Tensor factorization has proven useful in a wide range of applications, from
sensor array processing to communications, speech and audio signal processing,
and machine learning. With few recent exceptions, all tensor factorization
algorithms were originally developed for centralized, in-memory computation on
a single machine; and the few that break away from this mold do not easily
incorporate practically important constraints, such as nonnegativity. A new
constrained tensor factorization framework is proposed in this paper, building
upon the Alternating Direction method of Multipliers (ADMoM). It is shown that
this simplifies computations, bypassing the need to solve constrained
optimization problems in each iteration; and it naturally leads to distributed
algorithms suitable for parallel implementation on regular high-performance
computing (e.g., mesh) architectures. This opens the door for many emerging big
data-enabled applications. The methodology is exemplified using nonnegativity
as a baseline constraint, but the proposed framework can more-or-less readily
incorporate many other types of constraints. Numerical experiments are very
encouraging, indicating that the ADMoM-based nonnegative tensor factorization
(NTF) has high potential as an alternative to state-of-the-art approaches.

本篇研究提出了一种基于 ADMoM 的约束张量分解框架，构建分布式算法，有效节省计算量，可以更容易地纳入其他类型的约束条件下优化计算，其中以非负性为基线限制，实践结果非常鼓舞人心，说明 ADMoM 非负张量分解 (NTF) 作为一种替代非常有潜力。