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COMPE 467 - Pattern Recognition

Dimensionality Reduction. COMPE 467 - Pattern Recognition. Dimensionality Reduction. We can reduce dimensionality by combining features . Principle Component Analysis seeks a projection that best represents the data in a least square sense. 1. Principal Component Analysis. 1.

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COMPE 467 - Pattern Recognition

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  1. Dimensionality Reduction COMPE 467 - Pattern Recognition

  2. Dimensionality Reduction • We can reducedimensionalitybycombiningfeatures. • PrincipleComponentAnalysisseeks a projectionthatbestrepresentsthe data in a leastsquare sense. 1

  3. Principal Component Analysis 1

  4. Principal Component Analysis This function is minimized if xo is equal to mean  1

  5. Principal Component Analysis • The sample mean is the zero-degree representation of the entire dataset. • Simple, but provides no information about the variability in the data. • A better representation can be obtained with a projection, a line, through the sample mean 1

  6. Principal Component Analysis 1

  7. Principal Component Analysis 1

  8. Principal Component Analysis 1

  9. Principal Component Analysis 1

  10. Principal Component Analysis 1

  11. Principal Component Analysis 1

  12. Principal Component Analysis 1

  13. Principal Component Analysis 1

  14. PCA - Example HOW ? 1

  15. PCA - Example HOW ? 1

  16. PCA – Example (cont.) m 1

  17. PCA – Example (cont.) Continue and find principle components. 1

  18. References • R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, New York: John Wiley, 2001. • Robi Polikar, “Theory and Applications of Pattern Recognition – Lecture Presentations”, Rowan University, Glassboro, NJ.

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