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# Analysis of multivariable and high dimensional data

Listed as Statistics Topic D in the Course Planner.

Go to this course in the University Course Planner.

## Description

Multivariate analysis of data is performed with the aims to 1. understand the structure in data and summarise the data in simpler ways; 2. understand the relationship of one part of the data to another part; and 3. make decisions or draw inferences based on data. The statistical analyses of multivariate data extend those of univariate data, and in doing so require more advanced mathematical theory and computational techniques. The course begins with a discussion of the three classical methods Principal Component Analysis, Canonical Correlation Analysis and Discriminant Analysis which correspond to the aims above. We also learn about Cluster Analysis, Factor Analysis and newer methods including Independent Component Analysis. For most real data the underlying distribution is not known, but if the assumptions of multivariate normality of the data hold, extra properties can be derived. Our treatment combines ideas, theoretical properties and a strong computational component for each of the different methods we discuss. For the computational part -- with Matlab -- we make use of real data and learn the use of simulations in order to assess the performance of different methods in practice. Topics covered: 1. Introduction to multivariate data, the multivariate normal distribution 2. Principal Component Analysis, theory and practice 3. Canonical Correlation Analysis, theory and practice 4. Discriminant Analysis, Fisher's LDA, linear and quadratic DA 5. Cluster Analysis: hierarchical and k-means methods 6. Factor Analysis and latent variables 7. Independent Component Analysis including an Introduction to Information Theory The course will be based on my forthcoming monograph Analysis of Multivariate and High-Dimensional Data - Theory and Practice, to be published by Cambridge University Press.

## Content

YearSemesterLevelUnits
2013243
 Inge KochLecturer for this course