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 "cheeger inequalities for submodular transformations"):
  Abstract: The Cheeger inequality for undirected graphs, which relates the conductance of an undirected graph and the second smallest eigenvalue of its normalized Laplacian, is a cornerstone of spectral graph theory. The Cheeger inequality has been extended to directed graphs and hypergraphs using normalized Laplacians for those, that are no longer linear but piecewise linear transformations. #R##N#In this paper, we introduce the notion of a submodular transformation $F:\{0,1\}^n \to \mathbb{R}^m$, which applies $m$ submodular functions to the $n$-dimensional input vector, and then introduce the notions of its Laplacian and normalized Laplacian. With these notions, we unify and generalize the existing Cheeger inequalities by showing a Cheeger inequality for submodular transformations, which relates the conductance of a submodular transformation and the smallest non-trivial eigenvalue of its normalized Laplacian. This result recovers the Cheeger inequalities for undirected graphs, directed graphs, and hypergraphs, and derives novel Cheeger inequalities for mutual information and directed information. #R##N#Computing the smallest non-trivial eigenvalue of a normalized Laplacian of a submodular transformation is NP-hard under the small set expansion hypothesis. In this paper, we present a polynomial-time $O(\log n)$-approximation algorithm for the symmetric case, which is tight, and a polynomial-time $O(\log^2n+\log n \cdot \log m)$-approximation algorithm for the general case. #R##N#We expect the algebra concerned with submodular transformations, or \emph{submodular algebra}, to be useful in the future not only for generalizing spectral graph theory but also for analyzing other problems that involve piecewise linear transformations, e.g., deep learning.

Includes members:
  Member "finding cheeger cuts in hypergraphs via heat equation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "optimizing generalized pagerank methods for seed expansion community detection")
  Member "polynomial time algorithms for submodular laplacian systems":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "quadratic decomposable submodular function minimization theory and practice")
  Member "submodular hypergraphs p laplacians cheeger inequalities and spectral clustering":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "parameterized objectives and algorithms for clustering bipartite graphs and hypergraphs")
  Member "inhomogoenous hypergraph clustering with applications":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "hypergraph motifs concepts algorithms and discoveries")
  Member "spectral properties of hypergraph laplacian and approximation algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "diffusion operator and spectral analysis for directed hypergraph laplacian")
  Member "improved cheeger s inequality and analysis of local graph partitioning using vertex expansion and expansion profile":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "generalizing the hypergraph laplacian via a diffusion process with mediators")
  Member "heat kernel based community detection":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "connectivity driven communication in multi agent reinforcement learning through diffusion processes on graphs")
  Member "provable submodular minimization using wolfe s algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "quadratic decomposable submodular function minimization theory and practice")

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)