has no parameters for fine tuning, unlike some existing methods [@Elhamifar2016DissimilaritySelection; @Elhamifar2012SeeObjects]. This makes IPM dataset- and problem-independent.

-   Robustness of the proposed solution is investigated theoretically.

-   The superiority of the proposed algorithm is shown in different computer vision applications.

Problem Statement and Related Work {#sec:pr}
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Let $\boldsymbol{a}_1, \boldsymbol{a}_2,\ldots, \boldsymbol{a}_M\in \mathbb{R}^N$ be $M$ given data points of dimension $N$. We define an $M\times N$ matrix, $\boldsymbol{A}$, such that $\boldsymbol{a}_m^T$ is the $m^{th}$ row of A, for $m=1,2,\ldots, M$. The goal is to reduce this matrix into a $K\times N$ matrix, $\boldsymbol{A}_R$, based on an optimality metric. In this section, we introduce some related work on matrix subset selection and data selection.

 Selection Based on Diversity
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Consider a large system of equations $\boldsymbol{y}=\boldsymbol{Aw}$, which can be interpreted as a simple linear classifier in which $\boldsymbol{y}$ is the vector of labels, $\boldsymbol{A}$ represents the training data and $\boldsymbol{w}$ is the classifier weights. An optimal sense for data selection is to reduce this system of equations to a smaller system, $\boldsymbol{y}_R=\boldsymbol{A}_R\hat{\boldsymbol{w}}$, such that the reduced subsystem estimates the same classifier as the original system, i.e., the estimation error of $\hat{\boldsymbol{w}}$ is minimized [@Derezinski2018SubsamplingSampling]. A typical selection objective is to minimize 