## Naive Bayesian Classifier

yet another general purpose Naive Bayesian classifier.

##Installation You can install this package using the following `pip`

command:

`$ sudo pip install naiveBayesClassifier`

##Example

```
"""
Suppose you have some texts of news and know their categories.
You want to train a system with this pre-categorized/pre-classified
texts. So, you have better call this data your training set.
"""
from naiveBayesClassifier import tokenizer
from naiveBayesClassifier.trainer import Trainer
from naiveBayesClassifier.classifier import Classifier
newsTrainer = Trainer(tokenizer.Tokenizer(stop_words = [], signs_to_remove = ["?!#%&"]))
# You need to train the system passing each text one by one to the trainer module.
newsSet =[
{'text': 'not to eat too much is not enough to lose weight', 'category': 'health'},
{'text': 'Russia is trying to invade Ukraine', 'category': 'politics'},
{'text': 'do not neglect exercise', 'category': 'health'},
{'text': 'Syria is the main issue, Obama says', 'category': 'politics'},
{'text': 'eat to lose weight', 'category': 'health'},
{'text': 'you should not eat much', 'category': 'health'}
]
for news in newsSet:
newsTrainer.train(news['text'], news['category'])
# When you have sufficient trained data, you are almost done and can start to use
# a classifier.
newsClassifier = Classifier(newsTrainer.data, tokenizer.Tokenizer(stop_words = [], signs_to_remove = ["?!#%&"]))
# Now you have a classifier which can give a try to classifiy text of news whose
# category is unknown, yet.
unknownInstance = "Even if I eat too much, is not it possible to lose some weight"
classification = newsClassifier.classify(unknownInstance)
# the classification variable holds the possible categories sorted by
# their probablity value
print classification
```

* Note*: Definitely you will need much more training data than the amount in the above example. Really, a few lines of text like in the example is out of the question to be sufficient training set.

##What is the Naive Bayes Theorem and Classifier It is needless to explain everything once again here. Instead, one of the most eloquent explanations is quoted here.

The following explanation is quoted from another Bayes classifier which is written in Go.

BAYESIAN CLASSIFICATION REFRESHER: suppose you have a set of classes (e.g. categories) C := {C_1, ..., C_n}, and a document D consisting of words D := {W_1, ..., W_k}. We wish to ascertain the probability that the document belongs to some class C_j given some set of training data associating documents and classes.

By Bayes' Theorem, we have that

`P(C_j|D) = P(D|C_j)*P(C_j)/P(D).`

The LHS is the probability that the document belongs to class C_j given the document itself (by which is meant, in practice, the word frequencies occurring in this document), and our program will calculate this probability for each j and spit out the most likely class for this document.

P(C_j) is referred to as the "prior" probability, or the probability that a document belongs to C_j in general, without seeing the document first. P(D|C_j) is the probability of seeing such a document, given that it belongs to C_j. Here, by assuming that words appear independently in documents (this being the "naive" assumption), we can estimate

`P(D|C_j) ~= P(W_1|C_j)*...*P(W_k|C_j)`

where P(W_i|C_j) is the probability of seeing the given word in a document of the given class. Finally, P(D) can be seen as merely a scaling factor and is not strictly relevant to classificiation, unless you want to normalize the resulting scores and actually see probabilities. In this case, note that

`P(D) = SUM_j(P(D|C_j)*P(C_j))`

One practical issue with performing these calculations is the possibility of float64 underflow when calculating P(D|C_j), as individual word probabilities can be arbitrarily small, and a document can have an arbitrarily large number of them. A typical method for dealing with this case is to transform the probability to the log domain and perform additions instead of multiplications:

log P(C_j|D) ~ log(P(C_j)) + SUM_i(log P(W_i|C_j))

where i = 1, ..., k. Note that by doing this, we are discarding the scaling factor P(D) and our scores are no longer probabilities; however, the monotonic relationship of the scores is preserved by the log function.

If you are very curious about Naive Bayes Theorem, you may find the following list helpful:

#Improvements This classifier uses a very simple tokenizer which is just a module to split sentences into words. If your training set is large, you can rely on the available tokenizer, otherwise you need to have a better tokenizer specialized to the language of your training texts.

## TODO

- inline docs
- unit-tests

## AUTHORS

- Mustafa Atik @muatik
- Nejdet Yucesoy @nejdetckenobi