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: "computational limits for matrix completion"
  Abstract: Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is incoherent and the subsample is drawn uniformly at random. Are these assumptions necessary? #R##N#It is well known that Matrix Completion in its full generality is NP-hard. However, little is known if make additional assumptions such as incoherence and permit the algorithm to output a matrix of slightly higher rank. In this paper we prove that Matrix Completion remains computationally intractable even if the unknown matrix has rank $4$ but we are allowed to output any constant rank matrix, and even if additionally we assume that the unknown matrix is incoherent and are shown $90%$ of the entries. This result relies on the conjectured hardness of the $4$-Coloring problem. We also consider the positive semidefinite Matrix Completion problem. Here we show a similar hardness result under the standard assumption that $\mathrm{P}\ne \mathrm{NP}.$ #R##N#Our results greatly narrow the gap between existing feasibility results and computational lower bounds. In particular, we believe that our results give the first complexity-theoretic justification for why distributional assumptions are needed beyond the incoherence assumption in order to obtain positive results. On the technical side, we contribute several new ideas on how to encode hard combinatorial problems in low-rank optimization problems. We hope that these techniques will be helpful in further understanding the computational limits of Matrix Completion and related problems.

Connected through hyperedge HE-1 (induced by source paper "low rank approximation from communication complexity"):
  with members:
    - "on the complexity of robust pca and l1 norm low rank matrix approximation"
    - "parameterized low rank binary matrix approximation"
    - "relative error tensor low rank approximation"
    - "tensor robust principal component analysis exact recovery of corrupted low rank tensors via convex optimization"
    - "low rank passthrough neural networks"
    - "greedy bi criteria approximations for k medians and k means"
    - "computing approximate psd factorizations"
    - "input sparsity and hardness for robust subspace approximation"

Connected through hyperedge HE-2 (induced by source paper "on clustering incomplete data"):
  with members:
    - "parameterized k clustering the distance matters"
    - "approximation schemes for low rank binary matrix approximation problems"
    - "parameterized algorithms for the matrix completion problem"
    - "approximation algorithms for stochastic clustering"
    - "parameterized low rank binary matrix approximation"
    - "independence clustering without a matrix"
    - "dispersion on trees"
    - "mapreduce and streaming algorithms for diversity maximization in metric spaces of bounded doubling dimension"

Connected through hyperedge HE-3 (induced by source paper "variety membership testing algebraic natural proofs and geometric complexity theory"):
  with members:
    - "alternating minimization scaling algorithms and the null cone problem from invariant theory"
    - "barriers for rank methods in arithmetic complexity"
    - "succinct hitting sets and barriers to proving algebraic circuits lower bounds"
    - "discovering the roots uniform closure results for algebraic classes under factoring"
    - "towards an algebraic natural proofs barrier via polynomial identity testing"
    - "on the complexity of the permanent in various computational models"
    - "the complexity of tensor rank"
    - "rectangular kronecker coefficients and plethysms in geometric complexity theory"

Connected through hyperedge HE-4 (induced by source paper "reducibility and computational lower bounds for problems with planted sparse structure"):
  with members:
    - "sherali adams integrality gaps matching the log density threshold"
    - "on finding dense common subgraphs"
    - "robust sparse estimation tasks in high dimensions"
    - "the power of sum of squares for detecting hidden structures"
    - "bayesian estimation from few samples community detection and related problems"
    - "sum of squares lower bounds for refuting any csp"
    - "feeling the bern adaptive estimators for bernoulli probabilities of pairwise comparisons"
    - "statistical query lower bounds for robust estimation of high dimensional gaussians and gaussian mixtures"

Connected through hyperedge HE-5 (induced by source paper "parameterized algorithms for the matrix completion problem"):
  with members:
    - "the parameterized complexity of positional games"
    - "h index manipulation by merging articles"
    - "sparse subspace clustering algorithm theory and applications"
    - "matrix completion from noisy entries"
    - "matrix completion from a few entries"
    - "a simpler approach to matrix completion"
    - "matrix completion with noise"
    - "the parameterized complexity of global constraints"

Connected through hyperedge HE-6 (induced by source paper "optimal sample complexity for matrix completion and related problems via 120001 s 2 regularization"):
  with members:
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "how to escape saddle points efficiently"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "fast algorithms for robust pca via gradient descent"
    - "matrix completion has no spurious local minimum"
    - "recovery guarantee of weighted low rank approximation via alternating minimization"
    - "a geometric analysis of phase retrieval"
    - "efficient approaches for escaping higher order saddle points in non convex optimization"

Connected through hyperedge HE-7 (induced by source paper "provable efficient online matrix completion via non convex stochastic gradient descent"):
  with members:
    - "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm"
    - "matrix completion has no spurious local minimum"
    - "simple efficient and neural algorithms for sparse coding"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "global convergence of stochastic gradient descent for some non convex matrix problems"
    - "fast exact matrix completion with finite samples"
    - "understanding alternating minimization for matrix completion"
    - "phase retrieval via matrix completion"

Connected through hyperedge HE-8 (induced by source paper "nearly optimal robust matrix completion"):
  with members:
    - "fast matrix completion without the condition number"
    - "guaranteed rank minimization via singular value projection"
    - "a simpler approach to matrix completion"
    - "exact matrix completion via convex optimization"

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.CC(Computational Complexity)