Convex clustering concepts.

<p>For clarity, we present three random data points extracted from the three classes in the Iris dataset. Black points denote the original data points <b><i>X</i></b> and blue points denote the cluster centers <b><i>U</i></b>. At <i>μ</i> = 0, <b><i>X</i></b> and <b><i>U</i></b> coincide. At intermediate <i>μ</i> values (middle figure), <b><i>U</i></b> coalesces towards its cluster center. For sufficiently large <i>μ</i>, <b><i>U</i></b> converges to cluster centers (right figure). Note that in this demonstration, only the left two points have non-zero pairwise weights <i>w</i>_<i>ij</i>. Hence, the two resulting clusters reflect the two graphs defined by the matrix of weights.