Hierarchical clustering projection showing genetic relationships among populations in and near the British Isles.

<p>Hierarchical clustering projection showing genetic relationships among populations in and near the British Isles.</p

Magnified view of the convex clustering results for the HGDP data in Europe and Central Asia.

<p>Magnified view of the convex clustering results for the HGDP data in Europe and Central Asia.</p

Hierarchical clustering of the European populations from the POPRES data.

<p>Hierarchical clustering of the European populations from the POPRES data.</p

Magnified view of the convex clustering results for the HGDP data in East Asia.

<p>Magnified view of the convex clustering results for the HGDP data in East Asia.</p

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.</p

Convex clustering of the breast cancer samples.

<p>Points on the plot indicate data vectors projected onto the first and third principal components (PCs) of the sample. Lines trace the cluster centers as they traverse the regularization path.</p

Convex clustering of the European populations from the POPRES data using <i>ϕ</i> = 10 and <i>k</i> = 40.

<p>Convex clustering of the European populations from the POPRES data using <i>ϕ</i> = 10 and <i>k</i> = 40.</p

Effects of the parameters <i>k</i> and <i>ϕ</i> on cluster paths in the Iris data.

<p>Black, red, and green points denote the species Iris-setosa, Iris-versicolor, and Iris-virginica, respectively. These points are projections of the Iris dataset on the first two principal components (PCs). Lines trace the cluster centers as they traverse the regularization path. The subtle impact of <i>ϕ</i> is revealed in two cases. At <i>k</i> = 50, a red dot coalesces with the right cluster at <i>ϕ</i> = 0, but with the left cluster for larger values of <i>ϕ</i>. At <i>k</i> = 5 or <i>k</i> = 10, the two green dots at the extreme lower left corner coalesce later at the largest value of <i>ϕ</i>.</p

Convex clustering of the HGDP data using a large number of nearest neighbors to infer intercontinental connections (<i>k</i> = 4, <i>ϕ</i> = 1).

<p>Convex clustering of the HGDP data using a large number of nearest neighbors to infer intercontinental connections (<i>k</i> = 4, <i>ϕ</i> = 1).</p

Magnified view of results from convex clustering of Northeast Europe.

<p>Magnified view of results from convex clustering of Northeast Europe.</p