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 "complexity and approximation of the fuzzy k means problem"):
  Abstract: The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy $K$-means problem has not been studied from a complexity theoretic or algorithmic perspective. We show that optimal solutions for fuzzy $K$-means cannot, in general, be expressed by radicals over the input points. Surprisingly, this already holds for very simple inputs in one-dimensional space. Hence, one cannot expect to compute optimal solutions exactly. We give the first $(1+\epsilon)$-approximation algorithms for the fuzzy $K$-means problem. First, we present a deterministic approximation algorithm whose runtime is polynomial in $N$ and linear in the dimension $D$ of the input set, given that $K$ is constant, i.e. a polynomial time approximation algorithm given a fixed $K$. We achieve this result by showing that for each soft clustering there exists a hard clustering with comparable properties. Second, by using techniques known from coreset constructions for the $K$-means problem, we develop a deterministic approximation algorithm that runs in time almost linear in $N$ but exponential in the dimension $D$. We complement these results with a randomized algorithm which imposes some natural restrictions on the input set and whose runtime is comparable to some of the most efficient approximation algorithms for $K$-means, i.e. linear in the number of points and the dimension, but exponential in the number of clusters.

Includes members:
  Member "coresets for k means and k median clustering and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rk means fast clustering for relational data")
  Member "the hardness of approximation of euclidean k means":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "explainable k means and k medians clustering")
  Member "a theoretical and experimental comparison of the em and sem algorithm":
    also connected through other hyperedges:
      (none)

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)