14,063 research outputs found
Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets
Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence
(NMF-KL) is one of the most significant NMF problems and equivalent to
Probabilistic Latent Semantic Indexing (PLSI), which has been successfully
applied in many applications. For sparse count data, a Poisson distribution and
KL divergence provide sparse models and sparse representation, which describe
the random variation better than a normal distribution and Frobenius norm.
Specially, sparse models provide more concise understanding of the appearance
of attributes over latent components, while sparse representation provides
concise interpretability of the contribution of latent components over
instances. However, minimizing NMF with KL divergence is much more difficult
than minimizing NMF with Frobenius norm; and sparse models, sparse
representation and fast algorithms for large sparse datasets are still
challenges for NMF with KL divergence. In this paper, we propose a fast
parallel randomized coordinate descent algorithm having fast convergence for
large sparse datasets to archive sparse models and sparse representation. The
proposed algorithm's experimental results overperform the current studies' ones
in this problem
Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards
We discuss an approach for solving sparse or dense banded linear systems
on a Graphics Processing Unit (GPU) card. The
matrix is possibly nonsymmetric and
moderately large; i.e., . The ${\it split\ and\
parallelize}{\tt SaP}{\bf A}{\bf A}_ii=1,\ldots,P{\bf A}_i{\tt SaP::GPU}{\tt PARDISO}{\tt SuperLU}{\tt MUMPS}{\tt SaP::GPU}{\tt MKL}{\tt SaP::GPU}{\tt SaP::GPU}$ is publicly available and distributed as
open source under a permissive BSD3 license.Comment: 38 page
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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