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 non convex geometry of low rank matrix optimization"
  Abstract: This work considers two popular minimization problems: (i) the minimization of a general convex function $f(X)$ with the domain being positive semi-definite matrices; (ii) the minimization of a general convex function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$ with the domain being general matrices. Despite their optimal statistical performance in the literature, these two optimization problems have a high computational complexity even when solved using tailored fast convex solvers. To develop faster and more scalable algorithms, we follow the proposal of Burer and Monteiro to factor the low-rank variable $X = UU^\top $ (for semi-definite matrices) or $X=UV^\top $ (for general matrices) and also replace the nuclear norm $\|X\|_*$ with $(\|U\|_F^2+\|V\|_F^2)/2$. In spite of the non-convexity of the resulting factored formulations, we prove that each critical point either corresponds to the global optimum of the original convex problems or is a strict saddle where the Hessian matrix has a strictly negative eigenvalue. Such a nice geometric structure of the factored formulations allows many local search algorithms to find a global optimizer even with random initializations.

Connected through hyperedge HE-1 (induced by source paper "fair principal component analysis and filter design"):
  with members:
    - "efficient fair principal component analysis"
    - "fair dimensionality reduction and iterative rounding for sdps"
    - "convex formulations for fair principal component analysis"
    - "the price of fair pca one extra dimension"
    - "global optimality in low rank matrix optimization"
    - "robust computation of linear models by convex relaxation"

Connected through hyperedge HE-2 (induced by source paper "spherical principal component analysis"):
  with members:
    - "global optimality in low rank matrix optimization"

Connected through hyperedge HE-3 (induced by source paper "the global optimization geometry of shallow linear neural networks"):
  with members:
    - "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"
    - "how to escape saddle points efficiently"

Connected through hyperedge HE-4 (induced by source paper "nonconvex robust low rank matrix recovery"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "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"
    - "the global optimization geometry of low rank matrix optimization"
    - "fast algorithms for robust pca via gradient descent"
    - "matrix completion has no spurious local minimum"

Connected through hyperedge HE-5 (induced by source paper "towards the optimal construction of a loss function without spurious local minima for solving quadratic equations"):
  with members:
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "on the optimization landscape of tensor decompositions"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "phasemax convex phase retrieval via basis pursuit"
    - "matrix completion has no spurious local minimum"
    - "an elementary proof of convex phase retrieval in the natural parameter space via the linear program phasemax"
    - "a geometric analysis of phase retrieval"
    - "phase retrieval meets statistical learning theory a flexible convex relaxation"

Connected through hyperedge HE-6 (induced by source paper "nonconvex low rank matrix recovery with arbitrary outliers via median truncated gradient descent"):
  with members:
    - "how to escape saddle points efficiently"
    - "low rank positive semidefinite matrix recovery from corrupted rank one measurements"
    - "rapid robust and reliable blind deconvolution via nonconvex optimization"
    - "matrix completion has no spurious local minimum"
    - "symmetry saddle points and global geometry of nonconvex matrix factorization"
    - "an overview of low rank matrix recovery from incomplete observations"
    - "nearly optimal robust matrix completion"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"

Connected through hyperedge HE-7 (induced by source paper "global optimality in low rank matrix optimization"):
  with members:
    - "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"
    - "the global optimization geometry of low rank matrix optimization"
    - "matrix completion has no spurious local minimum"
    - "a geometric analysis of phase retrieval"

Connected through hyperedge HE-8 (induced by source paper "introduction to nonnegative matrix factorization"):
  with members:
    - "on the complexity of robust pca and l1 norm low rank matrix approximation"
    - "on restricted nonnegative matrix factorization"
    - "matrix completion has no spurious local minimum"
    - "low rank approximation with entrywise ell_1 norm error"
    - "input sparsity and hardness for robust subspace approximation"
    - "sketching as a tool for numerical linear algebra"
    - "the matching polytope has exponential extension complexity"
    - "a practical algorithm for topic modeling with provable guarantees"

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)