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 "on the k means median cost function"):
  Abstract: In this work, we study the $k$-means cost function. The (Euclidean) $k$-means problem can be described as follows: given a dataset $X \subseteq \mathbb{R}^d$ and a positive integer $k$, find a set of $k$ centers $C \subseteq \mathbb{R}^d$ such that $\Phi(C, X) \stackrel{def}{=} \sum_{x \in X} \min_{c \in C} ||x - c||^2$ is minimized. Let $\Delta_k(X) \stackrel{def}{=} \min_{C \subseteq \mathbb{R}^d} \Phi(C, X)$ denote the cost of the optimal $k$-means solution. It is simple to observe that for any dataset $X$, $\Delta_k(X)$ decreases as $k$ increases. We try to understand this behaviour more precisely. For any dataset $X \subseteq \mathbb{R}^d$, integer $k \geq 1$, and a small precision parameter $\varepsilon > 0$, let $\mathcal{L}_{X}^{k, \varepsilon}$ denote the smallest integer such that $\Delta_{\mathcal{L}_{X}^{k, \varepsilon}}(X) \leq \varepsilon \cdot \Delta_{k}(X)$. We show upper and lower bounds on this quantity. Our techniques generalize for the metric $k$-median problem in arbitrary metrics and we give bounds in terms of the doubling dimension of the metric. Finally, we observe that for any dataset $X$, we can compute a set $S$ of size $O \left(\mathcal{L}_{X}^{k, \frac{\varepsilon}{c}} \right)$ such that $\Delta_{S}(X) \leq \varepsilon \cdot \Delta_k(X)$ using the $D^2$-sampling algorithm which is also known as the $k$-means++ seeding procedure. In the previous statement, $c$ is some fixed constant. We also discuss some applications of our bounds.

Includes members:
  Member "turning big data into tiny data constant size coresets for k means pca and projective clustering":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "fair clustering with multiple colors")
  Member "a unified framework for approximating and clustering data":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "approximating spectral clustering via sampling a review")

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)