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 sample complexity for matrix completion and related problems via 120001 s 2 regularization"):
  Abstract: We study the strong duality of non-convex matrix factorization: we show under certain dual conditions, non-convex matrix factorization and its dual have the same optimum. This has been well understood for convex optimization, but little was known for matrix factorization. We formalize the strong duality of matrix factorization through a novel analytical framework, and show that the duality gap is zero for a wide class of matrix factorization problems. Although matrix factorization problems are hard to solve in full generality, under certain conditions the optimal solution of the non-convex program is the same as its bi-dual, and we can achieve global optimality of the non-convex program by solving its bi-dual. #R##N#We apply our framework to matrix completion and robust Principal Component Analysis (PCA). While a long line of work has studied these problems, for basic problems in this area such as matrix completion, the information-theoretically optimal sample complexity was not known, and the sample complexity bounds if one also requires computational efficiency are even larger. In this work, we show that exact recoverability and strong duality hold with optimal sample complexity guarantees for matrix completion, and nearly-optimal guarantees for exact recoverability of robust PCA. For matrix completion, under the standard incoherence assumption that the underlying rank-$r$ matrix $X^*\in \mathbb{R}^{n\times n}$ with skinny SVD $U \Sigma V^T$ has $\max\{\|U^Te_i\|_2^2, \|V^Te_i\|_2^2\} \leq \frac{\mu r}{n}$ for all $i$, to the best of our knowledge we give (1) the first non-efficient algorithm achieving the optimal $O(\mu n r \log n)$ sample complexity, and (2) the first efficient algorithm achieving $O(\kappa^2\mu n r \log n)$ sample complexity, which matches the known $\Omega(\mu n r \log n)$ information-theoretic lower bound for constant condition number $\kappa$.

Includes members:
  Member "complete dictionary recovery over the sphere i overview and the geometric picture":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "how to escape saddle points efficiently":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "understanding global loss landscape of one hidden layer relu neural networks")
  Member "complete dictionary recovery over the sphere ii recovery by riemannian trust region method":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "fast algorithms for robust pca via gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the convergence of stochastic gradient descent with low rank projections for convex low rank matrix problems")
  Member "matrix completion has no spurious local minimum":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "recovery guarantee of weighted low rank approximation via alternating minimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "weighted matrix completion from non random non uniform sampling patterns")
  Member "a geometric analysis of phase retrieval":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "efficient approaches for escaping higher order saddle points in non convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "necpd an online tensor decomposition with optimal stochastic gradient descent")

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)