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Singulärwertzerlegung

In: Mathematische Einführung in Data Science

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  • Sven-Ake Wegner

Abstract

Zusammenfassung Wir präsentieren zunächst einen nur auf Standardmethoden der Linearen Algebra basierenden Zugang zur Singulärwertzerlegung für nicht-quadratische Matrizen. Mithilfe der Courant-Fischer-Formel stellen wir dann den Zusammenhang zum bereits in Kapitel 6 diskutierten gierigen Algorithmus her. Es folgen Anwendungen zur Dimensionalitätsreduktion von Datenmengen und zur Bestapproximation niedrigeren Ranges von Datenmatrizen. Als konkretes Beispiel behandeln wir die Bildkompression. Schließlich illustrieren wir die Hauptkomponentenanalyse (englisch: Principal Component Analysis oder PCA), sowie die Methode des kollaborativen Filterns anhand einer Datenmenge von Filmbewertungen.

Suggested Citation

  • Sven-Ake Wegner, 2023. "Singulärwertzerlegung," Springer Books, in: Mathematische Einführung in Data Science, chapter 0, pages 91-116, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-68697-3_7
    DOI: 10.1007/978-3-662-68697-3_7
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