Poster
Interpolating Convex and Non-Convex Tensor Decompositions via the Subspace Norm
Qinqing Zheng · Ryota Tomioka
210 C #79
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Abstract
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Abstract:
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 for recovering a th order rank one tensor of size by recursive unfolding. In this paper, we first improve this bound to by a much simpler approach, but with a more careful analysis. Then we propose a new norm called the \textit{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 bound, in which the parameter 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 .
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