# 2023/24 Taught Postgraduate Module Catalogue

## MATH5745M Multivariate Methods

### 15 creditsClass Size: 90

Module manager: Ruheyan Nuermaimaiti
Email: R.Nuermaimaiti@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2023/24

### Pre-requisite qualifications

MATH5741M, or equivalent.

### This module is mutually exclusive with

 MATH3772 Multivariate Analysis MATH5772M Multivariate&Cluster Analysis

This module is not approved as an Elective

### Module summary

In big data with multiple variables, it is vital to discover pattern and infer valuable information from the data. This module introduces basic techniques from multivariate statistics, with the aim to discover, describe and exploit dependencies between variables in complex datasets.

### Objectives

To introduce basic techniques from multivariate statistics, with the aim to discover, describe and exploit dependencies between variables in complex datasets.

Learning outcomes
On completion of the module, the student should:
- be able to discover and exploit dependency between variables;
- be able to reduce the dimension of a dataset with dependent components, and interpret the results;
- be able to identify clusters in a given data set;
- be able to visualise similarities between observations in lower dimension.

### Syllabus

- Introduction to multivariate analysis
- Statistical dependence, covariance matrix
- High dimensional problems, the "curse of dimensionality"
- Principal Component Analysis (PCA), dimension reduction
- Clustering, K-means method, distances between/within clusters
- Multidimensional Scaling (MDS)

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Practical 11 1.00 11.00 Private study hours 117.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 150.00

### Private study

The student will be expected to complete regular written worksheet assignments testing their understanding of theoretical course elements.

The student will learn to perform analysis using the software package R, which includes performing dimension reduction such as principal component analysis and factor analysis, clustering such as hierarchical and k-means clustering, multi-dimensional scaling, and learning different types of plots for presenting high-dimensional data into informative two-dimensional. Part of the assessment for the module consists of a practical, where the student will apply these techniques to a real-world data set.

### Opportunities for Formative Feedback

Monitoring by regular worksheets and achievement in supervised practical sessions.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Practical Report 30.00 Total percentage (Assessment Coursework) 30.00

There is no resit available for the coursework components of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 70.00 Total percentage (Assessment Exams) 70.00

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