So I am quite certain I’m going to have more in-depth questions as I work through the material a few times. Yet up front, a few points on which I’d appreciate clarification:
Still working on fully securing my Linear Algebra knowledge, but I know the variables ‘U’ and ‘V’ can have a somewhat ‘loaded’ context (orthogonal ?)-- For example in computer graphics. Is there some particular reason we are chosing these to start with in the decomposition ? And what if our equation is longer-- Can we go U, V, W, etc ? Or is it ‘standard practice’ to just compress whatever derivatives we are dealing we in our lead up functions to only U and V ?
Along with this, in the given first generic example it appears as if the elements of U and V are rather simply broken up into a neat sort of ‘order of operations’ sort of method where the equation is simple, thus works out nicely. But when we move on to the Logistic Regression, it seems(?) as if we are deducing our derivatives on much larger ‘chunks’ of the final equation.
Sorry if I am not being clear on this, but how are we supposed to know where our ‘break / inflection points’ are ? Wherever their is a new elementary computation involving an additional variable ?