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 "optimal analysis of subset selection based l_p low rank approximation"):
  Abstract: We study the low rank approximation problem of any given matrix $A$ over $\mathbb{R}^{n\times m}$ and $\mathbb{C}^{n\times m}$ in entry-wise $\ell_p$ loss, that is, finding a rank-$k$ matrix $X$ such that $\|A-X\|_p$ is minimized. Unlike the traditional $\ell_2$ setting, this particular variant is NP-Hard. We show that the algorithm of column subset selection, which was an algorithmic foundation of many existing algorithms, enjoys approximation ratio $(k+1)^{1/p}$ for $1\le p\le 2$ and $(k+1)^{1-1/p}$ for $p\ge 2$. This improves upon the previous $O(k+1)$ bound for $p\ge 1$ \cite{chierichetti2017algorithms}. We complement our analysis with lower bounds; these bounds match our upper bounds up to constant $1$ when $p\geq 2$. At the core of our techniques is an application of \emph{Riesz-Thorin interpolation theorem} from harmonic analysis, which might be of independent interest to other algorithmic designs and analysis more broadly. #R##N#As a consequence of our analysis, we provide better approximation guarantees for several other algorithms with various time complexity. For example, to make the algorithm of column subset selection computationally efficient, we analyze a polynomial time bi-criteria algorithm which selects $O(k\log m)$ columns. We show that this algorithm has an approximation ratio of $O((k+1)^{1/p})$ for $1\le p\le 2$ and $O((k+1)^{1-1/p})$ for $p\ge 2$. This improves over the best-known bound with an $O(k+1)$ approximation ratio. Our bi-criteria algorithm also implies an exact-rank method in polynomial time with a slightly larger approximation ratio.

Includes members:
  Member "on the complexity of robust pca and l1 norm low rank matrix approximation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "low rank approximation from communication complexity")
  Member "towards a zero one law for entrywise low rank approximation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "relative error tensor low rank approximation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "how to escape saddle points efficiently":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")
  Member "fast algorithms for robust pca via gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems")
  Member "low rank approximation of binary matrices column subset selection and generalizations":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "streaming ptas for binary ell_0 low rank approximation")
  Member "optimal cur matrix decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "sketching transformed matrices with applications to natural language processing")
  Member "near optimal column based matrix reconstruction":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "good feature matching towards accurate robust vo vslam with low latency")

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)