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: "computing a nonnegative matrix factorization provably"
  Abstract: In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r \times m$ respectively. In some applications, it makes sense to ask instead for the product $AW$ to approximate $M$ -- i.e. (approximately) minimize $\norm{M - AW}_F$ where $\norm{}_F$ denotes the Frobenius norm; we refer to this as Approximate NMF. This problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc. In the past decade NMF has become enormously popular in machine learning, where $A$ and $W$ are computed using a variety of local search heuristics. Vavasis proved that this problem is NP-complete. We initiate a study of when this problem is solvable in polynomial time: #R##N#1. We give a polynomial-time algorithm for exact and approximate NMF for every constant $r$. Indeed NMF is most interesting in applications precisely when $r$ is small. #R##N#2. We complement this with a hardness result, that if exact NMF can be solved in time $(nm)^{o(r)}$, 3-SAT has a sub-exponential time algorithm. This rules out substantial improvements to the above algorithm. #R##N#3. We give an algorithm that runs in time polynomial in $n$, $m$ and $r$ under the separablity condition identified by Donoho and Stodden in 2003. The algorithm may be practical since it is simple and noise tolerant (under benign assumptions). Separability is believed to hold in many practical settings. #R##N#To the best of our knowledge, this last result is the first example of a polynomial-time algorithm that provably works under a non-trivial condition on the input and we believe that this will be an interesting and important direction for future work.

Connected through hyperedge HE-1 (induced by source paper "convergence to second order stationarity for non negative matrix factorization provably and concurrently"):
  with members:
    - "how to escape saddle points efficiently"
    - "matrix completion has no spurious local minimum"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "descent methods for nonnegative matrix factorization"
    - "on the complexity of nonnegative matrix factorization"

Connected through hyperedge HE-2 (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-3 (induced by source paper "dimensionality reduction for tukey regression"):
  with members:
    - "tight bounds for the subspace sketch problem with applications"
    - "tight bounds for ell_p oblivious subspace embeddings"
    - "input sparsity and hardness for robust subspace approximation"
    - "robust optimization for deep regression"
    - "sketching as a tool for numerical linear algebra"
    - "quantile regression for large scale applications"
    - "low rank approximation and regression in input sparsity time"
    - "iterative row sampling"

Connected through hyperedge HE-4 (induced by source paper "learning distributions generated by one layer relu networks"):
  with members:
    - "learning one convolutional layer with overlapping patches"
    - "ffjord free form continuous dynamics for scalable reversible generative models"
    - "learning two layer neural networks with symmetric inputs"
    - "learning relus via gradient descent"
    - "recovery guarantees for one hidden layer neural networks"
    - "convergence analysis of two layer neural networks with relu activation"
    - "pixel recurrent neural networks"
    - "unsupervised representation learning with deep convolutional generative adversarial networks"

Connected through hyperedge HE-5 (induced by source paper "generalized separable nonnegative matrix factorization"):
  with members:
    - "on identifiability of nonnegative matrix factorization"
    - "hierarchical clustering of hyperspectral images using rank two nonnegative matrix factorization"
    - "learning the information divergence"
    - "a practical algorithm for topic modeling with provable guarantees"
    - "learning topic models going beyond svd"
    - "on the complexity of nonnegative matrix factorization"
    - "non negative matrix factorization with sparseness constraints"

Connected through hyperedge HE-6 (induced by source paper "a quantum inspired classical algorithm for separable non negative matrix factorization"):
  with members:
    - "a quantum inspired classical algorithm for recommendation systems"
    - "quantum inspired low rank stochastic regression with logarithmic dependence on the dimension"
    - "quantum inspired sublinear classical algorithms for solving low rank linear systems"
    - "learning topic models going beyond svd"
    - "on the complexity of nonnegative matrix factorization"

Connected through hyperedge HE-7 (induced by source paper "nonnegative matrix factorization with local similarity learning"):
  with members:
    - "robust recovery of subspace structures by low rank representation"
    - "sparse subspace clustering algorithm theory and applications"
    - "robust principal component analysis"
    - "on the complexity of nonnegative matrix factorization"

Connected through hyperedge HE-8 (induced by source paper "fast convolutive nonnegative matrix factorization through coordinate and block coordinate updates"):
  with members:
    - "a high performance parallel algorithm for nonnegative matrix factorization"
    - "julia a fresh approach to numerical computing"
    - "on the complexity of nonnegative matrix factorization"

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.DS(Data Structures and Algorithms)