Explanation on arg min Would someone be so kind to explain this to me:
$$\pi_nk=\left\{\begin{array}{cl}1&\textrm{if }k=\arg\min_j\left\Vert\mathbf x_n-\mu_j\right\Vert^2\\0&\textrm{otherwise}\end{array}\right..$$
Especially the $\arg\min$ part.
(It's from the $k$-means algorithm.)

$arg min$ (or $arg max$) return the input for minimum (or maximum) output.
For example:
The graph illustrat  $f(x)=(sin(x-0.5)+cos(x)^2)*2$ 
The global minmum of $f(x)$ is $min(f(x)) \approx$ -2, while the $arg min(f(x)) \approx$ 4.9 .

