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I would like to classify a text using neural networks. The text would consist of "address" and "non-address" texts.

My question is, how do I represent the text as a numeric values to input to my neural networks?

Should I do character level representation or word level? Thank you

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Based on the question, it sounds like some grounding in the fundamentals of text analysis would be helpful. There are no shortage of resources worth exploring. Here are some suggestions:

NLP R tutorial http://www.r-bloggers.com/natural-language-processing-tutorial/

Toronto's Deep Learning Lab - focus on neural nets http://deeplearning.net/demos/

Stanford's NLP Lab http://nlp.stanford.edu/software/index.shtml

Cambridge's Textual Analysis Lab http://www.cl.cam.ac.uk/~fh295/simlex.html

National Center for Text Mining http://nactem.ac.uk/

Corpus manuals to English language dictionaries http://clu.uni.no/icame/manuals/

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You might use one-hot encoding, so one neuron represents one letter. That being said, it seems to me that neural networks and NLP in general are bit of overkill for your problem. You might get what you want with just some clever feature engineering

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