Which mathematical technique forms the foundation of collaborative filtering, one of the most widely used approaches in retail recommendation systems?

In today's retail world, recommendation systems are powered by sophisticated mathematical algorithms that determine what products to suggest to customers. These systems analyze purchase history, browsing behavior, and demographic data to create personalized shopping experiences. How well do you understand the mathematical foundations behind retail recommendation engines that shape our shopping decisions every day?

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Matrix factorization and singular value decomposition (SVD)
Fourier transforms and wave function analysis
Differential calculus and partial derivatives
Euclidean geometry and trigonometric functions