169 research outputs found
A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence
A novel framework for a unifying treatment of quaternion valued adaptive
filtering algorithms is introduced. This is achieved based on a rigorous
account of quaternion differentiability, the proposed I-gradient, and the use
of augmented quaternion statistics to account for real world data with
noncircular probability distributions. We first provide an elegant solution for
the calculation of the gradient of real functions of quaternion variables
(typical cost function), an issue that has so far prevented systematic
development of quaternion adaptive filters. This makes it possible to unify the
class of existing and proposed quaternion least mean square (QLMS) algorithms,
and to illuminate their structural similarity. Next, in order to cater for both
circular and noncircular data, the class of widely linear QLMS (WL-QLMS)
algorithms is introduced and the subsequent convergence analysis unifies the
treatment of strictly linear and widely linear filters, for both proper and
improper sources. It is also shown that the proposed class of HR gradients
allows us to resolve the uncertainty owing to the noncommutativity of
quaternion products, while the involution gradient (I-gradient) provides
generic extensions of the corresponding real- and complex-valued adaptive
algorithms, at a reduced computational cost. Simulations in both the strictly
linear and widely linear setting support the approach
In-ear EEG biometrics for feasible and readily collectable real-world person authentication
The use of EEG as a biometrics modality has been investigated for about a
decade, however its feasibility in real-world applications is not yet
conclusively established, mainly due to the issues with collectability and
reproducibility. To this end, we propose a readily deployable EEG biometrics
system based on a `one-fits-all' viscoelastic generic in-ear EEG sensor
(collectability), which does not require skilled assistance or cumbersome
preparation. Unlike most existing studies, we consider data recorded over
multiple recording days and for multiple subjects (reproducibility) while, for
rigour, the training and test segments are not taken from the same recording
days. A robust approach is considered based on the resting state with eyes
closed paradigm, the use of both parametric (autoregressive model) and
non-parametric (spectral) features, and supported by simple and fast cosine
distance, linear discriminant analysis and support vector machine classifiers.
Both the verification and identification forensics scenarios are considered and
the achieved results are on par with the studies based on impractical on-scalp
recordings. Comprehensive analysis over a number of subjects, setups, and
analysis features demonstrates the feasibility of the proposed ear-EEG
biometrics, and its potential in resolving the critical collectability,
robustness, and reproducibility issues associated with current EEG biometrics
Hypergraph -Laplacian: A Differential Geometry View
The graph Laplacian plays key roles in information processing of relational
data, and has analogies with the Laplacian in differential geometry. In this
paper, we generalize the analogy between graph Laplacian and differential
geometry to the hypergraph setting, and propose a novel hypergraph
-Laplacian. Unlike the existing two-node graph Laplacians, this
generalization makes it possible to analyze hypergraphs, where the edges are
allowed to connect any number of nodes. Moreover, we propose a semi-supervised
learning method based on the proposed hypergraph -Laplacian, and formalize
them as the analogue to the Dirichlet problem, which often appears in physics.
We further explore theoretical connections to normalized hypergraph cut on a
hypergraph, and propose normalized cut corresponding to hypergraph
-Laplacian. The proposed -Laplacian is shown to outperform standard
hypergraph Laplacians in the experiment on a hypergraph semi-supervised
learning and normalized cut setting.Comment: Extended version of our AAAI-18 pape
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Design of Positive-Definite Quaternion Kernels
This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/LSP.2015.2457294Quaternion reproducing kernel Hilbert spaces (QRKHS) have been proposed recently and provide a highdimensional feature space (alternative to the real-valued multikernel approach) for general kernel-learning applications. The current challenge within quaternion-kernel learning is the lack of general quaternion-valued kernels, which are necessary to exploit the full advantages of the QRKHS theory in real-world problems. This letter proposes a novel way to design quaternionvalued kernels, this is achieved by transforming three complex kernels into quaternion ones and then combining their real and imaginary parts. Building on this general construction, our emphasis is on a new quaternion kernel of polynomial features, which is assessed in the prediction of bodysensor networks applications.F. Tobar acknowledges financial support to EPSRC grant number EP/L000776/1
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