This paper introduces ALL0CORE, a new form of probabilistic non-negative
tensor decomposition. ALL0CORE is a Tucker decomposition where the number of
non-zero elements (i.e., the L0-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.
ALL0CORE -- i.e., allocated L0-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 ALL0CORE typically requires only tiny fractions (e.g.,~1%) of the full
core to achieve the same results as full Tucker decomposition at only a
correspondingly tiny fraction of the cost.

该论文介绍了 ALL0CORE，一种新型的概率性非负张量分解方法，它是一种具有 L0 约束核的 Tucker 分解方法，通过在推断过程中在核张量上分配非零元素的位置和值来实现。ALL0CORE 既具有 CP 分解的计算可行性，又具有 Tucker 分解的潜在结构，通过一系列真实数据实验证明，ALL0CORE 通常只需使用核的极小比例即可以相应极小的成本达到与完整的 Tucker 分解相同的结果。