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 "hierarchical clustering objective functions and algorithms"):
  Abstract: Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a specific objective, Dasgupta framed similarity-based hierarchical clustering as a combinatorial optimization problem, where a `good' hierarchical clustering is one that minimizes some cost function. He showed that this cost function has certain desirable properties. #R##N#We take an axiomatic approach to defining `good' objective functions for both similarity and dissimilarity-based hierarchical clustering. We characterize a set of "admissible" objective functions (that includes Dasgupta's one) that have the property that when the input admits a `natural' hierarchical clustering, it has an optimal value. #R##N#Equipped with a suitable objective function, we analyze the performance of practical algorithms, as well as develop better algorithms. For similarity-based hierarchical clustering, Dasgupta showed that the divisive sparsest-cut approach achieves an $O(\log^{3/2} n)$-approximation. We give a refined analysis of the algorithm and show that it in fact achieves an $O(\sqrt{\log n})$-approx. (Charikar and Chatziafratis independently proved that it is a $O(\sqrt{\log n})$-approx.). This improves upon the LP-based $O(\log n)$-approx. of Roy and Pokutta. For dissimilarity-based hierarchical clustering, we show that the classic average-linkage algorithm gives a factor 2 approx., and provide a simple and better algorithm that gives a factor 3/2 approx.. #R##N#Finally, we consider `beyond-worst-case' scenario through a generalisation of the stochastic block model for hierarchical clustering. We show that Dasgupta's cost function has desirable properties for these inputs and we provide a simple 1 + o(1)-approximation in this setting.

Includes members:
  Member "hierarchical clustering better than average linkage":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "bisect and conquer hierarchical clustering via max uncut bisection")
  Member "hierarchical clustering with structural constraints":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "deep discriminative clustering analysis")
  Member "hierarchical clustering via spreading metrics":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "hierarchical correlation clustering and tree preserving embedding")
  Member "approximate hierarchical clustering via sparsest cut and spreading metrics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "hierarchical correlation clustering and tree preserving embedding")
  Member "a cost function for similarity based hierarchical clustering":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "hierarchical correlation clustering and tree preserving embedding")
  Member "on the practically interesting instances of maxcut":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "bilu linial stability certified algorithms and the independent set problem")
  Member "a uniqueness theorem for clustering":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a fixed point view a model based clustering framework")
  Member "improved spectral norm bounds for clustering":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "analysis of ward s method")

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)