981 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
Joint Tensor Factorization and Outlying Slab Suppression with Applications
We consider factoring low-rank tensors in the presence of outlying slabs.
This problem is important in practice, because data collected in many
real-world applications, such as speech, fluorescence, and some social network
data, fit this paradigm. Prior work tackles this problem by iteratively
selecting a fixed number of slabs and fitting, a procedure which may not
converge. We formulate this problem from a group-sparsity promoting point of
view, and propose an alternating optimization framework to handle the
corresponding () minimization-based low-rank tensor
factorization problem. The proposed algorithm features a similar per-iteration
complexity as the plain trilinear alternating least squares (TALS) algorithm.
Convergence of the proposed algorithm is also easy to analyze under the
framework of alternating optimization and its variants. In addition,
regularization and constraints can be easily incorporated to make use of
\emph{a priori} information on the latent loading factors. Simulations and real
data experiments on blind speech separation, fluorescence data analysis, and
social network mining are used to showcase the effectiveness of the proposed
algorithm
Block-Simultaneous Direction Method of Multipliers: A proximal primal-dual splitting algorithm for nonconvex problems with multiple constraints
We introduce a generalization of the linearized Alternating Direction Method
of Multipliers to optimize a real-valued function of multiple arguments
with potentially multiple constraints on each of them. The function
may be nonconvex as long as it is convex in every argument, while the
constraints need to be convex but not smooth. If is smooth, the
proposed Block-Simultaneous Direction Method of Multipliers (bSDMM) can be
interpreted as a proximal analog to inexact coordinate descent methods under
constraints. Unlike alternative approaches for joint solvers of
multiple-constraint problems, we do not require linear operators of a
constraint function to be invertible or linked between each
other. bSDMM is well-suited for a range of optimization problems, in particular
for data analysis, where is the likelihood function of a model and
could be a transformation matrix describing e.g. finite differences or basis
transforms. We apply bSDMM to the Non-negative Matrix Factorization task of a
hyperspectral unmixing problem and demonstrate convergence and effectiveness of
multiple constraints on both matrix factors. The algorithms are implemented in
python and released as an open-source package.Comment: 13 pages, 4 figure
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