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

For example, finding one person with two accounts 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 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 research papers focusing on stylometry should assist you in finding the best technique for the job.

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