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Understanding Principal Component Analysis: Data Reduction and Interpretation

Learn how Principal Component Analysis explains variance-covariance structure through linear combinations of variables, leading to data reduction and interpretation without normality assumption.

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Understanding Principal Component Analysis: Data Reduction and Interpretation

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  1. 主成分分析

  2. Principal Component Analysis • Explain the variance-covariance structure of a set of variables through a few linear combinations of these variables • Objectives • Data reduction • Interpretation • Does not need normality assumption in general

  3. Principal Components

  4. Result （主成分解）

  5. Result （总方差不变）

  6. Proportion of Total Variance due to the kth Principal Component

  7. Concept of Principal Components

  8. Sample Principal Components

  9. Sample Principal Components

  10. Example : Pained Turtles

  11. Example

  12. Example : Turtle Data

  13. Example : Scree Plot

  14. Example

  15. 几何解释

  16. 几何解释

  17. 几何解释

  18. 几何解释

  19. 几何解释

  20. 几何解释

  21. 几何解释

  22. 几何解释

  23. 样本主成分

  24. Example: Pained Turtles

  25. Example

  26. Example: Scree Plot

  27. Example

  28. 样本主成分的近似平面解释

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