than convex relaxation-based algorithms with complexity $O(M^3)$ [@Joshi2009Sensor_selection]. Moreover, IPM performs faster than K-medoids algorithm, whose complexity is of order $O(KN(M-K)^2)$ [@Vijaya2004Leaders--Subleaders:Sets].

$\boldsymbol{A}$ and $K$\
**Output**:$\;\boldsymbol{A}_{\mathbb{T}}$\
**Initialization:**\
$\boldsymbol{A}^{(1)} \longleftarrow \boldsymbol{A}$\
$\mathbb{T}=\{\}$\
$ \text{for}\; k=1, \cdots ,K $\
end

[0.48]{} ![A toy example that illustrates the first iteration of IPM. (Left) The most matched sample with the first right singular vector, $\boldsymbol{v}$, is selected. (Right) The rest of samples are projected on the null space of the selected sample in order to continue selection in the lower dimensional subspace.[]{data-label="fig:intution"}](Figures/opt_new1.pdf "fig:"){width="1\columnwidth"}

[0.48]{} ![A toy example that illustrates the first iteration of IPM. (Left) The most matched sample with the first right singular vector, $\boldsymbol{v}$, is selected. (Right) The rest of samples are projected on the null space of the selected sample in order to continue selection in the lower dimensional subspace.[]{data-label="fig:intution"}](Figures/opt_new2.pdf "fig:"){width="1\columnwidth"}

A Lower Bound on Maximum Correlation
------------------------------------

In this section, we will derive a lower bound on the maximum of the absolute value of the correlation coefficient between data points $\boldsymbol{a}_1, \boldsymbol{a}_2,\ldots, \boldsymbol{a}_M$ and $\boldsymbol{v}$, when data are normalized on the unit sphere. Figure \[fig:intution\] shows an intuitive example for one iteration of the proposed algorithm. First, the leading singular 