Which mathematical concept forms the foundation of collaborative filtering algorithms widely used in retail personalization systems?

In today's data-driven retail environment, mathematical algorithms power sophisticated personalization systems that tailor shopping experiences to individual consumers. These algorithms analyze vast amounts of customer data to predict preferences, optimize product recommendations, and enhance customer engagement. How well do you understand the mathematical foundations behind modern retail personalization technologies?

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Matrix factorization and linear algebra
Differential calculus and partial derivatives
Bayesian probability and Markov chains
Euclidean geometry and triangulation