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 "understanding alternating minimization for matrix completion"):
  Abstract: Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still poorly understood. This is in part because the heuristic is iterative and non-convex in nature. We give a new algorithm based on Alternating Minimization that provably recovers an unknown low-rank matrix from a random subsample of its entries under a standard incoherence assumption. Our results reduce the sample size requirements of the Alternating Minimization approach by at least a quartic factor in the rank and the condition number of the unknown matrix. These improvements apply even if the matrix is only close to low-rank in the Frobenius norm. Our algorithm runs in nearly linear time in the dimension of the matrix and, in a broad range of parameters, gives the strongest sample bounds among all subquadratic time algorithms that we are aware of. #R##N#Underlying our work is a new robust convergence analysis of the well-known Power Method for computing the dominant singular vectors of a matrix. This viewpoint leads to a conceptually simple understanding of Alternating Minimization. In addition, we contribute a new technique for controlling the coherence of intermediate solutions arising in iterative algorithms based on a smoothed analysis of the QR factorization. These techniques may be of interest beyond their application here.

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 "efficient and practical stochastic subgradient descent for nuclear norm regularization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sum suboptimal unitary multi task learning framework for spatiotemporal data prediction")
  Member "calibrating data to sensitivity in private data analysis":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "locally private hypothesis selection")
  Member "beating randomized response on incoherent matrices":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "mvg mechanism differential privacy under matrix valued query")
  Member "beyond worst case analysis in private singular vector computation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "pd ml lite private distributed machine learning from lighweight cryptography")
  Member "projection free online learning":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems")
  Member "the power of convex relaxation near optimal matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "ell_0 motivated low rank sparse subspace clustering")
  Member "matrix completion from noisy entries":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "matrix completion with prior subspace information via maximizing correlation")

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.LG(Machine Learning)