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Suitably Representing Data

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Book cover The Puzzle of Granular Computing

Part of the book series: Studies in Computational Intelligence ((SCI,volume 138))

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Abstract

We may organize the search for the metric d at the basis of the cost function ℓ into two main steps: search for a sound representation of the data and use of a metric appropriate to the representation. The term sound stands for a representation allowing to better understanding the data, for instance by decoupling original signals, removing noise, discarding meaningless details, and alike. The result of the splitting could prove less efficient than the direct metric, but more manageable in most cases. Essentially, we are looking for rewriting the metric instances \(d(\boldsymbol y_i,\boldsymbol y_j)\) as a composition \(d'(g(\boldsymbol y_i),g(\boldsymbol y_j))\), with g optimizing the cost function C, namely:

$$g=\arg\max_{\widetilde g}\textsf C[\widetilde g]=\arg\max_{\widetilde g}\left\{\sum_{\boldsymbol y\in \mathfrak Y}\sum_{j=1}^k \ell\left[ D(\widetilde g(\boldsymbol y)),d_j\right]\right\}. ~~(7.1)$$

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Authors
  1. Bruno Apolloni
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  2. Witold Pedrycz
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  3. Simone Bassis
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  4. Dario Malchiodi
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Apolloni, B., Pedrycz, W., Bassis, S., Malchiodi, D. (2008). Suitably Representing Data. In: The Puzzle of Granular Computing. Studies in Computational Intelligence, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79864-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-79864-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79863-7

  • Online ISBN: 978-3-540-79864-4

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