E9 205 Machine Learning for Signal Processing Dimensionality - - PowerPoint PPT Presentation

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E9 205 Machine Learning for Signal Processing Dimensionality - - PowerPoint PPT Presentation

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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

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E9 205 Machine Learning for Signal Processing

21-08-2019

Dimensionality Reduction - I

Instructor - Sriram Ganapathy (sriramg@iisc.ac.in)

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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.

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Direction of Maximum Variance

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Minimum Error Formulation

PRML - C. Bishop (Sec. 12.1)

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PCA Example

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Principal Component Analysis

❖ First eigenvectors of data covariance matrix ❖ Residual error from PCA

PRML - C. Bishop (Sec. 12.1)

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PCA

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

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PCA

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

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PCA - Reconstruction

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

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Whitening the Data

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