FunkSVD: math, code, prediction, and validation

Understand basic FunkSVD and focus on validation cases

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Today I would like to include the below parts:

1. FunkSVD: math, process, and code
2. Based on 1, make predictions, validation and will give emphasis on the different cases in order to help to understand the validation process

Let’s get started.

FunkSVD: briefly intro

1. FunkSVD is a kind of matrix factorization. The original algorithm proposed by Simon Funk in his blog post [3] factorized the user-item rating matrix as the product of two lower dimensional matrices[1].
2. The predicted ratings can be computed as R=HW, where R is the user-item rating matrix, H contains the user’s latent factors and W is the item’s latent factors. Specifically, the predicted rating r for user u will give to item i is computed as:

Pic from Wiki[1]

There are three matrices in this function:

• User-rating matrix: known ratings + to be predicted ratings
• User’s latent matrix: which needs to construct