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
| 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
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
Reading list
The reading list is available from the Library websiteLast updated: 20/04/2009
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- Undergraduate module catalogue
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