Papers › Interpolating Convex and Non-Convex Tensor Decompositions via the Subspace Norm
Interpolating Convex and Non-Convex Tensor Decompositions via the Subspace Norm
Qinqing Zheng, Ryota Tomioka
We consider the problem of recovering a low-rank tensor from its noisy observation. Previous work has shown a recovery guarantee with signal to noise ratio O(n^(⌈K/2 ⌉/2)) for recovering a $K$th order rank one tensor of size n×⋯×n by recursive unfolding. In this paper, we first improve this bound to O(n^(K/4)) by a much simpler approach, but with a more careful analysis. Then we propose a new norm called the subspace norm, which is based on the Kronecker products of factors obtained by the proposed simple estimator. The imposed Kronecker structure allows us to show a nearly ideal O(√(n)+√(Hᴷ⁻¹)) bound, in which the parameter H controls the blend from the non-convex estimator to mode-wise nuclear norm minimization. Furthermore, we empirically demonstrate that the subspace norm achieves the nearly ideal denoising performance even with H=O(1).
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