# Intro

Mahout currently has two implementations of Bayesian classifiers. One is the traditional Naive Bayes approach, and the other is called Complementary Naive Bayes.

# Implementations

The Naive Bayes implementations in Mahout follow the paper http://people.csail.mit.edu/jrennie/papers/icml03-nb.pdf Before we get to the actual algorithm lets discuss the terminology

Given, in an input set of classified documents:

1. j = 0 to N features
2. k = 0 to L labels

Then:

1. Normalized Frequency for a term(feature) in a document is calculated by dividing the term frequency by the root mean square of terms frequencies in that document
2. Weight Normalized Tf for a given feature in a given label = sum of Normalized Frequency of the feature across all the documents in the label.
3. Weight Normalized Tf-Idf for a given feature in a label is the Tf-idf calculated using standard idf multiplied by the Weight Normalized Tf

Once Weight Normalized Tf-idf(W-N-Tf-idf) is calculated, the final weight matrix for Bayes and Cbayes are calculated as follows

We calculate the sum of W-N-Tf-idf for all the features in a label called as Sigma_k or sumLabelWeight

For Bayes

```Weight = Log [ ( W-N-Tf-Idf + alpha_i ) / ( Sigma_k + N  ) ]
```

For CBayes

We calculate the Sum of W-N-Tf-Idf across all labels for a given feature. We call this sumFeatureWeight of Sigma_j
Also we sum the entire W-N-Tf-Idf weights for all feature,label pair in the train set. Call this Sigma_jSigma_k

Final Weight is calculated as

```Weight = Log [ ( Sigma_j - W-N-Tf-Idf + alpha_i ) / ( Sigma_jSigma_k - Sigma_k + N  ) ]
```

# Examples

In Mahout's example code, there are two samples that can be used:

1. Wikipedia Bayes Example - Classify Wikipedia data.
1. Twenty Newsgroups - Classify the classic Twenty Newsgroups data.
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