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: "pose graph optimization in the complex domain lagrangian duality conditions for zero duality gap and optimal solutions"
  Abstract: Pose Graph Optimization (PGO) is the problem of estimating a set of poses from pairwise relative measurements. PGO is a nonconvex problem, and currently no known technique can guarantee the computation of an optimal solution. In this paper, we show that Lagrangian duality allows computing a globally optimal solution, under certain conditions that are satisfied in many practical cases. Our first contribution is to frame the PGO problem in the complex domain. This makes analysis easier and allows drawing connections with the recent literature on unit gain graphs. Exploiting this connection we prove non-trival results about the spectrum of the matrix underlying the problem. The second contribution is to formulate and analyze the dual problem in the complex domain. Our analysis shows that the duality gap is connected to the number of eigenvalues of the penalized pose graph matrix, which arises from the solution of the dual. We prove that if this matrix has a single eigenvalue in zero, then (i) the duality gap is zero, (ii) the primal PGO problem has a unique solution, and (iii) the primal solution can be computed by scaling an eigenvector of the penalized pose graph matrix. The third contribution is algorithmic: we exploit the dual problem and propose an algorithm that computes a guaranteed optimal solution for PGO when the penalized pose graph matrix satisfies the Single Zero Eigenvalue Property (SZEP). We also propose a variant that deals with the case in which the SZEP is not satisfied. The fourth contribution is a numerical analysis. Empirical evidence shows that in the vast majority of cases (100% of the tests under noise regimes of practical robotics applications) the penalized pose graph matrix does satisfy the SZEP, hence our approach allows computing the global optimal solution. Finally, we report simple counterexamples in which the duality gap is nonzero, and discuss open problems.

Connected through hyperedge HE-1 (induced by source paper "local supports global deep camera relocalization with sequence enhancement"):
  with members:
    - "beyond tracking selecting memory and refining poses for deep visual odometry"
    - "understanding the limitations of cnn based absolute camera pose regression"
    - "deeptam deep tracking and mapping"
    - "guided feature selection for deep visual odometry"
    - "geonet unsupervised learning of dense depth optical flow and camera pose"
    - "inloc indoor visual localization with dense matching and view synthesis"
    - "vidloc a deep spatio temporal model for 6 dof video clip relocalization"
    - "geometric loss functions for camera pose regression with deep learning"

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.RO(Robotics)