# An implementation of Fraud Eagle¶

Fraud Eagle is an algorithm working on review graph, which is a bipartite graph consisting of reviewer nodes and products nodes. The aim of Fraud Eagle is finding fraudsters and fake reviews given by them.

This algorithm has been introduced by Leman Akoglu *et al.* in the 7th International AAAI Conference onf Weblogs and Social Media. Their paper Opinion Fraud Detection in Online Reviews by Network Effects is available online. See it for more information.

This package is a part of Review Graph Mining Project which provides other algorithms, datasets, and helper libraries.

## Graph model¶

Fraud Eagle algorithm assumes review data are represented in a bipartite graph. This bipartite graph has two kinds of nodes; reviewers and products. One reviewer node and one product node are connected if the reviewer posts a review to the product. In other words, an edge in the graph represents a review. Each review has a rating score. We assume the score is normalized in 0 to 1.

Here is a sample of the bipartite graph.

## Usage¶

### Construct a graph¶

In order to run the Fraud Eagle algorithm, you need to create a bipartite graph which represents your review data. The graph constructor is `fraud_eagle.ReviewGraph()`

, which is an alias of `fraud_eagle.graph.ReviewGraph`

. It takes a parameter epsilon from 0 to 0.5 not including both ends. See the original article Opinion Fraud Detection in Online Reviews by Network Effects for more details about this parameter.

You can instance the bipartite graph by

```
import fraud_eagle as feagle
# Create a graph with a parameter `epsilon`.
epsilon = 0.25
graph = feagle.ReviewGraph(epsilon)
```

Then, you need to add reviewer nodes, product nodes, and review edges. `new_reviewer()`

and `new_product()`

methods of the graph create a reviewer node and a product node, respectively, and add them to the graph. Both methods take one argument name, i.e. ID of the node. Note that, the names must be unique in a graph.

`add_review()`

method add a review to the graph. It takes a reviewer, a product, and a normalized rating score which the reviewer posted to the product. The normalized rating scores mean they must be in 0 to 1.

For example, let us assume there are two reviewers and three products like the below.

The graph can be constructed by the following code.

```
# Create reviewers and products.
# Note that don't create them using fraud_eagle.graph.Reviewer and
# fraud_eagle.graph.Product.
reviewers = [graph.new_reviewer("reviewer-{0}".format(i)) for i in range(2)]
products = [graph.new_product("product-{0}".format(i)) for i in range(3)]
graph.add_review(reviewers[0], products[0], 0.2)
graph.add_review(reviewers[0], products[1], 0.9)
graph.add_review(reviewers[0], products[2], 0.6)
graph.add_review(reviewers[1], products[0], 0.1)
graph.add_review(reviewers[1], products[1], 0.7)
```

### Analysis¶

`update()`

runs one iteration of loopy belief propagation algorithm. This method returns the amount of update in the iteration. You need to run iterations until the amount of update becomes enough small. It’s depended to the review data and the parameter epsilon that how many iterations are required to the amount of update becomes small. Moreover, sometimes it won’t be converged. Thus, you should set some limitation to the iterations.

```
print("Start iterations.")
max_iteration = 10000
for i in range(max_iteration):
# Run one iteration.
diff = graph.update()
print("Iteration {0} ends. (diff={1})".format(i + 1, diff))
if diff < 10**-5: # Set 10^-5 as an acceptable small number.
break
```

### Result¶

Each reviewer has an anomalous score which representing how the reviewer is anomalous. The score is normalized in 0 to 1. To obtain that score, use `anomalous_score`

property.

The `ReviewGraph`

has `reviewers`

property, which returns a collection of reviewers the graph has. Thus, the following code outputs all reviewers’ anomalous score.

```
for r in graph.reviewers:
print(r.name, r.anomalous_score)
```

On the other hand, each product has a summarized ratings computed from all reviews posted to the product according to each reviewers’ anomalous score. The summarized ratings are also normalized in 0 to 1. `summary`

property returns such summarized rating.

The `ReviewGraph`

also has `products`

property, which returns a collection of products. Thus, the following code outputs all products’ summarized ratings.

```
for p in graph.products:
print(p.name, p.summary)
```