human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "the global optimization geometry of low rank matrix optimization"
  Abstract: This paper considers general rank-constrained optimization problems that minimize a general objective function $f(X)$ over the set of rectangular $n\times m$ matrices that have rank at most $r$. To tackle the rank constraint and also to reduce the computational burden, we factorize $X$ into $UV^T$ where $U$ and $V$ are $n\times r$ and $m\times r$ matrices, respectively, and then optimize over the small matrices $U$ and $V$. We characterize the global optimization geometry of the nonconvex factored problem and show that the corresponding objective function satisfies the robust strict saddle property as long as the original objective function $f$ satisfies restricted strong convexity and smoothness properties, ensuring global convergence of many local search algorithms (such as noisy gradient descent) in polynomial time for solving the factored problem. We also provide a comprehensive analysis for the optimization geometry of a matrix factorization problem where we aim to find $n\times r$ and $m\times r$ matrices $U$ and $V$ such that $UV^T$ approximates a given matrix $X^\star$. Aside from the robust strict saddle property, we show that the objective function of the matrix factorization problem has no spurious local minima and obeys the strict saddle property not only for the exact-parameterization case where $rank(X^\star) = r$, but also for the over-parameterization case where $rank(X^\star)   r$. These geometric properties imply that a number of iterative optimization algorithms (such as gradient descent) converge to a global solution with random initialization.

Connected through hyperedge HE-1 (induced by source paper "the non convex geometry of low rank matrix optimization"):
  with members:
    - "global optimality in low rank matrix optimization"
    - "how to escape saddle points efficiently"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "low rank positive semidefinite matrix recovery from corrupted rank one measurements"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "overcomplete tensor decomposition via convex optimization"
    - "finding a sparse vector in a subspace linear sparsity using alternating directions"
    - "matrix completion has no spurious local minimum"

Connected through hyperedge HE-2 (induced by source paper "the global optimization geometry of shallow linear neural networks"):
  with members:
    - "the non convex geometry of low rank matrix optimization"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "amp inspired deep networks for sparse linear inverse problems"
    - "deep linear neural networks with arbitrary loss all local minima are global"
    - "depth creates no bad local minima"
    - "global optimality conditions for deep neural networks"
    - "an analytical formula of population gradient for two layered relu network and its applications in convergence and critical point analysis"
    - "global optimality in low rank matrix optimization"

Connected through hyperedge HE-3 (induced by source paper "nonconvex robust low rank matrix recovery"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "the non convex geometry of low rank matrix optimization"
    - "subgradient descent learns orthogonal dictionaries"
    - "global optimality in low rank matrix optimization"
    - "nonconvex low rank matrix recovery with arbitrary outliers via median truncated gradient descent"
    - "low rank positive semidefinite matrix recovery from corrupted rank one measurements"
    - "fast algorithms for robust pca via gradient descent"
    - "matrix completion has no spurious local minimum"

Connected through hyperedge HE-4 (induced by source paper "on landscape of lagrangian functions and stochastic search for constrained nonconvex optimization"):
  with members:
    - "dropping convexity for more efficient and scalable online multiview learning"
    - "online multiview representation learning dropping convexity for better efficiency"
    - "stochastic approximation for canonical correlation analysis"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "efficient algorithms for large scale generalized eigenvector computation and canonical correlation analysis"
    - "matrix completion has no spurious local minimum"
    - "a geometric analysis of phase retrieval"
    - "symmetry saddle points and global geometry of nonconvex matrix factorization"

Connected through hyperedge HE-5 (induced by source paper "dropping symmetry for fast symmetric nonnegative matrix factorization"):
  with members:
    - "efficient and non convex coordinate descent for symmetric nonnegative matrix factorization"

Connected through hyperedge HE-6 (induced by source paper "global optimality in low rank matrix optimization"):
  with members:
    - "the non convex geometry of low rank matrix optimization"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "low rank positive semidefinite matrix recovery from corrupted rank one measurements"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "geometry of factored nuclear norm regularization"
    - "matrix completion has no spurious local minimum"
    - "a geometric analysis of phase retrieval"

Connected through hyperedge HE-7 (induced by source paper "geometry of factored nuclear norm regularization"):
  with members:
    - "the non convex geometry of low rank matrix optimization"
    - "global optimality in low rank matrix optimization"
    - "how to escape saddle points efficiently"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "matrix completion has no spurious local minimum"
    - "a geometric analysis of phase retrieval"
    - "symmetry saddle points and global geometry of nonconvex matrix factorization"

Connected through hyperedge HE-8 (induced by source paper "symmetry saddle points and global geometry of nonconvex matrix factorization"):
  with members:
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "fast algorithms for robust pca via gradient descent"
    - "matrix completion has no spurious local minimum"
    - "a geometric analysis of phase retrieval"
    - "efficient approaches for escaping higher order saddle points in non convex optimization"
    - "provable efficient online matrix completion via non convex stochastic gradient descent"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "provable ica with unknown gaussian noise and implications for gaussian mixtures and autoencoders"

Question: Please tell me which class the center node 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.IT(Information Theory)