We study federated spectral estimation when a large matrix is horizontally partitioned across servers that cannot share raw data. We propose FLICKER, a target-specific gradient-based power iteration that recovers a singular direction associated with a prescribed spectral target using only matrix-vector products on local blocks. Different target directions can be recovered independently and in parallel. We establish non-asymptotic convergence guarantees and provide a recursive grid-search procedure for spectral target selection. Building on FLICKER, we develop BiFLICKER for federated community detection in bipartite networks, together with a sequential projected variant for nearby or repeated singular directions. Under a sparse bipartite stochastic block model, we show that properly rescaled leading singular values from a reference server provide valid global targets, and that Sequential BiFLICKER achieves a vanishing misclustering rate and exact recovery under stronger sparsity conditions. Simulations show that BiFLICKER remains close to centralized spectral clustering and is more robust than existing federated spectral baselines when local sample sizes are small. On a LastFM user-artist network naturally partitioned by country, Sequential BiFLICKER attains an overall ARI of 0.94 against centralized clustering while revealing cross-country communities with distinct listening profiles.

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