3,516 research outputs found
Multi-tensor Completion for Estimating Missing Values in Video Data
Many tensor-based data completion methods aim to solve image and video
in-painting problems. But, all methods were only developed for a single
dataset. In most of real applications, we can usually obtain more than one
dataset to reflect one phenomenon, and all the datasets are mutually related in
some sense. Thus one question raised whether such the relationship can improve
the performance of data completion or not? In the paper, we proposed a novel
and efficient method by exploiting the relationship among datasets for
multi-video data completion. Numerical results show that the proposed method
significantly improve the performance of video in-painting, particularly in the
case of very high missing percentage
Recovery Guarantees for Quadratic Tensors with Limited Observations
We consider the tensor completion problem of predicting the missing entries
of a tensor. The commonly used CP model has a triple product form, but an
alternate family of quadratic models which are the sum of pairwise products
instead of a triple product have emerged from applications such as
recommendation systems. Non-convex methods are the method of choice for
learning quadratic models, and this work examines their sample complexity and
error guarantee. Our main result is that with the number of samples being only
linear in the dimension, all local minima of the mean squared error objective
are global minima and recover the original tensor accurately. The techniques
lead to simple proofs showing that convex relaxation can recover quadratic
tensors provided with linear number of samples. We substantiate our theoretical
results with experiments on synthetic and real-world data, showing that
quadratic models have better performance than CP models in scenarios where
there are limited amount of observations available
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