Advertisement

Data and Relations

  • Thomas A. Runkler
Chapter

Abstract

The popular Iris benchmark set is used to introduce the basic concepts of data analysis. Data scales (nominal, ordinal, interval, ratio) must be accounted for because certain mathematical operations are only appropriate for specific scales. Numerical data can be represented by sets, vectors, or matrices. Data analysis is often based on dissimilarity measures (like inner product norms, Lebesgue/Minkowski norms) or on similarity measures (like cosine, overlap, Dice, Jaccard, Tanimoto). Sequences can be analyzed using sequence relations (like Hamming, Levenshtein, edit distance). Data can be extracted from continuous signals by sampling and quantization. The Nyquist condition allows sampling without loss of information.

Keywords

Feature Vector Quantization Level Quantization Error Edit Distance Dissimilarity Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Anderson. The Irises of the Gaspe Peninsula. Bull. of the American Iris Society, 59:2–5, 1935.Google Scholar
  2. 2.
    J. C. Bezdek, J. M. Keller, R. Krishnapuram, L. I. Kuncheva, and N. R. Pal. Will the real iris data please stand up? IEEE Transactions on Fuzzy Systems, 7(3):368–369, 1999.CrossRefGoogle Scholar
  3. 3.
    M. Blum, R. W. Floyd, V. Pratt, R. Rivest, and R. Tarjan. Time bounds for selection. Journal of Computer and System Sciences, 7:488–461, 1973.MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. A. Fisher. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7:179–188, 1936.Google Scholar
  5. 5.
    R. W. Hamming. Error detecting and error correcting codes. The Bell System Technical Journal, 26(2):147–160, April 1950.MathSciNetGoogle Scholar
  6. 6.
    V. I. Levenshtein. Binary codes capable of correcting deletions, insertions and reversals. Soviet Physics Doklady, 10(8):707–710, 1966.MathSciNetGoogle Scholar
  7. 7.
    S. S. Stevens. On the theory of scales of measurement. Science, 103(2684):677–680, 1946.MATHCrossRefGoogle Scholar

Copyright information

© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden 2012

Authors and Affiliations

  1. 1.MünchenGermany

Personalised recommendations