The ALℓ_0CORE Tensor Decomposition for Sparse Count Data

This paper introduces ALℓ_0CORE, a new form of probabilistic non-negative tensor decomposition. ALℓ_0CORE is a Tucker decomposition where the number of non-zero elements (i.e., the ℓ_0-norm) of the core tensor is constrained to a preset value Q much smaller than the size of the core. While the user dictates the total budget Q, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. ALℓ_0CORE – i.e., allocated ℓ_0-constrained core– thus enjoys both the computational tractability of CP decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that ALℓ_0CORE typically requires only tiny fractions (e.g., 1 full Tucker decomposition at only a correspondingly tiny fraction of the cost.