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 "geometry of factored nuclear norm regularization"):
  Abstract: This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many applications in machine learning, signal processing, and control. The statistical performance of nuclear norm regularization has been studied extensively in literature using convex analysis techniques. Despite its optimal performance, the resulting optimization has high computational complexity when solved using standard or even tailored fast convex solvers. To develop faster and more scalable algorithms, we follow the proposal of Burer-Monteiro to factor the matrix variable $X$ into the product of two smaller rectangular matrices $X=UV^T$ and also replace the nuclear norm $\|X\|_*$ with $(\|U\|_F^2+\|V\|_F^2)/2$. In spite of the nonconvexity of the factored formulation, we prove that when the convex loss function $f(X)$ is $(2r,4r)$-restricted well-conditioned, each critical point of the factored problem either corresponds to the optimal solution $X^\star$ of the original convex optimization or is a strict saddle point where the Hessian matrix has a strictly negative eigenvalue. Such a geometric structure of the factored formulation allows many local search algorithms to converge to the global optimum with random initializations.

Includes members:
  Member "the non convex geometry of low rank matrix optimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair principal component analysis and filter design")
  Member "global optimality in low rank matrix optimization":
    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 to escape saddle points efficiently":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")
  Member "no spurious local minima in nonconvex low rank problems a unified geometric analysis":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "no spurious local minima in deep quadratic networks")
  Member "complete dictionary recovery over the sphere ii recovery by riemannian trust region method":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "the global optimization geometry of low rank matrix optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the non convex geometry of low rank matrix optimization")
  Member "matrix completion has no spurious local minimum":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "a geometric analysis of phase retrieval":
    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)