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Analogies Between Binary Images: Application to Chinese Characters

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Book cover Computational Approaches to Analogical Reasoning: Current Trends

Part of the book series: Studies in Computational Intelligence ((SCI,volume 548))

Abstract

The purpose of this chapter is to show how it is possible to efficiently extract the structure of a set of objects by use of the notion of proportional analogy. As a proportional analogy involves four objects, the very naïve approach to the problem, has basically a complexity of \(O(n^4)\) for a given set of \(n\) objects. We show, under some conditions on proportional analogy, how to reduce this complexity to \(O(n^2)\) by considering an equivalent problem, that of enumerating analogical clusters that are informative and not redundant. We further show how some improvements make the task tractable. We illustrate our technique with a task related with natural language processing, that of clustering Chinese characters. In this way, we re-discover the graphical structure of these characters.

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Notes

  1. 1.
    $$\begin{aligned} {\text {5,000}}^4 \times 0.8~\text {ms}/8&> 5^4 \times 10^9 \times 0.1\,\text {s} \\&> 125 \times 10^{8}\,\text {s} \\&> 1250 \times 10^{7}/( 3.1563 \times 10^7 )\;\text {years} \\&> 394.2\,\text {years}. \\ \end{aligned}$$
  2. 2.

    This comes from the fact that some analogies between strings of characters admit multiple solutions. When this is the case, then, there is not transitivity for : : in the general case for the objects considered (see [18, p. 113]).

  3. 3.

    Font designed by Nagao Sadakazu (snagao@tkb.att.ne.jp). We use version 1.1 of 1999.

  4. 4.

    We use a machine with 4 Gb memory equipped with an Intel Core i5 processor at 1.7 GHz.

  5. 5.

    See http://wiki.debian.org.hk/w/Make_Debian_support_Chinese.

  6. 6.

    See http://www.unicode.org/reports/tr38/tr38-10.html.

  7. 7.

    Reference [25] is the first mention of the edit distance constraint in terms of similarities; [2] gives the equivalent expression with edit distances; [17] is the published form of the proceedings in which [2] appeared, with few years delay. The edit distance constraint is necessary between strings of symbols to avoid many spurious analogies that would be formed without it.

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Authors and Affiliations

  1. Graduate School of Information, Production and Systems, Waseda University, 808-0135 Hibikino 2-7, Wakamatsu-ku, Kitakyushu-shi, Fukuoka-ken, Japan

    Yves Lepage

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  1. Yves Lepage
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Correspondence to Yves Lepage .

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Editors and Affiliations

  1. IRIT-CNRS, University of Toulouse, Toulouse, France

    Henri Prade

  2. IRIT-CNRS, University of Toulouse, Toulouse, France

    Gilles Richard

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Lepage, Y. (2014). Analogies Between Binary Images: Application to Chinese Characters. In: Prade, H., Richard, G. (eds) Computational Approaches to Analogical Reasoning: Current Trends. Studies in Computational Intelligence, vol 548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54516-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-54516-0_2

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