Algorithm 3 K-means clustering algorithm

$$\begin{array}{cc}\hfill & 1:\text{Generate an initial set of}K\text{centroids}{m}_1,m_2,\dots ,m_K;\hfill \\ \hfill & 2:\text{Alternate between the following two steps}\hfill \\ \hfill & 3:\text{Assign each point}x\text{to the}‘‘\text{closest}’’\text{cluster}\hfill \\ \hfill & \text{arg}\underset{j\in \{1,2,\dots ,K\}}{\text{min}}\Vert x-m_j{\Vert }^2;\hfill \\ \hfill & 4:\text{Calculate the new cluster centroids}\hfill \\ \hfill & m_j^{new}=\frac{1}{\Vert S_j\Vert }\sum _{x\in S_j}x,j=1,2,\dots ,K;\hfill \\ \hfill & 5:\text{Stop when cluster assignment no longer changes}.\hfill \end{array}$$