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E9 205 Machine Learning for Signal Processing Dimensionality Reduction - I 21-08-2019 Instructor - Sriram Ganapathy (sriramg@iisc.ac.in) Principal Component Analysis Reducing the data of dimension to lower dimension

  1. E9 205 Machine Learning for Signal Processing Dimensionality Reduction - I 21-08-2019 Instructor - Sriram Ganapathy (sriramg@iisc.ac.in)

  2. Principal Component Analysis ❖ Reducing the data of dimension to lower dimension ❖ Projecting the data into subspace which preserves maximum data variance ❖ Maximize variance in projected space ❖ Equivalent formulated as minimizing the error between the original and projected data points.

  3. Direction of Maximum Variance

  4. Minimum Error Formulation PRML - C. Bishop (Sec. 12.1)

  5. PCA Example

  6. Principal Component Analysis ❖ First eigenvectors of data covariance matrix ❖ Residual error from PCA PRML - C. Bishop (Sec. 12.1)

  7. PCA Handwritten digits used for PCA training… PRML - C. Bishop (Sec. 12.1)

  8. PCA Eigen Values Residual Error PRML - C. Bishop (Sec. 12.1)

  9. PCA - Reconstruction Eigenvectors PCA - Reconstruction PRML - C. Bishop (Sec. 12.1)

  10. Whitening the Data Original Data Standardization Whitening PRML - C. Bishop (Sec. 12.1)

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