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 "far field compression for fast kernel summation methods in high dimensions"):
  Abstract: We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions for each point in the set. Direct summation is equivalent to a (dense) matrix-vector multiplication and scales quadratically with the number of points. Fast kernel summation algorithms reduce this cost to log-linear or linear complexity. #R##N#Treecodes and Fast Multipole Methods (FMMs) deliver tremendous speedups by constructing approximate representations of interactions of points that are far from each other. In algebraic terms, these representations correspond to low-rank approximations of blocks of the overall interaction matrix. Existing approaches require an excessive number of kernel evaluations with increasing $d$ and number of points in the dataset. #R##N#To address this issue, we use a randomized algebraic approach in which we first sample the rows of a block and then construct its approximate, low-rank interpolative decomposition. We examine the feasibility of this approach theoretically and experimentally. We provide a new theoretical result showing a tighter bound on the reconstruction error from uniformly sampling rows than the existing state-of-the-art. We demonstrate that our sampling approach is competitive with existing (but prohibitively expensive) methods from the literature. We also construct kernel matrices for the Laplacian, Gaussian, and polynomial kernels -- all commonly used in physics and data analysis. We explore the numerical properties of blocks of these matrices, and show that they are amenable to our approach. Depending on the data set, our randomized algorithm can successfully compute low rank approximations in high dimensions. We report results for data sets with ambient dimensions from four to 1,000.

Includes members:
  Member "sketching as a tool for numerical linear algebra":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "matrix coherence and the nystrom method":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "compressive pca for low rank matrices on graphs")
  Member "askit approximate skeletonization kernel independent treecode in high dimensions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "matrox modular approach for improving data locality in hierarchical mat rix app rox imation")
  Member "revisiting the nystrom method for improved large scale machine learning":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "improved bounds for the nystrom method with application to kernel classification":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "large scale kernel methods and applications to lifelong robot learning")
  Member "improved matrix algorithms via the subsampled randomized hadamard transform":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "improved subsampled randomized hadamard transform for linear svm")
  Member "optimized m2l kernels for the chebyshev interpolation based fast multipole method":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a fast directional bem for large scale acoustic problems based on the burton miller formulation")
  Member "fast approximation of matrix coherence and statistical leverage":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sketching transformed matrices with applications to natural language processing")

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)