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 "robustness of spectral methods for community detection"):
  Abstract: The present work is concerned with community detection. Specifically, we consider a random graph drawn according to the stochastic block model~: its vertex set is partitioned into blocks, or communities, and edges are placed randomly and independently of each other with probability depending only on the communities of their two endpoints. In this context, our aim is to recover the community labels better than by random guess, based only on the observation of the graph. #R##N#In the sparse case, where edge probabilities are in $O(1/n)$, we introduce a new spectral method based on the distance matrix $D^{(l)}$, where $D^{(l)}_{ij} = 1$ iff the graph distance between $i$ and $j$, noted $d(i, j)$ is equal to $\ell$. We show that when $\ell \sim c\log(n)$ for carefully chosen $c$, the eigenvectors associated to the largest eigenvalues of $D^{(l)}$ provide enough information to perform non-trivial community recovery with high probability, provided we are above the so-called Kesten-Stigum threshold. This yields an efficient algorithm for community detection, since computation of the matrix $D^{(l)}$ can be done in $O(n^{1+\kappa})$ operations for a small constant $\kappa$. #R##N#We then study the sensitivity of the eigendecomposition of $D^{(l)}$ when we allow an adversarial perturbation of the edges of $G$. We show that when the considered perturbation does not affect more than $O(n^\varepsilon)$ vertices for some small $\varepsilon > 0$, the highest eigenvalues and their corresponding eigenvectors incur negligible perturbations, which allows us to still perform efficient recovery.

Includes members:
  Member "graph powering and spectral robustness":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "renyi entropy bounds on the active learning cost performance tradeoff")
  Member "learning communities in the presence of errors":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "robust clustering oracle and local reconstructor of cluster structure of graphs")
  Member "semidefinite programs on sparse random graphs and their application to community detection":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "computational hardness of certifying bounds on constrained pca problems")
  Member "how robust are reconstruction thresholds for community detection":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "improper learning for non stochastic control")
  Member "spectral redemption in clustering sparse networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "community detection thresholds and the weak ramanujan property":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "from tree matching to sparse graph alignment")

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.DS(Data Structures and Algorithms)