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 "osnap faster numerical linear algebra algorithms via sparser subspace embeddings"):
  Abstract: An "oblivious subspace embedding (OSE)" given some parameters eps,d is a distribution D over matrices B in R^{m x n} such that for any linear subspace W in R^n with dim(W) = d it holds that Pr_{B ~ D}(forall x in W ||B x||_2 in (1 +/- eps)||x||_2) > 2/3 We show an OSE exists with m = O(d^2/eps^2) and where every B in the support of D has exactly s=1 non-zero entries per column. This improves previously best known bound in [Clarkson-Woodruff, arXiv:1207.6365]. Our quadratic dependence on d is optimal for any OSE with s=1 [Nelson-Nguyen, 2012]. We also give two OSE's, which we call Oblivious Sparse Norm-Approximating Projections (OSNAPs), that both allow the parameter settings m = \~O(d/eps^2) and s = polylog(d)/eps, or m = O(d^{1+gamma}/eps^2) and s=O(1/eps) for any constant gamma>0. This m is nearly optimal since m >= d is required simply to no non-zero vector of W lands in the kernel of B. These are the first constructions with m=o(d^2) to have s=o(d). In fact, our OSNAPs are nothing more than the sparse Johnson-Lindenstrauss matrices of [Kane-Nelson, SODA 2012]. Our analyses all yield OSE's that are sampled using either O(1)-wise or O(log d)-wise independent hash functions, which provides some efficiency advantages over previous work for turnstile streaming applications. Our main result is essentially a Bai-Yin type theorem in random matrix theory and is likely to be of independent interest: i.e. we show that for any U in R^{n x d} with orthonormal columns and random sparse B, all singular values of BU lie in [1-eps, 1+eps] with good probability. #R##N#Plugging OSNAPs into known algorithms for numerical linear algebra problems such as approximate least squares regression, low rank approximation, and approximating leverage scores implies faster algorithms for all these problems.

Includes members:
  Member "lower bounds for oblivious subspace embeddings":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "streaming low rank matrix approximation with an application to scientific simulation")
  Member "low rank approximation and regression in input sparsity time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "iterative row sampling":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "sparsity lower bounds for dimensionality reducing maps":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "privacy preserving learning via deep net pruning")
  Member "fast matrix rank algorithms and applications":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "low distortion subspace embeddings in input sparsity time and applications to robust linear regression":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "the fast cauchy transform and faster robust linear regression":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "optimal sketching for kronecker product regression and low rank approximation")
  Member "randomized algorithms for matrices and data":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "solving tall dense linear programs in nearly linear time")

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)