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Comprehensive Overview of Dimensionality Reduction Techniques in Data Mining

Explore Dimensionality Reduction methods like PCA, Kernel PCA, and ICA for efficient data projection, signal representation, and classification. Learn through theory, algorithms, and examples in image and audio analysis. Discover optimal solutions and comparative analyses.

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Comprehensive Overview of Dimensionality Reduction Techniques in Data Mining

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  1. Feature Extraction (I) Data Mining IIYear 2009-10Lluís Belanche Alfredo Vellido

  2. Dimensionality reduction (1)

  3. Dimensionality reduction (2)

  4. Signal representation vs classification

  5. Principal Components Analysis (PCA) • General goal : project the data onto a new subspace so that a maximum of relevantinformation is preserved • In PCA, relevantinformation is variance (dispersion).

  6. PCA Theory (1)

  7. PCA Theory (2)

  8. PCA Theory (3)

  9. PCA Theory (4)

  10. Algorithm for PCA

  11. PCA examples (1)

  12. PCA examples (2)

  13. PCA examples (2)

  14. PCA examples (3)

  15. PCA examples (4)

  16. Two solutions: in which sense are they optimal? • In the signal representation sense • In the signal separation sense • In both • In none

  17. Other approaches to FE • Kernel PCA: perform PCA in xΦ(x), where K(x,y) = < Φ(x), Φ(y)> is a kernel • ICA (Independent Components Analysis): • Seeks statistical independence of features (PCA seeks uncorrelated features) • Equivalence to PCA iff features are Gaussian • Image and audio analysis brings own methods • Series expansion descriptors (from the DFT, DCT or DST) • Moment-based features • Spectral features • Wavelet descriptors • Cao, J.J. et al. A comparison of PCA, KPCA and ICA for dimensionality reduction. Neurocomputing 55, pp. 321-336 (2003)

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