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  • On the Use of the Chi-squared Distance for the Structured Learning of Graph Embeddings

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    Author(s)
    Zhao, H
    Robles-Kelly, A
    Zhou, J
    Griffith University Author(s)
    Zhou, Jun
    Year published
    2011
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    Abstract
    In this paper, we describe the use of concepts from the areas of structural and statistical pattern recognition for the purposes of recovering a mapping which can be viewed as an operator on the graph attribute-set. This mapping can be used to embed graphs into spaces where tasks such as classification and retrieval can be effected. To do this, we depart from concepts in graph theory so as to introduce mappings as operators over graph spaces. This treatment leads to the recovery of a mapping based upon the graph attributes which is related to the edge-space of the graphs under study. As a result, the recovered mapping is a ...
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    In this paper, we describe the use of concepts from the areas of structural and statistical pattern recognition for the purposes of recovering a mapping which can be viewed as an operator on the graph attribute-set. This mapping can be used to embed graphs into spaces where tasks such as classification and retrieval can be effected. To do this, we depart from concepts in graph theory so as to introduce mappings as operators over graph spaces. This treatment leads to the recovery of a mapping based upon the graph attributes which is related to the edge-space of the graphs under study. As a result, the recovered mapping is a linear operator over the attribute set which is associated with the graph topology. To recover this mapping, we employ an optimisation approach whose cost function is based upon the Chi-squared distance and is related to the target function used in discrete Markov Random Field approaches. Thus, the method presented here provides a link between concepts in graph theory, statistical inference and linear operators. We illustrate the utility of the recovered embedding for purposes of shape categorisation and retrieval. We also compare our results to those yielded by alternatives.
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    Conference Title
    Proceedings - 2011 International Conference on Digital Image Computing: Techniques and Applications, DICTA 2011
    DOI
    https://doi.org/10.1109/DICTA.2011.78
    Copyright Statement
    © 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subject
    Computer vision
    Publication URI
    http://hdl.handle.net/10072/51691
    Collection
    • Conference outputs

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