# 2008/09 Taught Postgraduate Module Catalogue

## MATH5772M Multivariate and Cluster Analysis

### 15 creditsClass Size: 100

Module manager: Dr S. Barber
Email: stuart@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### Pre-requisite qualifications

MATH2715 or MATH2735.

### This module is mutually exclusive with

 MATH3772 Multivariate Analysis

This module is not approved as an Elective

### Objectives

By the end of this module, students should be able to:

- relate joint, marginal and conditional distributions and their properties with particular reference to the normal distribution;
- obtain and use Hotelling's T-squared statistic for the one sample and two sample problems;
- derive, discuss the properties of, and interpret principal components;
- use the factor analysis model, and interpret the results of fitting such a model;
- derive, discuss the properties of, and interpret decision rules in discriminant analysis;
- use hierarchical methods on similarity or distance matrices to partition data into clusters;
- use multidimensional scaling to construct low-dimensional representations of data;
- use a statistical package with real data to facilitate an appropriate analysis and write a report giving and interpreting the results.

### Syllabus

1. Introduction to multivariate analysis and review of matrix algebra.
2. Multivariate distributions; moments; conditional and marginal distributions; linear combinations.
3. Multivariate normal and Wishart distributions; maximum likelihood estimation.
4. Hotelling's T2 test; likelihood vs. union-intersection approach; simultaneous confidence intervals.
5. Principal component analysis; dimension reduction; covariance vs. correlation matrix.
6. Factor analysis; common and specific factors; Heywood cases; interpretation of factor loadings; determination of number of factors.
7. Discriminant analysis; maximum likelihood and Bayesian discriminant rules for normal data; misclassification probabilities and assessment by cross-validation; Fisher's discriminant rule.
8. Cluster analysis, similarity matrix, distance matrix, hierarchical methods.
9. Multidimensional scaling, metric scaling, nonmetric scaling, horseshoe effect.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 7 1.00 7.00 Lecture 26 1.00 26.00 Practical 4 1.00 4.00 Private study hours 113.00 Total Contact hours 37.00 Total hours (100hr per 10 credits) 150.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Coursework 20.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 3 hr 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated