Latent space for cross domain numerical features

I would like to find the shared latent space between two set of features. I have source and target domain features already extracted from images. I have 4 set of feature vectors for normal and abnormal source and target domains. I would like to train on normal source and target features and predict on abnormal sets. How do I that?

I have this idea, that if I create a shared space between two domains and give it to a classifier, it will predict if shared space for testing phase is different, then it is abnormal. I have read some literature for images, but I am no sure how to do it for numerical features?