Cross Validated Asked by Minstein on October 20, 2020

I got two matrices **A** and **B**, the dimension of **A** is m x n, where n represents the number of samples, and m represents the number of features. Then after dimensionality reduction, e.g., by NMF, I got **B**, of which the dimension is m x k, where the m features are the same in **A**, and k is the number of factors or new basis.

I want to project **A** onto **B** to get each sample’s weights on each factor (**A** = **B** X **C**). Previously I obtained weights (C) by linear regression, which aims to reconstruct A. I am wondering if there are any other ways to get the weights because sometimes the linear regression does not work well.

I also tried to get the **C** by **C** = **A** X **B**, or by calculating similarities between n samples and k factors. I’d like to know whether the above two strategies are reasonable or not?

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