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Kernmethode

In: Mathematische Einführung in Data Science

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  • Sven-Ake Wegner

Abstract

Zusammenfassung Als Nächstes betrachten wir Datenmengen, die nicht linear trennbar sind. Um diese dennoch mit den Methoden der letzten zwei Kapitel zu behandeln, bilden wir unsere gegebene, nicht linear trennbare, Datenmenge in einen höherdimensionalen (und manchmal sogar unendlichdimensionalen!) Raum ab. Ist dann die abgebildete Datenmenge linear trennbar, so können wir auf diese den Perzeptronalgorithmus oder die SVM-Methode anwenden und erhalten einen induzierten Klassifizierer für die Originaldaten. Letzteres führt auf den sogenannten Kernel-Trick, bei dem man den höherdimensionalen Raum gar nicht genau zu kennen braucht und trotzdem einen Klassifizierer durch Lösung eines quadratischen Optimierungsproblems bestimmen kann. Die Frage nach der Existenz einer dafür benötigten Kernfunktion behandeln wir in Form der Mercer-Bedingung.

Suggested Citation

  • Sven-Ake Wegner, 2023. "Kernmethode," Springer Books, in: Mathematische Einführung in Data Science, chapter 0, pages 211-227, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-68697-3_15
    DOI: 10.1007/978-3-662-68697-3_15
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