How do I get latent features for a new row of data when doing non-negative matrix factorization?
Given a dataset represented by a data matrix $X$, we can solve $||X-HT||$ using gradient descent, setting coefficients equal to zero if they become negative. This gives us an $H$. If we get a new row of data $x_{new}$, then we can find the corresponding reduced features $w_{new}$(weights for the latent features) by solving the equation: 

$argmin_{w_{new}} = ||x_{new}-w_{new}T||$.