Application of matrix decomposition in collaborative filtering recommendation algorithm

Generally in recommender systems, data is often expressed using the user-item matrix. The user scores the items they have touched, and the score indicates the user's liking for the item, the higher the score, the more the user likes the item. And this matrix is often sparse, the blank item is the user has not touched the item, the recommendation System task is to select some of the items recommended to the user.

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For this user-item matrix, you can use data from non-empty items to predict the data for blank items, that is, to predict the user's rating of items that they have not touched, and to recommend high-scoring items to the user based on the forecast. There are many ways to predict scoring, this article focuses on how to use matrix decomposition to make this prediction.

1. Singular value decomposition SVD

To understand SVD in detail, recommend a blog singular value decomposition (SVD) principle and its application in dimensionality reduction.
At this point, the user-item corresponding to the MXN matrix M SVD decomposition, and by selecting some of the larger singular values to reduce the dimension at the same time, that is, the matrix M decomposition to:

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where M is the user's dimension, n is the dimension of the item, K is the larger K singular value of the matrix M, and K is often much smaller than M and N, which is why SVD can be used to reduce dimensionality.
If we want to predict the first user's rating of J Items Mij, then only the calculation is required. In this way, we can get a predictive score for all the places in the scoring table that have no ratings. Recommend to users by finding the highest number of items corresponding to the item.

--to be continued--

Application of matrix decomposition in collaborative filtering recommendation algorithm