What kind of algorithm to use for finding matches? Lets say it’s a dating website. People answer several questions and create a profile. There are more then 50 questions that they answer. The goal is to provide best match for each individual based out of all 50 questions.

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A dating website optimizes how to get you to pay rather than actually match you up with somebody. They don’t want you to actually match, because when you do you leave the site and stop paying. However you do want to keep interest up just enough to prevent quitting in frustration. It’s a balancing act.

smart

Is this one of those things where your client asked you something and now you’re asking us?

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I believe dating apps used the ELO ranking system in the past

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You want labeled data for how well the matches actually go. Do you have that?

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I think it's mostly based on looks...

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So much of actual dating app behavior is about swiping on looks, not the questions. If you’re actually working on a dating app, focus there first.

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With no matches or historical data, I suppose you could use unsupervised learning, clustering data together based on similarities (whatever it may be - text, categorical features, etc). I would then identify the cluster the user falls in, and filter out all undesired genders based on the sexual orientation (that is, if your goal is to match similar profiles). Lastly, I’d order the matches by similarity ranking.

With matches, I suppose you could use supervised learning to train a model for probability of a match. Then conducting the same operations of filtering / ranking.

This is an entirely a cursory thought, so perhaps I may be way off.

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https://en.m.wikipedia.org/wiki/Association_rule_learning

If the idea is to match people based on similar answers on a survey I'd go with this.

If you can calculate a preference matrix you can use the gale-Shapley algorithm

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