Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Provable Tensor Factorization with Missing Data   We study the problem of low-rank tensor factorization in the presence of
missing data. We ask the following question: how many sampled entries do we
need, to efficiently and exactly reconstruct a tensor with a low-rank
orthogonal decomposition? We propose a novel alternating minimization based
method which iteratively refines estimates of the singular vectors. We show
that under certain standard assumptions, our method can recover a three-mode
$n\times n\times n$ dimensional rank-$r$ tensor exactly from $O(n^{3/2} r^5
\log^4 n)$ randomly sampled entries. In the process of proving this result, we
solve two challenging sub-problems for tensors with missing data. First, in the
process of analyzing the initialization step, we prove a generalization of a
celebrated result by Szemer\'edie et al. on the spectrum of random graphs.
Next, we prove global convergence of alternating minimization with a good
initialization. Simulations suggest that the dependence of the sample size on
dimensionality $n$ is indeed tight.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph