human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "fast exact matrix completion with finite samples"):
  Abstract: Matrix completion is the problem of recovering a low rank matrix by observing a small fraction of its entries. A series of recent works [KOM12,JNS13,HW14] have proposed fast non-convex optimization based iterative algorithms to solve this problem. However, the sample complexity in all these results is sub-optimal in its dependence on the rank, condition number and the desired accuracy. #R##N#In this paper, we present a fast iterative algorithm that solves the matrix completion problem by observing $O(nr^5 \log^3 n)$ entries, which is independent of the condition number and the desired accuracy. The run time of our algorithm is $O(nr^7\log^3 n\log 1/\epsilon)$ which is near linear in the dimension of the matrix. To the best of our knowledge, this is the first near linear time algorithm for exact matrix completion with finite sample complexity (i.e. independent of $\epsilon$). #R##N#Our algorithm is based on a well known projected gradient descent method, where the projection is onto the (non-convex) set of low rank matrices. There are two key ideas in our result: 1) our argument is based on a $\ell_{\infty}$ norm potential function (as opposed to the spectral norm) and provides a novel way to obtain perturbation bounds for it. 2) we prove and use a natural extension of the Davis-Kahan theorem to obtain perturbation bounds on the best low rank approximation of matrices with good eigen-gap. Both of these ideas may be of independent interest.

Includes members:
  Member "computational limits for matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "low rank approximation from communication complexity")
  Member "fast matrix completion without the condition number":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a survey of optimization methods from a machine learning perspective")
  Member "understanding alternating minimization for matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "recommendation on a budget column space recovery from partially observed entries with random or active sampling")
  Member "rank aggregation via nuclear norm minimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "weighted matrix completion from non random non uniform sampling patterns")
  Member "the power of convex relaxation near optimal matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "ell_0 motivated low rank sparse subspace clustering")
  Member "guaranteed rank minimization via singular value projection":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the importance of phase in complex compressive sensing")
  Member "matrix completion from a few entries":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "matrix completion with prior subspace information via maximizing correlation")
  Member "exact matrix completion via convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.NA(Numerical Analysis)