sparse representation

A sparse representation is a data encoding scheme in which a signal or dataset is expressed in a basis where the majority of coefficients are exactly zero or below a significance threshold. The concept is defined by three parameters: (1) the ambient dimension of the original space, (2) the sparsity level k (number of nonzero coefficients), and (3) the basis or dictionary in which sparsity is achieved. It persists through formal mathematical notation in optimization constraints (minimize L0/L1 norm subject to data fidelity) and is institutionalized in compressed sensing theory, sparse coding algorithms (K-SVD, matching pursuit), and feature engineering pipelines. [formal: representatio sparsa | substrate: behavior | horizon: hours | explicit: yes | epoch: 0.01]