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: "convergence of stochastic gradient descent for pca"
  Abstract: We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\reals^d$. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the non-convex nature of the problem, analyzing its performance has been a challenge. In particular, existing guarantees rely on a non-trivial eigengap assumption on the covariance matrix, which is intuitively unnecessary. In this paper, we provide (to the best of our knowledge) the first eigengap-free convergence guarantees for SGD in the context of PCA. This also partially resolves an open problem posed in \cite{hardt2014noisy}. Moreover, under an eigengap assumption, we show that the same techniques lead to new SGD convergence guarantees with better dependence on the eigengap.

Connected through hyperedge HE-1 (induced by source paper "exponentially convergent stochastic k pca without variance reduction"):
  with members:
    - "the fast convergence of incremental pca"
    - "fast stochastic algorithms for svd and pca convergence properties and convexity"
    - "optimal and adaptive algorithms for online boosting"
    - "global convergence of stochastic gradient descent for some non convex matrix problems"
    - "a stochastic pca and svd algorithm with an exponential convergence rate"
    - "the noisy power method a meta algorithm with applications"
    - "matrix completion from a few entries"
    - "robust principal component analysis"

Connected through hyperedge HE-2 (induced by source paper "subspace estimation from incomplete observations a high dimensional analysis"):
  with members:
    - "scaling limit exact and tractable analysis of online learning algorithms with applications to regularized regression and pca"
    - "the scaling limit of high dimensional online independent component analysis"
    - "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm"
    - "online learning for sparse pca in high dimensions exact dynamics and phase transitions"
    - "provable efficient online matrix completion via non convex stochastic gradient descent"
    - "convergence of a grassmannian gradient descent algorithm for subspace estimation from undersampled data"
    - "online matrix completion and online robust pca"
    - "global convergence of a grassmannian gradient descent algorithm for subspace estimation"

Connected through hyperedge HE-3 (induced by source paper "on the regret minimization of nonconvex online gradient ascent for online pca"):
  with members:
    - "introduction to online convex optimization"
    - "follow the compressed leader faster online learning of eigenvectors and faster mmwu"
    - "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm"
    - "matrix completion has no spurious local minimum"
    - "provable efficient online matrix completion via non convex stochastic gradient descent"
    - "the fast convergence of incremental pca"
    - "provable bounds for learning some deep representations"
    - "near optimal algorithms for online matrix prediction"

Connected through hyperedge HE-4 (induced by source paper "compositional stochastic average gradient for machine learning and related applications"):
  with members:
    - "accelerated method for stochastic composition optimization with nonsmooth regularization"
    - "fast stochastic variance reduced admm for stochastic composition optimization"
    - "learning from conditional distributions via dual kernel embeddings"
    - "provable efficient online matrix completion via non convex stochastic gradient descent"
    - "adam a method for stochastic optimization"
    - "adadelta an adaptive learning rate method"
    - "making gradient descent optimal for strongly convex stochastic optimization"

Connected through hyperedge HE-5 (induced by source paper "averaging stochastic gradient descent on riemannian manifolds"):
  with members:
    - "riemannian stochastic variance reduced gradient algorithm with retraction and vector transport"
    - "complete dictionary recovery over the sphere ii recovery by riemannian trust region method"
    - "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm"
    - "fast stochastic algorithms for svd and pca convergence properties and convexity"

Connected through hyperedge HE-6 (induced by source paper "communication efficient algorithms for distributed stochastic principal component analysis"):
  with members:
    - "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm"
    - "even faster svd decomposition yet without agonizing pain"
    - "the fast convergence of incremental pca"
    - "fast stochastic algorithms for svd and pca convergence properties and convexity"
    - "optimal principal component analysis in distributed and streaming models"
    - "a stochastic pca and svd algorithm with an exponential convergence rate"
    - "communication efficient distributed dual coordinate ascent"
    - "improved distributed principal component analysis"

Connected through hyperedge HE-7 (induced by source paper "smooth sensitivity based approach for differentially private principal component analysis"):
  with members:
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "fast rates for empirical risk minimization of strict saddle problems"
    - "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm"
    - "efficient frequent directions algorithm for sparse matrices"
    - "robust shift and invert preconditioning faster and more sample efficient algorithms for eigenvector computation"
    - "low rank approximation and regression in input sparsity time"
    - "beating randomized response on incoherent matrices"
    - "beyond worst case analysis in private singular vector computation"

Connected through hyperedge HE-8 (induced by source paper "follow the compressed leader faster online learning of eigenvectors and faster mmwu"):
  with members:
    - "lazysvd even faster svd decomposition yet without agonizing pain"
    - "sdca without duality regularization and individual convexity"
    - "even faster svd decomposition yet without agonizing pain"
    - "pca with gaussian perturbations"
    - "improved svrg for non strongly convex or sum of non convex objectives"
    - "spectral smoothing via random matrix perturbations"
    - "online linear optimization via smoothing"
    - "the noisy power method a meta algorithm with applications"

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.LG(Machine Learning)