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 "is input sparsity time possible for kernel low rank approximation"):
  Abstract: Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly. In this work we study the limits of computationally efficient low-rank kernel approximation. We show that for a broad class of kernels, including the popular Gaussian and polynomial kernels, computing a relative error $k$-rank approximation to $K$ is at least as difficult as multiplying the input data matrix $A \in \mathbb{R}^{n \times d}$ by an arbitrary matrix $C \in \mathbb{R}^{d \times k}$. Barring a breakthrough in fast matrix multiplication, when $k$ is not too large, this requires $\Omega(nnz(A)k)$ time where $nnz(A)$ is the number of non-zeros in $A$. This lower bound matches, in many parameter regimes, recent work on subquadratic time algorithms for low-rank approximation of general kernels [MM16,MW17], demonstrating that these algorithms are unlikely to be significantly improved, in particular to $O(nnz(A))$ input sparsity runtimes. At the same time there is hope: we show for the first time that $O(nnz(A))$ time approximation is possible for general radial basis function kernels (e.g., the Gaussian kernel) for the closely related problem of low-rank approximation of the kernelized dataset.

Includes members:
  Member "improved rectangular matrix multiplication using powers of the coppersmith winograd tensor":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new algorithms and hardness for incremental single source shortest paths in directed graphs")
  Member "how to fake multiply by a gaussian matrix":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sketches for matrix norms faster smaller and more general")
  Member "revisiting the nystrom method for improved large scale machine learning":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "low rank approximation and regression in input sparsity time":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "faster algorithms for rectangular matrix multiplication":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "deterministic algorithms for decremental approximate shortest paths faster and simpler")
  Member "explicit approximations of the gaussian kernel":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "generalization guarantees for sparse kernel approximation with entropic optimal features")

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)