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 "diffusion operator and spectral analysis for directed hypergraph laplacian"):
  Abstract: In spectral graph theory, the Cheeger's inequality gives upper and lower bounds of edge expansion in normal graphs in terms of the second eigenvalue of the graph's Laplacian operator. Recently this inequality has been extended to undirected hypergraphs and directed normal graphs via a non-linear operator associated with a diffusion process in the underlying graph. #R##N#In this work, we develop a unifying framework for defining a diffusion operator on a directed hypergraph with stationary vertices, which is general enough for the following two applications. #R##N#1. Cheeger's inequality for directed hyperedge expansion. #R##N#2. Quadratic optimization with stationary vertices in the context of semi-supervised learning. #R##N#Despite the crucial role of the diffusion process in spectral analysis, previous works have not formally established the existence of the corresponding diffusion processes. In this work, we give a proof framework that can indeed show that such diffusion processes are well-defined. In the first application, we use the spectral properties of the diffusion operator to achieve the Cheeger's inequality for directed hyperedge expansion. In the second application, the diffusion operator can be interpreted as giving a continuous analog to the subgradient method, which moves the feasible solution in discrete steps towards an optimal solution.

Includes members:
  Member "spectral properties of hypergraph laplacian and approximation algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "cheeger inequalities for submodular transformations")
  Member "improved cheeger s inequality and analysis of local graph partitioning using vertex expansion and expansion profile":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "generalizing the hypergraph laplacian via a diffusion process with mediators")
  Member "partitioning well clustered graphs spectral clustering works":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "hypergraph markov operators eigenvalues and approximation algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "hypergcn a new method of training graph convolutional networks on hypergraphs")
  Member "approximation algorithm for sparsest k partitioning":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "planted models for k way edge and vertex expansion")

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.DM(Discrete Mathematics)