Advanced Matrix Factorization Jungle: A Living Map of Structured Factorization Algorithms and Phase Transitions
IgorCarron · x · 2026-09-20
Igor Carron updates his living document, the Advanced Matrix Factorization Jungle, mapping the ecosystem of matrix factorizations that impose structural assumptions—sparsity, low-rank, non-negativity, subspace membership—on the unknowns.
- Lineage: Sparse Coding & Dictionary Learning (Olshausen & Field) and NMF (Lee & Seung) were widely used but under-theorized; compressed sensing (Candès, Romberg, Tao, Donoho) and nuclear norms as convex rank proxies opened the floodgates
- Why a jungle: one method spans multiple loss functions and proxies, each with many algorithm implementations
- Phase transitions: sharp boundaries in parameter space serve as acid tests for algorithms, often signaling hard computational limits
- Applications range from video surveillance to recommendation systems, blending randomized linear algebra, nonconvex optimization, and probabilistic modeling
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