slides/2014-04-10-PageRank.html

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name: inverse
layout: true
class: left, top, inverse

---

# PageRank

.center[
.white-background[
<img src="img/PageRanks-Example.svg.png" width=85% />
]
]

???

## Web page importance

  + Also used to model importance of people, places... anything that has a
    reputation
  + inbound links are important, but scaled by the importance of the source
  + C is still important, even though it only has one inbound edge

---

## Random Walks

  + Starting from a random page, what is the likelihood of winding up on a
    target page?
  + Starting point captured by initial constant
  + Stopping captured by "damping factor" (0.85)

.white-background[
<img src="img/pagerank.png" width=100% />
]

???

## Original

  + Original paper did not divide by N
  + This gives relative weights of pages, but not a formal probability because
    sum will not add up to N
  + Either way is fine for our purposes

---

## Example

  + ```B```, ```C```, ```D```, all link to ```A```
  + ```B``` has PageRank of 0.5, 4 links
  + ```C``` has PageRank of 0.7, 4 links
  + ```D``` has PageRank of 0.2, 1 link

.white-background[
<img src="img/pagerank.png" width=100% />
]

  + 0.15/4 + 0.85 * sum(PR/links for (pr,links) in pages)
  + 0.15/4 + 0.85 * sum(0.5/4, 0.7/4, 0.2/1)
  + 0.15/4 + 0.85 * 0.465
  + .43275

---

## Other Pages

  + But how did we know the PageRank of other pages?
  + Start with something and calculate iteratively until convergence (sound familiar?)

---

## Representing Graphs

  + Adjacency Matrix - represent graph edges in a matrix

<br />

| V | A | B | C | D |
|---|---|---|---|---|
| A | 0 | 0 | 0 | 0 |
| B | 1 | 0 | 1 | 0 |
| C | 1 | 0 | 0 | 1 |
| D | 1 | 1 | 0 | 0 |

???

## Diversion

  + Take a step back so we can motivate how to express these calculations as
    linear algebra
  + Using linear algebra can help us translate graph concepts to fairly elegant
    code, as well as realize some optimizations
  + Draw the graph!
  + Symmetric? When?

---

## Representing Graphs

.left-column[

  + Adjacency List - for each vertex, list all connections

]

.right-column[
```csv
A []
B [A,C]
C [A,D]
D [A,B]
```
]

???

## Diversion

  + You can think of this as keys (vertex) and values (list of vertices)
  + When would thinking in key-values be useful? MapReduce
  + Back to matrix representation

---

## Eigenvector

  + PageRank formula divides by number of links
  + Adjacency matrix typically normalized such that all columns sum to 1
  + PageRank scores are entries in the largest eigenvector of the matrix
    representation

.white-background[
<img src="img/pagerank-eigen.png" width=100% />
]

---

## Eigenvector centrality

  + Another measurement for graphs, using the simple adjacency matrix
  + Relative influence of a node (no normalization)

---

## Adversarial

  + Source does not want to be discovered
  + Patterns are purposefully hidden: so discover the patterns of hiding
  + If adversary knows your techniques, they can take advantage of weakness

???

## Weakness

  + Reading: paper discovering hiding patterns
  + Weakness of pagerank?
  + We assume that these links are legitimate.
  + What happens if the links are not conveying authority?

---

## Google Bomb

  + Milder forms of adversarial work

<img src="img/Google_Bomb_Miserable_Failure.png" width=100% />

???

## Link farms

  + Link farms try to create fake links to pages,
  + [JC Penny's link farm](http://www.nytimes.com/2011/02/13/business/13search.html?pagewanted=all)

---

## Hubs & Authorities

.left-column[

  + Earlier in the web, there was more structure
  + Hubs: collected links to different resources
  + Authorities: Gave out specific information
  + Score separately?
]
.right-column[
<img src="img/early-yahoo.jpg" width=100% />
]

???

## Alternatives

  + Some other interesting network analysis tools

---

## HITS

  + Authority score
    + sum(hub(i) for i in inbound_links)
  + Hub score
    + sum(authority(i) for i in outbound_links)
  + Normalize
    + to ensure convergence, square root sum of squares of scores

???

## Iterative

  + Sill iterative, but now using inbound and outbound links to judge
  + Hubs have outbound links to authoritive pages
  + Authorities have inbound links from good hubs

---

# *Break*

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