Performance of Rank-One Tensor Approximation on Incomplete Data
This work addresses the performance degradation in tensor signal estimation for scenarios with incomplete data, which is incremental as it builds on existing tensor approximation methods.
The paper tackles the problem of estimating a rank-one tensor signal from incomplete noisy observations, showing that performance analysis reduces to a random matrix model and quantifying the performance loss due to random entry deletion for memory cost reduction.
We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral analysis gives access to the reconstruction performance. These results shed light on and specify the loss of performance induced by an artificial reduction of the memory cost of a tensor via the deletion of a random part of its entries.