Is there an equivalent in NMF to PCA projection? For example lets say you have 2 datasets of data which are generated by a highly similar process, one which is noisy (dataset 2) and one which is not (dataset 1). Lets assume by PCA you can see distinct clusters in dataset 1 by looking at pc1 vs pc2 but not in dataset 2. For PCA you can use the use the loadings from a PCA of dataset#1 with the values from dataset 2 to project it onto dataset1 pca space. This might be in the hopes that it can help you avoid noise in the signal(there are other strategies you could use on dataset 2 alone but i am interested in the projection aspect) . Is there an equivalent strategy for NMF.
Same scenario now with NMF, lets say i did an NMF with equivalent ranks on both datasets(which are now non negative for this example) and now have 2 WxH matrix sets(W1,H1),(W2,H2). Could i equivalently use w1 and the data from something of the form W1xH2 to recreate my dataset then do PCA. I.e use the W1 feature weights along with the sample weights from H2. Is this mathematically acceptable? Essentially I want to use information from dataset 1 to help cluster dataset 2.