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Recommend keywords based on past keywords searched

If the only information you have is what the user searched for, then the simplest thing to do is recommend topics based on the topics that others who have searched for the same things have searched for.

For example, Joe searches for fried green tomatoes and purple gummi worms. If Sam then searches for purple gummi worms, then you might recommend he also look at fried green tomatoes.

Of course, this model doesn't work well if you only have a handful of participants. But if you have many people searching you can say, based on your analysis of previous searches, that if somebody searches for X, then there is a high probability that he'll search for Y.

This is broadly known as Collaborative filtering.

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