PageRank all the things!
summary
Explains how to build an N×N link matrix for directed graphs, scale each column by outbound links, and find the eigenvector with eigenvalue 1 via power iteration to produce PageRank-style scores; implementation notes include scaling each iteration, stopping on tolerance or after ~1000 iterations, and preventing sinks with teleportation using alpha=0.85. Gives a PHP implementation using math-php and a power-iteration package and shows a volleyball case where a team drops from 2nd to 6th in PageRank and the narrator’s team later wins the league.
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chapters (31)
- 0:00Start
- 0:51Story time
- 4:21Vectors as coordinates
- 4:51Scalar multiplication
- 6:22Matrix-vector multiplication
- 8:35Matrix as a transformation
- 9:11Chaining transformations
- 11:32Matrix multiplication as chained transformation
- 12:02Square matrices
- 14:07Web pages and links
- 16:16Chicken and egg problem
- 16:39Approach
- 17:35Creating the matrix M
- 18:53Equation s = Ms
- 19:53Eigenvalue problem
- 22:04PageRank as simulated surfing
- 24:01Power Method
- 24:55Implementation in PHP
- 25:50Behind the scenes
- 26:21Implementation concerns
- 27:48Preventing reducible matrices
- 28:50PageRank in general
- 29:19Influence in social networks
- 29:50Food chains
- 30:59Reverse CodeRank
- 31:28CodeRank for PHP
- 31:41Package dependencies
- 32:32Back to our story...
- 34:19The results
- 34:51The end
- 35:26Feedback & Questions
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