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原文摘要

The joint use of graph structure and node-specific information is central to transductive node classification, yet a fundamental theoretical question remains: when does graph structure actually help? We provide the first deterministic, non-asymptotic, distribution-free answer to this question. We build on nuclear-norm graph clustering and generalized convex clustering. Our formulation of the latter incorporates node features, partial labels, and general convex loss functions, making it suitable for transductive node classification. We analyze each problem separately to characterize when graph structure alone, or node information alone, is sufficient for perfect recovery. We then formulate a unified convex optimization problem through a shared atomic norm representation and prove that combining the two sources expands the range of conditions under which perfect recovery is guaranteed beyond what either source alone can certify. This shows when node information can improve clustering and graph structure can improve classification.