Scenario: You are a data scientist tasked with improving the recommendation system of a video streaming platform. The current system uses collaborative filtering but lacks robust user similarity measurements. The management believes that incorporating advanced user similarity metrics could lead to more accurate and personalized recommendations.

Discussion Question: Given the scenario, how would you go about implementing and comparing various user similarity measurements? Can you explain the mathematical principles behind each of these methods and how they capture different aspects of user behavior and preferences? Share your insights on the potential strengths and weaknesses of these metrics in capturing similarity within a diverse user base.