2 research outputs found
Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers
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.Comment: Submitted to the IEEE Transactions on Signal Processin
Parallel algorithms for large scale constrained tensor decomposition
Summarization: Most tensor decomposition algorithms were developed for in-memory computation on a single machine. There are a few recent exceptions that were designed for parallel and distributed computation, but these cannot 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, yielding algorithms that are naturally amenable to parallel implementation. The methodology is exemplified using nonnegativity as a baseline constraint, but the proposed framework can incorporate many other types of constraints. Numerical experiments are encouraging, indicating that ADMoM-based nonnegative tensor factorization (NTF) has high potential as an alternative to state-of-the-art approaches.Παρουσιάστηκε στο: Acoustics, Speech and Signal Processing IEEE International Conference o