Principal Component Analysis: Theory and Applications

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Page 3 of 4

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

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

Explores moment-generating functions, linear combinations, and normality of random variables.

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

On PCA includes interactive exercises and emphasizes minimizing information loss.

Covers random variables, probability functions, expectations, variances, and joint distributions.

Explores linear dimensionality reduction through PCA, variance maximization, and real-world applications like medical data analysis.