Learning doubly stochastic and nearly idempotent affinity matrix for graph-based clustering

In graph-based clustering, a relevant affinity matrix is crucial for good results. Double stochasticity of the has been shown to be an important condition, both in theory and practice. this paper, we emphasize idempotency as another key condition. fact, theorem from Sinkhorn, R. (1968) allows us exhibit bijective relationship between set doubly stochastic idempotent matrices order n (modulo permutation rows columns) on one hand, possible partitions objects other hand. Thereby, properties are necessary sufficient conditions properly modeling clustering or graph partitioning tasks using matrices. Yet, leads NP-hard discrete optimization problem. context, our main contribution introduction new relaxed model that efficiently learns double nearly clustering. Our approach leverages existing their associated Laplacian The resulting problem bi-convex can addressed by Alternating Direction Method Multipliers scheme. Furthermore, requires less parameters contrast most recent works. experimental results obtained several real-world benchmarks, interest method importance taking into account