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Visual Rank Using Image Similarity - IT Assignment Help
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Assignment Task:
Task:
Introduction
This assignment is based on the well-known PageRank algorithm developed by Google to help in ranking webpages. Although much has changed with Google’s techniques and it is not known exactly how much of a role the original PageRank algorithm plays in current webpage rankings, it remains an important tool in Google’s arsenal.
A different application of PageRank came about when some of Google’s engineers suggested applying it to images. They came up with the ‘VisualRank’ algorithm. We shall attempt something similar in this assignment, albeit with much more simplistic tools!
A pedagogical description of the PageRank algorithm is available at:
https://www.amsi.org.au/teacher_modules/pdfs/Maths_delivers/Pagerank5.pdf
Both algorithms are described below.
PageRank
The PageRank algorithm treats the internet as a directed graph, with webpages represented by vertices and hyperlinks to pages represented by directed edges. PageRank then simulates a hypothetical user browsing the internet by clicking on links at random. A rank is then assigned to each page based on the likelihood of finding the user there.
For example, consider the following mini-internet, with four webpages:
The location of the hypothetical user can be expressed using a vector of probabilities. If the user were to start on page 2 above, the initial vector of probabilities would be:
0=[0 1 0 0]
Then, after clicking on the only link on page 2, the user would end up on page 1 with certainty:
1=[1 0 0 0]
At this point, the user can either follow a link back to page 2 or continue to page 3. The user picks one of these two links at random and ends up on either of those pages with probability 1/2:
1 1
2=[0 2 2 0]
This process can be described using the adjacency matrix for the directed graph:
|
0 |
1 |
1 |
0 |
|
A=[1 |
0 |
0 |
0] |
|
1 |
1 |
0 |
1 |
|
0 |
1 |
0 |
0 |
The probability of following a link from a webpage is distributed equally among all links on that webpage. Since each row of the adjacency matrix corresponds to links from a webpage, we can form the required matrix of link-following likelihoods by normalising each row so that they sum to 1:
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