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I am trying to understand how can I calculate the similarity between userid and itemid. Here is the user-based table.The table didn't have rating /score information.

userid | itemid1 | itemid2 | itemid3 ... | itemid10000

1 | 1 | 0 | 1 | 1

2 | 0 | 1 | 1 | 1

3 | 0 | 0 | 0 | 1

1)Can I still use KNN method (like manhattan distance or euclidean distance) and cosine similarity method to calculate the similarity score? If so,how can I get these scores as vector matrix.

2)Suppose we have itemid > 100,000,000, so the table is very sparse. So do we have any method to control sparse data to deal with collaborative filtering problems.

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Basically with kNN approach you cannot compute similarity between user and product. You can compute similarity between user-user or product-product to give recommendations. kNN methods dont deal really well with sparse matrices, for such matrices matrix decomposition algorithms are better. Here is a good Python library called Surprise Python with implementations of kNN based algorithms, matrix factorization based algorithms and many more.

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