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 "dimension detection with local homology"):
  Abstract: Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena associated to the data. Among the many dimension detection algorithms proposed in various fields, a few can provide theoretical guarantee on the correctness of the estimated dimension. However, the correctness usually requires certain regularity of the input: the input points are either uniformly randomly sampled in a statistical setting, or they form the so-called $(\varepsilon,\delta)$-sample which can be neither too dense nor too sparse. #R##N#Here, we propose a purely topological technique to detect dimensions. Our algorithm is provably correct and works under a more relaxed sampling condition: we do not require uniformity, and we also allow Hausdorff noise. Our approach detects dimension by determining local homology. The computation of this topological structure is much less sensitive to the local distribution of points, which leads to the relaxation of the sampling conditions. Furthermore, by leveraging various developments in computational topology, we show that this local homology at a point $z$ can be computed \emph{exactly} for manifolds using Vietoris-Rips complexes whose vertices are confined within a local neighborhood of $z$. We implement our algorithm and demonstrate the accuracy and robustness of our method using both synthetic and real data sets.

Includes members:
  Member "approximating local homology from samples":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sheaf theoretic stratification learning from geometric and topological perspectives")
  Member "towards persistence based reconstruction in euclidean spaces":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "time series featurization via topological data analysis")

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.CG(Computational Geometry)