Canonical polyadic (CP) decomposition is widely used for modeling multiway high-dimensional data, but it does not explicitly incorporate mode-specific structural information such as temporal smoothness, network cohesion, or functional regularity. We propose a structure-regularized CP (SR-CP) framework that uses a unified quadratic penalty to encode diverse structural priors through positive semidefinite matrices. A soft orthogonality-promoting penalty is further introduced to enhance component distinctiveness and numerical stability. For estimation, we develop a cyclic block-coordinate descent algorithm for both rank-one and rank-R decompositions. Each regularized mode-wise update is reformulated as a ridge-type problem, leading to a tensor-specific generalized cross-validation criterion for automatic selection of regularization parameters. We establish convergence rates, consistency, and whole-tensor reconstruction error bounds under general noise conditions. Simulations show improved factor recovery and tensor reconstruction relative to classical CP. A real-image completion study demonstrates robustness under severe missingness, and the FRED-MD application yields temporally coherent and interpretable macroeconomic factors. Overall, SR-CP offers a flexible and principled framework for incorporating structural priors into CP tensor decomposition.
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