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 "exact guarantees on the absence of spurious local minima for non negative rank 1 robust principal component analysis"):
  Abstract: This work is concerned with the non-negative rank-1 robust principal component analysis (RPCA), where the goal is to recover the dominant non-negative principal components of a data matrix precisely, where a number of measurements could be grossly corrupted with sparse and arbitrary large noise. Most of the known techniques for solving the RPCA rely on convex relaxation methods by lifting the problem to a higher dimension, which significantly increase the number of variables. As an alternative, the well-known Burer-Monteiro approach can be used to cast the RPCA as a non-convex and non-smooth $\ell_1$ optimization problem with a significantly smaller number of variables. In this work, we show that the low-dimensional formulation of the symmetric and asymmetric positive rank-1 RPCA based on the Burer-Monteiro approach has benign landscape, i.e., 1) it does not have any spurious local solution, 2) has a unique global solution, and 3) its unique global solution coincides with the true components. An implication of this result is that simple local search algorithms are guaranteed to achieve a zero global optimality gap when directly applied to the low-dimensional formulation. Furthermore, we provide strong deterministic and probabilistic guarantees for the exact recovery of the true principal components. In particular, it is shown that a constant fraction of the measurements could be grossly corrupted and yet they would not create any spurious local solution.

Includes members:
  Member "nonconvex optimization meets low rank matrix factorization an overview":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "nonconvex robust low rank matrix recovery":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "how much restricted isometry is needed in nonconvex matrix recovery":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sharp restricted isometry bounds for the inexistence of spurious local minima in nonconvex matrix recovery")
  Member "complete dictionary recovery over the sphere i overview and the geometric picture":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "global optimality in low rank matrix optimization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "spectral algorithms for computing fair support vector machines":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "fairness risk measures")
  Member "no spurious local minima in nonconvex low rank problems a unified geometric analysis":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "no spurious local minima in deep quadratic networks")
  Member "fast algorithms for robust pca via gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems")

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)