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

In today's data-driven retail environment, sophisticated mathematical algorithms power personalization systems that analyze customer behavior and preferences. These algorithms transform raw data into actionable insights, enabling retailers to create customized shopping experiences. Test your knowledge about the mathematical foundations that drive modern retail recommendation systems!

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Matrix factorization techniques that decompose the user-item interaction matrix into lower-dimensional latent factors
Bayesian probability networks that calculate likelihood ratios of purchase decisions
Quaternion rotation formulas that map consumer preferences to four-dimensional product spaces
Euclidean distance minimization between product feature vectors in normalized space