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 "clustering under perturbation resilience"):
  Abstract: Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption that the optimum clustering to the objective is preserved under small multiplicative perturbations to distances between points. The hope is that by exploiting the structure in such instances, one can overcome worst case hardness results. #R##N#In this paper, we provide several strong results within this framework. For center-based objectives, we present an algorithm that can optimally cluster instances resilient to perturbations of factor $(1 + \sqrt{2})$, solving an open problem of Awasthi et al.~\cite{ABS10}. For $k$-median, a center-based objective of special interest, we additionally give algorithms for a more relaxed assumption in which we allow the optimal solution to change in a small $\epsilon$ fraction of the points after perturbation. We give the first bounds known for $k$-median under this more realistic and more general assumption. We also provide positive results for min-sum clustering which is a generally much harder objective than center-based objectives. Our algorithms are based on new linkage criteria that may be of independent interest. #R##N#Additionally, we give sublinear-time algorithms, showing algorithms that can return an implicit clustering from only access to a small random sample.

Includes members:
  Member "bilu linial stable instances of max cut and minimum multiway cut":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "solving k 1 stable instances of k terminal cut with isolating cuts")
  Member "approximating k median via pseudo approximation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fair correlation clustering")
  Member "on the practically interesting instances of maxcut":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "bilu linial stability certified algorithms and the independent set problem")
  Member "improved spectral norm bounds for clustering":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "analysis of ward s method")
  Member "data stability in clustering a closer look":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on euclidean k means clustering with alpha center proximity")
  Member "clustering with spectral norm and the k means algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "center based clustering under perturbation stability":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "analysis of ward s method")
  Member "are stable instances easy":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the unreasonable effectiveness of the greedy algorithm greedy adapts to sharpness")

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.LG(Machine Learning)