Feedback on first draft

The papers need to be in the references at the end. (How is the Bibliography annotated?)

Each Figure need an explicit reference on the page. You cannot take a figure from somewhere and use it as you own. (Fair use is okay if you refer to the content in your text, but you need to give explicit reference so no one will think it is your own work.)

In the Matrix definition, keep the upper-lower case distinctions clear (I think one j should be J). Tell us that I is the number of customers and J the number of movies.

Minimizing squared error (on a held-out test set) was the goal of the Netflix prize; it should be factored out of the Approach 1. The regularization you state in Approach 2 is also used in Approach 1; these are different algorithms to perform the same optimization.

Please use the notation consistently; how are q and p related to u and m?

I'm not sure that the modification in "Modifying MF Calculations" are modifications. Isn't this equivalent to fixing one row/column of u and m to be 1?

Which of the papers was the "implicit feedback" from? Why/how does |N(u)|^{0.5} normalize this value?

"MF can beautifully consider these effects" seems like a strange comment. How does p_ depend on time? One of the problems is that most users have very few data points; estimating temporal changes seems even more difficult. Why are items static? Surely the interest in a movie changes over time!

I don't understand the confidence. Where does it come from? How can it be observed or learned? (Is c_ui a number multiplied or a function (your notation is ambiguous).

In the plot, what is v1 and v2?

Thanks for your comments. I addressed those issues. To clarify: 1. Modifying MF Calculations is a section that has subsections: Adding Biases, Additional Input Sources, Temporal Dynamics, Inputs with varying confidence levels. These are not applicable by just fixing one row/column of u and m to be 1. 2. Implicit feedback is from second paper. As you can read in the page, all these modifications are from second paper. 3. Unfortunately, the authors does not explain a lot about v1 and v2. So, this is not that obvious for me too. But, I added a sentence from the paper about that.