How do I build a recommend system based on user's past purchases?

Question

I am exploring approaches to build a model that shows personalized search results (with or without query) for a fashion eCommerce platform. For that I am first working on coming up with a bunch of products for each user and their corresponding likelihood to buy it.
I have user's purchase history i.e the list of all the products with the client has bought with brand name and the dress category that the product belongs to (shoe or top etc.)
So I want to populate client's search results with the items that the client is most likely to purchase based on what he has bought in the past. So I am trying to build a model that estimates the probability that the user is going to like a suggested item. The products are part of a larger product inventory.
Is this a content based filtering problem? Currently I am trying to create each client's vector profile based on his liking towards a brand or not? Is this the current way.

Oren Razon · Answer

Content-based filtering is relevant whenever you have features to learn from (features about the products  user). Sound like this is not your case as you mostly rely on the historical choices  preferences of your user base. Sounds like a classical use case for Collaborative-Filtering (CF) based approach.
There are many possible CF implementations, most common ones are:
Memory-based: User to User  Item to Item based similarity
Model-based: Matrix factorization
Of course, there are much more implementation options but these ones could give you a good starting point

How do I build a recommend system based on user's past purchases?

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