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 "embeddings of schatten norms with applications to data streams"):
  Abstract: Given an $n \times d$ matrix $A$, its Schatten-$p$ norm, $p \geq 1$, is defined as $\|A\|_p = \left (\sum_{i=1}^{\textrm{rank}(A)}\sigma_i(A)^p \right )^{1/p}$, where $\sigma_i(A)$ is the $i$-th largest singular value of $A$. These norms have been studied in functional analysis in the context of non-commutative $\ell_p$-spaces, and recently in data stream and linear sketching models of computation. Basic questions on the relations between these norms, such as their embeddability, are still open. Specifically, given a set of matrices $A^1, \ldots, A^{\operatorname{poly}(nd)} \in \mathbb{R}^{n \times d}$, suppose we want to construct a linear map $L$ such that $L(A^i) \in \mathbb{R}^{n' \times d'}$ for each $i$, where $n' \leq n$ and $d' \leq d$, and further, $\|A^i\|_p \leq \|L(A^i)\|_q \leq D_{p,q} \|A^i\|_p$ for a given approximation factor $D_{p,q}$ and real number $q \geq 1$. Then how large do $n'$ and $d'$ need to be as a function of $D_{p,q}$? #R##N#We nearly resolve this question for every $p, q \geq 1$, for the case where $L(A^i)$ can be expressed as $R \cdot A^i \cdot S$, where $R$ and $S$ are arbitrary matrices that are allowed to depend on $A^1, \ldots, A^t$, that is, $L(A^i)$ can be implemented by left and right matrix multiplication. Namely, for every $p, q \geq 1$, we provide nearly matching upper and lower bounds on the size of $n'$ and $d'$ as a function of $D_{p,q}$. Importantly, our upper bounds are {\it oblivious}, meaning that $R$ and $S$ do not depend on the $A^i$, while our lower bounds hold even if $R$ and $S$ depend on the $A^i$. As an application of our upper bounds, we answer a recent open question of Blasiok et al. about space-approximation trade-offs for the Schatten $1$-norm, showing in a data stream it is possible to estimate the Schatten-$1$ norm up to a factor of $D \geq 1$ using $\tilde{O}(\min(n,d)^2/D^4)$ space.

Includes members:
  Member "sketches for matrix norms faster smaller and more general":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "numerical linear algebra in the sliding window model")
  Member "spectrum estimation from samples":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "schatten norms in matrix streams hello sparsity goodbye dimension")
  Member "on approximating functions of the singular values in a stream":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "schatten norms in matrix streams hello sparsity goodbye dimension")
  Member "streaming symmetric norms via measure concentration":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "the johnson lindenstrauss lemma is optimal for linear dimensionality reduction":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "sub gaussian matrices on sets optimal tail dependence and applications")
  Member "principal component analysis and higher correlations for distributed data":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the communication complexity of optimization")
  Member "low rank approximation and regression in input sparsity time":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "osnap faster numerical linear algebra algorithms via sparser subspace embeddings":
    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.DS(Data Structures and Algorithms)