138 research outputs found
Singleshot : a scalable Tucker tensor decomposition
International audienceThis paper introduces a new approach for the scalable Tucker decomposition problem. Given a tensor X , the algorithm proposed, named Singleshot, allows to perform the inference task by processing one subtensor drawn from X at a time. The key principle of our approach is based on the recursive computations of the gradient and on cyclic update of the latent factors involving only one single step of gradient descent. We further improve the computational efficiency of Singleshot by proposing an inexact gradient version named Singleshotinexact. The two algorithms are backed with theoretical guarantees of convergence and convergence rates under mild conditions. The scalabilty of the proposed approaches, which can be easily extended to handle some common constraints encountered in tensor decomposition (e.g non-negativity), is proven via numerical experiments on both synthetic and real data sets
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
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