IX. Principle Component Analysis
Given by Sven Laur
Brief summary: Multivariate normal distribution. How any multivariate normal distribution can be constructed form a spherical normal distribution (white Gaussian noise) through an affine transformation. Direction of maximal variance. Principal component analysis as a way to reconstruct the affine transformation and its limitation. Principal component analysis as a maximum likelihood estimate method for determining parameters of a multivariate normal distribution. Principal component analysis as a way to reconstruct low-dimensional hyperplanes from disturbed data. Weighted PCA and independent component analysis as natural extensions of PCA. Principal curves and manifold learning as a non-linear dimensionality reduction method.
Materials: Lecture notes
- Bishop: Pattern Recognition and Machine Learning pages 559 - 599
- Bishop: Pattern Recognition and Machine Learning pages 599 - 603
- Try PCA and ICA methods on various image collections and interpret the results
- Built-in stats package in R: