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 "a mirroring theorem and its application to a new method of unsupervised hierarchical pattern classification"):
  Abstract: In this paper, we prove a crucial theorem called "Mirroring Theorem" which affirms that given a collection of samples with enough information in it such that it can be classified into classes and sub-classes then (i) There exists a mapping which classifies and sub- classifies these samples (ii) There exists a hierarchical classifier which can be constructed by using Mirroring Neural Networks (MNNs) in combination with a clustering algorithm that can approximate this mapping. Thus, the proof of the Mirroring theorem provides a theoretical basis for the existence and a practical feasibility of constructing hierarchical classifiers, given the maps. Our proposed Mirroring Theorem can also be considered as an extension to Kolmogrov's theorem in providing a realistic solution for unsupervised classification. The techniques we develop, are general in nature and have led to the construction of learning machines which are (i) tree like in structure, (ii) modular (iii) with each module running on a common algorithm (tandem algorithm) and (iv) self-supervised. We have actually built the architecture, developed the tandem algorithm of such a hierarchical classifier and demonstrated it on an example problem. approach, we developed a self-learning machine (based on our proposed Mirroring Theorem) which performs feature extraction and pattern learning simultaneously to recognize/classify the patterns in an unsupervised mode. This automatic feature extraction step, prior to unsupervised classification fulfills one more additional crucial requirement called dimensional reduction. Furthermore, by proving our stated mirroring theorem, we actually demonstrate that such unsupervised hierarchical classifiers mathematically exist. It is also proved that the hierarchical classifiers that do perform a level-by-level unsupervised classification can be approximated by a network of "nodes" forming a tree-like architecture. What we term as a "node", in this architecture, is actually an abstraction of an entity which executes two procedures: the "Mirroring Neural Network" (MNN) algorithm coupled with a clustering algorithm. The MNN performs automatic data reduction and feature extraction (see (18) for more details on MNN) and clustering does the subsequent step called unsupervised classification (of the extracted features of the MNN); these two steps are performed in tandem - hence our term Tandem Algorithm. The Mirroring Theorem provides a proof that this technique will always work provided sufficient information is contained in the ensemble of samples for it to be classified and sub-classified and certain continuity conditions for the mappings are satisfied. The Mirroring Theorem, we prove in this paper may be considered as an extension to Kolmogrov's theorem (19) in providing a practical method for unsupervised classification. The details of the theorem and how it can be used for developing an unsupervised hierarchical classifier are discussed in the next sections.

Includes members:
  Member "pattern recognition and memory mapping using mirroring neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "learning discriminative features using encoder decoder type deep neural nets")
  Member "dimensionality reduction and reconstruction using mirroring neural networks and object recognition based on reduced dimension characteristic vector":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pattern recognition and memory mapping using mirroring neural networks")
  Member "automatic pattern classification by unsupervised learning using dimensionality reduction of data with mirroring neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "pattern recognition and memory mapping using mirroring neural networks")

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.LG(Machine Learning)