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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

MATH3772Multivariate 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 typeNumberLength hoursStudent hours
Example Class71.007.00
Lecture261.0026.00
Practical41.004.00
Private study hours113.00
Total Contact hours37.00
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 typeNotes% of formal assessment
In-course AssessmentCoursework20.00
Total percentage (Assessment Coursework)20.00

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


Exams
Exam typeExam 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 website

Last updated: 20/04/2009

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