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I needed to make a system for recognizing people based on hundreds of text by finding similarities in their written text grammatically or similarities between words they choose for writing, I don't want it so accurate but wanted to know if it is possible.

For example, finding one person with two account or more on a forum or something in that case (texts already gathered). I'm just wondering if it's possible and what field should I research in for.

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The term you are looking for is stylometry, which is related to a technique in forensic linguistics called writeprint analysis. There are many different techniques to perform stylometric analysis, from the very basic 5-feature analysis classifying features such as the lexicon and idiosyncrasies unique to a person to more complex analysis utilizing neural networks and machine learning. Searching online for various research papers focusing on stylometry should assist you in finding the best technique for the job.

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