human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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 $\kappa$.

Question: Please tell me which class the center node 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)