per subject. Figure \[subfig:PIE-example\] shows 10 selected images from 520 images of a subject. As it can be seen, the results of K-medoids and DS3 algorithms are concentrated on side views, while our selection provides images from more diverse angles. Figure\[subfig:angles\] highlights this by showing the angles of selected images of each algorithm. IPM selects from 10 