Statistics Final Year Topic: Sensitivity of K-Means Cluster Assignments to Initialisation and Feature Scaling

This Statistics final year project uses simulated multivariate datasets with both separated and overlapping groups to investigate a specific question in multivariate analysis. The analysis is designed around known generating conditions so that the behaviour of competing statistical procedures can be checked.

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Why choose this project topic?

This study makes cluster stability an explicit, reproducible comparison. Working with simulated multivariate datasets with both separated and overlapping groups lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do feature scale and starting centres affect k-means cluster stability in controlled data structures?

Agree the scenario ranges, sample sizes and reporting measures for cluster stability before running the study.

Proposed project objectives

01Specify the data-generating conditions for simulated multivariate datasets with both separated and overlapping groups.
02Implement a reproducible analysis of cluster stability with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do feature scale and starting centres affect k-means cluster stability in controlled data structures?

A suggested research approach

Compare repeated initialisations under documented scaling choices. Evaluate within-cluster loss and assignment stability, using generating labels only as a simulation reference rather than assuming every dataset has true clusters. Write the analysis before inspecting favourable runs, record random seeds where simulation is used, and keep generated study data distinct from observed field data.

What you will need

A written design for simulated multivariate datasets with both separated and overlapping groups
Statistical software supporting multivariate analysis and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

A compact clustering solution does not prove that natural or socially meaningful groups exist in observed data.

Statistics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

Chapter 1Introduction
Chapter 2Literature Review
Chapter 3Theory and Methodology
Chapter 4Results and Applications
Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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