Deep embedded clustering

Initialize the encoder with a stacked denoising autoencoder followed by reconstruction fine-tuning; discard the decoder and initialize K cluster centers with k-means on embeddings. With z_i=f_theta(x_i), set s_ij=(1+||z_i−mu_j||²/alpha)^(-(alpha+1)/2), then q_ij=s_ij/sum_k s_ik; the reported experiments use alpha=1. At a target refresh compute f_j=sum_i q_ij and p_ij=(q_ij²/f_j)/sum_k(q_ik²/f_k). Hold P fixed while using minibatch gradient updates of encoder parameters and centers to reduce KL(P||Q)=sum_ij p_ij log(p_ij/q_ij). Recompute assignments and targets periodically and repeat. Hard labels are argmax_j q_ij; the reported stopping rule uses the fraction changing between checks. The pinned Python driver materializes the target weights for a subsequent Caffe optimization interval, confirming that it does not differentiate through target construction.