another more effective approach for subset selection, which chooses data such that the selected samples are able to approximate the rest of data accurately. This selection problem is formulated using a convex optimization problem and referred as sparse modeling representative selection (SMRS) algorithm [@Elhamifar2012SeeObjects]. The same goal is pursued by dissimilarity-based sparse subset selection (DS3), which is based on simultaneous sparse recovery for finding data representatives [@Elhamifar2016DissimilaritySelection]. Representative approaches, such as SMRS and DS3, provide more suitable subset rather than selecting some diverse samples. However, their computational burden is not tractable for large datasets. Moreover, SMRS and DS3 algorithms utilize some parameters in their implementation, which makes their fine tuning difficult.

In order to address above issues, we propose a novel representative-based selection method, referred to as Iterative Projection and Matching (IPM). In our algorithm, at each iteration the maximum information from structure of the data is captured by one selected sample, and the captured information is neglected in the next iterations by projection on the null-space of previously selected samples. In summary, this paper makes the following contributions:

-   The complexity of IPM is linear w.r.t. number of original data. Hence, IPM is tractable for larger datasets.

-   IPM 