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 "tighter low rank approximation via sampling the leveraged element"):
  Abstract: In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being chosen based on the leverage scores of its row and column, and then involves weighted alternating minimization over the factored form of the intended low-rank matrix, to minimize error only on these samples. Our method can leverage input sparsity, yet produce approximations in {\em spectral} (as opposed to the weaker Frobenius) norm; this combines the best aspects of otherwise disparate current results, but with a dependence on the condition number $\kappa = \sigma_1/\sigma_r$. In particular we require $O(nnz(M) + \frac{n\kappa^2 r^5}{\epsilon^2})$ computations to generate a rank-$r$ approximation to $M$ in spectral norm. In contrast, the best existing method requires $O(nnz(M)+ \frac{nr^2}{\epsilon^4})$ time to compute an approximation in Frobenius norm. Besides the tightness in spectral norm, we have a better dependence on the error $\epsilon$. Our method is naturally and highly parallelizable. #R##N#Our new approach enables two extensions that are interesting on their own. The first is a new method to directly compute a low-rank approximation (in efficient factored form) to the product of two given matrices; it computes a small random set of entries of the product, and then executes weighted alternating minimization (as before) on these. The sampling strategy is different because now we cannot access leverage scores of the product matrix (but instead have to work with input matrices). The second extension is an improved algorithm with smaller communication complexity for the distributed PCA setting (where each server has small set of rows of the matrix, and want to compute low rank approximation with small amount of communication with other servers).

Includes members:
  Member "turning big data into tiny data constant size coresets for k means pca and projective clustering":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair clustering with multiple colors")
  Member "low rank matrix approximation in linear time":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "multiplicative rank 1 approximation using length squared sampling")
  Member "fast matrix completion without the condition number":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a survey of optimization methods from a machine learning perspective")
  Member "relative errors for deterministic low rank matrix approximations":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "blinkml efficient maximum likelihood estimation with probabilistic guarantees")
  Member "principal component analysis and higher correlations for distributed data":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the communication complexity of optimization")
  Member "understanding alternating minimization for matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "recommendation on a budget column space recovery from partially observed entries with random or active sampling")
  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 "improved matrix algorithms via the subsampled randomized hadamard transform":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "improved subsampled randomized hadamard transform for linear svm")

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)