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

Trafficking and Syrian refugee smuggling: evidence from the Balkan Route

As of March 2016, 4.8 million Syrian refugees were scattered in two dozen countries by the civil war. Refugee smuggling has been a major catalyst of human trafficking in the Middle East and Europe migrant crises. Data on the extent to which smuggling devolved into trafficking in this refugee wave is, however, scarce. This article investigates how Syrian refugees interact with smugglers, shedding light on how human smuggling and human trafficking interrelated on the Balkan Route. I rely on original evidence from in-depth interviews (n = 123) and surveys (n = 100) with Syrian refugees in Jordan, Turkey, Greece, Serbia, and Germany; as well as ethnographic observations in thirty-five refugee camps or other sites in these countries. I argue that most smugglers functioned as guides, informants, and allies in understudied ways—thus refugee perceptions diverge dramatically from government policy assumptions. I conclude with a recommendation for a targeted advice policy that would acknowledge the reality of migrant-smuggler relations, and more effectively curb trafficking instead of endangering refugees

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 pp-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 $p$-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 $p$-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 $p$-Laplacian. The proposed $p$-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