Figure 1
Model comparison experiments on synthetic linear hypergraphs. (a) Black pixels in the dyadic adjacency matrix (\(\gamma _0 = 4\)) represent edges, and they reveal 5 clusters in the diagonal blocks. (b) In the triadic adjacency matrix, colors reflect the number of triangles shared between nodes (\(\gamma _0 = 4\)). (c) The linear embedding achieves higher log-likelihoods than the periodic version for hypergraphs generated with different \(\gamma _0\). (d) Adjusted Rand Indices of K-means clustering based on the linear and periodic embedding are plotted against \(\gamma _0\). (e) Values in the heatmap represent the maximum likelihoods of the linear model \(\times 10^{-6}\) from Algorithm 3. The maxima are found along the diagonal when \(c_3^* = c_3\). (f) Values represent the Adjusted Rand Indices of K-means clustering based on the linear embedding for different values of \(c_3^*\) and \(c_3\).
