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

In today's data-driven retail environment, personalization algorithms power the customer experience by leveraging mathematical concepts to predict preferences and behaviors. These sophisticated systems employ various mathematical frameworks to transform raw customer data into actionable insights. How well do you understand the mathematical principles that underpin modern retail recommendation engines?

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Matrix factorization and singular value decomposition
Fourier transforms and wave function analysis
Differential calculus and Lagrangian mechanics
Euclidean geometry and triangulation methods