Joint unsupervised learning of deep representations and image clusters

Build a directed nearest-neighbor graph from current image features, with Gaussian edge weights and a distance-derived bandwidth. Measure cluster affinity using the symmetric sum of directed graph-degree linkage: A(C,D)=1/|C|² 1_C^T W_CD W_DC 1_C + 1/|D|² 1_D^T W_DC W_CD 1_D. During a forward period hold features fixed. For each cluster rank neighboring clusters by affinity; choose a merge using the loss consisting of negative nearest-neighbor affinity plus a term favoring its affinity gap over the remaining K_c−1 neighbors. Merge the selected cluster with its best neighbor. After a partially unrolled period, keep the resulting labels fixed and update the CNN using the paper’s approximate sample-level weighted triplet loss, encouraging same-cluster affinity relative to nearby different-cluster samples. The paper limits negative selection to at most K_c neighboring samples from other clusters in the training batch. Refresh features and graph affinities after neural updates and continue until the requested cluster count. Fast initial small clusters reduce the number of merge steps.