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 small samples with quality guarantees adaptivity with one2all pps"):
  Abstract: Clustering of data points is a fundamental tool in data analysis. We consider points $X$ in a relaxed metric space, where the triangle inequality holds within a constant factor. The {\em cost} of clustering $X$ by $Q$ is $V(Q)=\sum_{x\in X} d_{xQ}$. Two basic tasks, parametrized by $k \geq 1$, are {\em cost estimation}, which returns (approximate) $V(Q)$ for queries $Q$ such that $|Q|=k$ and {\em clustering}, which returns an (approximate) minimizer of $V(Q)$ of size $|Q|=k$. With very large data sets $X$, we seek efficient constructions of small samples that act as surrogates to the full data for performing these tasks. Existing constructions that provide quality guarantees are either worst-case, and unable to benefit from structure of real data sets, or make explicit strong assumptions on the structure. We show here how to avoid both these pitfalls using adaptive designs. #R##N#At the core of our design is the {\em one2all} construction of multi-objective probability-proportional-to-size (pps) samples: Given a set $M$ of centroids and $\alpha \geq 1$, one2all efficiently assigns probabilities to points so that the clustering cost of {\em each} $Q$ with cost $V(Q) \geq V(M)/\alpha$ can be estimated well from a sample of size $O(\alpha |M|\epsilon^{-2})$. For cost queries, we can obtain worst-case sample size $O(k\epsilon^{-2})$ by applying one2all to a bicriteria approximation $M$, but we adaptively balance $|M|$ and $\alpha$ to further reduce sample size. For clustering, we design an adaptive wrapper that applies a base clustering algorithm to a sample $S$. Our wrapper uses the smallest sample that provides statistical guarantees that the quality of the clustering on the sample carries over to the full data set. We demonstrate experimentally the huge gains of using our adaptive instead of worst-case methods.

Includes members:
  Member "turning big data into tiny data constant size coresets for k means pca and projective clustering":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair clustering with multiple colors")
  Member "fashion mnist a novel image dataset for benchmarking machine learning algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "a constant factor bi criteria approximation guarantee for k means":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "simple and sharp analysis of k means")
  Member "multi objective weighted sampling":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "sample complexity bounds for influence maximization")
  Member "the hardness of approximation of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "explainable k means and k medians clustering")
  Member "average distance queries through weighted samples in graphs and metric spaces high scalability with tight statistical guarantees":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "scalable distributed approximation of internal measures for clustering evaluation")
  Member "dimensionality reduction for k means clustering and low rank approximation":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "optimal time bounds for approximate clustering":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "layered sampling for robust optimization problems")

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)