41,444 research outputs found
An Open Source C++ Implementation of Multi-Threaded Gaussian Mixture Models, k-Means and Expectation Maximisation
Modelling of multivariate densities is a core component in many signal
processing, pattern recognition and machine learning applications. The
modelling is often done via Gaussian mixture models (GMMs), which use
computationally expensive and potentially unstable training algorithms. We
provide an overview of a fast and robust implementation of GMMs in the C++
language, employing multi-threaded versions of the Expectation Maximisation
(EM) and k-means training algorithms. Multi-threading is achieved through
reformulation of the EM and k-means algorithms into a MapReduce-like framework.
Furthermore, the implementation uses several techniques to improve numerical
stability and modelling accuracy. We demonstrate that the multi-threaded
implementation achieves a speedup of an order of magnitude on a recent 16 core
machine, and that it can achieve higher modelling accuracy than a previously
well-established publically accessible implementation. The multi-threaded
implementation is included as a user-friendly class in recent releases of the
open source Armadillo C++ linear algebra library. The library is provided under
the permissive Apache~2.0 license, allowing unencumbered use in commercial
products
An introduction to Lie group integrators -- basics, new developments and applications
We give a short and elementary introduction to Lie group methods. A selection
of applications of Lie group integrators are discussed. Finally, a family of
symplectic integrators on cotangent bundles of Lie groups is presented and the
notion of discrete gradient methods is generalised to Lie groups
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
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