Encoder-Decoder Symmetric Nonnegative Matrix Tri-Factorization for Graph Clustering

Symmetric nonnegative matrix tri-factorization (SNMTF) provides an interpretable, parts-based representation for graph data, where node memberships and cluster interactions jointly expose the community structure. Yet many SNMTF variants are decoder-only, reconstructing the graph without guaranteeing the latent variables are recoverable, which can yield drifting embeddings and unstable memberships. We introduce an encoder–decoder SNMTF (ED-SNMTF) that couples graph reconstruction with an encoder-consistency principle: the interaction matrix must be inferable by projecting the graph onto the learned membership space. This coupling induces implicit orthogonality: membership columns repel through the consistency term, so crisp clusters emerge without explicit orthogonality penalties or post hoc k-means. The optimization of the parameters of our model relies on GPU-accelerated computing with CUDA and is trained using the Adam optimizer, with a nonnegative projection step to guarantee feasibility and promote stable convergence. We evaluate ED-SNMTF on real-world networks and show that it outperforms both traditional baselines and recent deep methods.