Principal Component Analysis: Covariance Matrix and Eigenvalues

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Explores the generation of multivariate Gaussian distributions and the challenges of factorizing covariance matrices.

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Explores the technical derivation and properties of Multivariate Extreme Value models.

Covers the theory and applications of Principal Component Analysis, focusing on dimension reduction and eigenvectors.

Explains Gaussian functions, modeling data, likelihood function, and maximum likelihood optimization.

Explores the criteria for Gaussian random vectors to have a joint PDF.

Explores multivariate methods like PCA, SVD, PLS, and ICA for dimensionality reduction in functional brain imaging.

Explores statistical independence, Gaussian Mixture Models, and fitting data with Gaussian functions.

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Covers the multivariate normal distribution, moment-generating function, and combinatorics.