Convex Formulation for Kernel PCA and its Use in Semi-Supervised Learning

© 2017 IEEE.  Personal use of this material is permitted.  Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a mere saddle point. Although these insights do not imply any algorithmic improvement, they can be used to further understand the method, formulate possible extensions, and properly address them. As an example, a new convex optimization problem for semisupervised classification is proposed, which seems particularly well suited whenever the number of known labels is small. Our formulation resembles a least squares support vector machine problem with a regularization parameter multiplied by a negative sign, combined with a variational principle for KPCA. Our primal optimization principle for semisupervised learning is solved in terms of the Lagrange multipliers. Numerical experiments in several classification tasks illustrate the performance of the proposed model in problems with only a few labeled data.The authors thank the following organizations. • EU: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC AdG A-DATADRIVE-B (290923). This paper reflects only the authors’ views, the Union is not liable for any use that may be made of the contained information. • Research Council KUL: GOA/10/09 MaNet, CoE PFV/10/002 (OPTEC), BIL12/11T; PhD/Postdoc grants. • Flemish Government: – FWO: G.0377.12 (Structured systems), G.088114N (Tensor based data similarity); PhD/Postdoc grants. – IWT: SBO POM (100031); PhD/Postdoc grants. • iMinds Medical Information Technologies SBO 2014. • Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO, Dynamical systems, control and optimization, 2012-2017)

Magnetic Eigenmaps for the visualization of directed networks

We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial Laplacian. Features such as density of links and directionality patterns are revealed by plotting the phases of the first magnetic eigenvectors. An interpretation of the magnetic eigenvectors is given in connection with the angular synchronization problem. Illustrations of our method are given for both artificial and real networks.The authors thank the following organizations. • EU: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC AdG A-DATADRIVE-B (290923). This paper reflects only the authors’ views, the Union is not liable for any use that may be made of the contained information. • Research Council KUL: GOA/10/09 MaNet, CoE PFV/10/002 (OPTEC), BIL12/11T; PhD/Postdoc grants. • Flemish Govern ment: – FWO: G.0377.12 (Structured systems), G.088114N (Tensor based data similarity); PhD/Postdoc grants. – IWT: SBO POM (100031); PhD/Postdoc grants. • iMinds Medical Information Technologies SBO 2014. • Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO, Dynamical systems, control and optimization, 2012–2017

Functional diffusion maps

Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional space. Although in practice we usually receive finite observations, they are still high-dimensional and hence dimensionality reduction methods are crucial. In this vein, the main state-of-the-art method for functional data analysis is Functional PCA. Nevertheless, this classic technique assumes that the data lie in a linear manifold, and hence it could have problems when this hypothesis is not fulfilled. In this research, attention has been placed on a non-linear manifold learning method: Diffusion Maps. The article explains how to extend this multivariate method to functional data and compares its behavior against Functional PCA over different simulated and real example

Spin-orbit torque from the introduction of Cu interlayers in Pt/Cu/Co/Pt nanolayered structures for spintronic devices

Spin currents can modify the magnetic state of ferromagnetic ultrathin films through spin-orbit torque. They may be generated by means of spin-orbit interactions by either bulk or interfacial phenomena. Electrical transport measurements reveal a 6-fold increase of the spin-orbit torque accompanied by a drastic reduction of the spin Hall magnetoresistance upon the introduction of an ultrathin Cu interlayer in a Pt/Cu/Co/Pt structure with perpendicular magnetic anisotropy. We analyze the dependence of the spin Hall magnetoresistance with the thickness of the interlayer, ranging from 0.5 to 15 nm, in the frame of a drift diffusion model that provides information on the expected spin currents and spin accumulations in the system. The results demonstrate that the major responsibility of both effects is spin memory loss at the interface. The enhancement of the spin-orbit torque when introducing an interlayer opens the possibility to design more efficient spintronic devices based on materials that are cheap and abundant such as copper. More specifically, spin-orbit torque magnetic random access memories and spin logic devices could benefit from the spin-orbit torque enhancement and cheaper material usage presented in this study

[Vuelta Valles Mineros 1981] [Material gráfico]

Contiene fotografías pertenecientes al archivo fotográfico del diario "Región", publicadas entre 1981 y 1982, aunque la mayoría de ellas se publicaron en mayo y junio de 1981Algunas no indican autoría. El resto de las fotografías firmadas por Foto Gudín (Luarca) y Foto E. Gar (Oviedo

[Equipos asturianos varios V] [Material gráfico]

Contiene fotografías pertenecientes al archivo fotográfico del diario "Región", publicadas entre 1967 y 1981Algunas fotos no indican autoría; el resto firmadas por Foto E. Gar (Oviedo), Foto A. Sánchez (Gijón), Trabajos Fotográficos Arrieta (Oviedo), Foto Macías (Avilés), Foto Arsenio (Trubia, Oviedo), Foto Gudín (Luarca), Foto-Color Sanmartino (La Felguera), Foto Mena (Oviedo