Codes, cryptography and algorithms · Maths EE idea · Ambitious
Ranking web pages with eigenvectors
A research question to start from
How does the PageRank method rank pages in a small network, and why does the damping factor guarantee a unique ranking?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Markov chains and eigenvectors with a clear theoretical question about uniqueness.
Mathematics you would need
- Stochastic matrices
- Stationary distributions
- Power iteration
- Perron–Frobenius ideas (cited)
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Build the matrix for a small network.
- Compute rankings by power iteration.
- Explain why damping ensures uniqueness and convergence.
- Test sensitivity to the damping factor.
Scope and difficulty
Ambitious. Ambitious.
Pitfalls
- Business history.
- Theorem quoted without explanation.
Where to start reading
Search a library catalogue or a university's open lecture notes for: PageRank damping factor uniqueness; power iteration convergence stochastic matrix. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).
Make it your EE
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