I'm trying to parse a paper about a new (to me) clustering algorithm into code, and I want to make sure I understand the math correctly... but the notation is holding me up. From page 3 , equation 2:
$$ L(\mathcal{M};x) = \sum_{j=1}^n \min_{m \in \mathcal{M}\cup\{x\}} d(m, x_j) $$
My interpretation of this is "The cost of assigning point $x$ to set $\mathcal{M}$ equals the sum of distances between $m$ and $x_j$ where $m$ is the closest object to $x_j$.
However, I'm afraid that my interpretation of this is muddied because I know that's how other, similar algorithms work. This might seem trivial, so I hope you will forgive me: Is this interpretation correct?