Recommendation systems with Implicit Feedback

As we went through the movielens dataset, the ratings information for movies by the users. We then created a latent factor model and minimized the RMSE loss.
Would the same approach be used for taking implicit feedback, like shopping purchase behaviour. I read the paper Collaborative Filtering for Implicit Feedback Datasets by Hu, Koren and Volinsky. They ended up using Alternating Least Squares. Here is an excerpt from page 4 of the paper

“These vectors will be known as the user-factors and the item-factors, respectively. Essentially, the vectors strive to map users and items into a common latent factor space where they can be directly compared. This is similar to matrix factorization techniques which are popular for explicit feedback data, with two important distinctions: (1) We need to account for the varying confidence levels, (2) Optimization should account for all possible u, i pairs, rather than only those corresponding to observed data.”

So my question is if I use the equation 4 which is

min sum( cui * (pui - xTuiYui))

without the regularization, is the problem still equivalent to the one with explicit feedback like movie lens ratings? I would like to think so, but can someone help.