Linear dimensionality reduction: Survey, insights, and generalizations

© 2015 John P. Cunningham and Zoubin Ghahramani. Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.

Coherence loss and recovery of an electron spin coupled inhomogeneously to a one-dimensional interacting spin bath: An adaptive time-dependent density-matrix renormalization group study

Coherence evolution and echo effect of an electron spin, which is coupled inhomogeneously to an interacting one-dimensional finite spin bath via hyperfine-type interaction, are studied using the adaptive time-dependent density-matrix renormalization group method. It is found that the interplay of the coupling inhomogeneity and the transverse intrabath interactions results in two qualitatively different coherence evolutions, namely, a coherence-preserving evolution characterized by periodic oscillation and a complete decoherence evolution. Correspondingly, the echo effects induced by an electron-spin flip at time tau exhibit stable recoherence pulse sequence for the periodic evolution and a single peak at root 2 tau for the decoherence evolution, respectively. With the diagonal intrabath interaction included, the specific feature of the periodic regime is kept, while the root 2 tau-type echo effect in the decoherence regime is significantly affected. To render the experimental verifications possible, the Hahn echo envelope as a function of tau is calculated, which eliminates the inhomogeneous broadening effect and serves for the identification of the different status of the dynamic coherence evolution, periodic versus decoherence.

Surface recombination in GaAs thin films with two-dimensional photonic crystals

The dynamics of spontaneous emission from GaAs slabs with photonic crystals etched into them are investigated both theoretically and experimentally. It is found that the intensity of spontaneous emission decreases significantly and that photonic crystals significantly shorten the lifetime of emission. The mechanics of enhancement and the reduction of emission from photonic crystals are analyzed by considering the surface recombination of GaAs. The measured and calculated lifetimes agree at a surface recombination velocity of 1.88x10(5) cm/s.

Research on improved methods of reduction of bend loss of silicon-on-insulator waveguides

Improved methods of reduction of bend loss of silicon-on-insulator waveguides were simulated and analyzed by means of effective index method (EIM) and two dimensional beam propagation method (2D-BPM). The simulation results indicate that two different methods, one of which are introducing an offset at the junction of two waveguides and the other is etching groove at the outside of bend waveguide, can decrease bend loss. And the later one is more effective. Meanwhile, experiments validate them. By etching groove, the insertion loss of bend waveguide of R = 16mm, transverse displacement 70mum was decreased 5dB. And its bend loss was almost eliminated.

High dimensional imagery geometry and it's applications

Because of information digitalization and the correspondence of digits and the coordinates, Information Science and high-dimensional space have consanguineous relations. With the transforming from the information issues to the point analysis in high-dimensional space, we proposed a novel computational theory, named High dimensional imagery geometry (HDIG). Some computational algorithms of HDIG have been realized using software, and how to combine with groups of simple operators in some 2D planes to implement the geometrical computations in high-dimensional space is demonstrated in this paper. As the applications, two kinds of experiments of HDIG, which are blurred image restoration and pattern recognition ones, are given, and the results are satisfying.

Reduction of dislocations in GaN epilayer grown on Si (111) substrates using a GaN intermedial layer

GaN intermedial layers grown under different pressures are inserted between GaN epilayers and AlN/Si(111) substrates. In situ optical reflectivity measurements show that a transition from the three-dimensional (3D) mode to the 2D one occurs during the GaN epilayer growth when a higher growth pressure is used during the preceding GaN intermedial layer growth, and an improvement of the crystalline quality of GaN epilayer will be made. Combining the in situ reflectivity and transmission electron microscopy (TEM) measurements, it is suggested that the lateral growth at the transition of growth mode is favourable for bending of dislocation lines, thus reducing the density of threading dislocations in the epilayer.

Effects of Ionizing Radiation on Three-Dimensional Human Vessel Models: Differential Effects According to Radiation Quality and Cellular Development

Little is known about the effects of space radiation on the human body. There are a number of potential chronic and acute effects, and one major target for noncarcinogenic effects is the human vasculature. Cellular stress, inflammatory response, and other radiation effects on endothelial cells may affect vascular function. This study was aimed at understanding the effects of space ionizing radiation on the formation and maintenance of capillary-like blood vessels. We used a 3D human vessel model created with human endothelial cells in a gel matrix to assess the effects of low-LET protons and high-LET iron ions. Iron ions were more damaging and caused significant reduction in the length of intact vessels in both developing and mature vessels at a dose of 80 cGy. Protons had no effect on mature vessels up to a dose of 3.2 Gy but did inhibit vessel formation at 80 cGy. Comparison with gamma radiation showed that photons had even less effect, although, as with protons, developing vessels were more sensitive. Apoptosis assays showed that inhibition of vessel development or deterioration of mature vessels was not due to cell death by apoptosis even in the case of iron ions. These are the first data to show the effects of radiation with varying linear energy transfer on a human vessel model. (C) 2011 In Radiation Research Society

Supervised Gaussian Process Latent Variable Model for Dimensionality Reduction

The Gaussian process latent variable model (GP-LVM) has been identified to be an effective probabilistic approach for dimensionality reduction because it can obtain a low-dimensional manifold of a data set in an unsupervised fashion. Consequently, the GP-LVM is insufficient for supervised learning tasks (e. g., classification and regression) because it ignores the class label information for dimensionality reduction. In this paper, a supervised GP-LVM is developed for supervised learning tasks, and the maximum a posteriori algorithm is introduced to estimate positions of all samples in the latent variable space. We present experimental evidences suggesting that the supervised GP-LVM is able to use the class label information effectively, and thus, it outperforms the GP-LVM and the discriminative extension of the GP-LVM consistently. The comparison with some supervised classification methods, such as Gaussian process classification and support vector machines, is also given to illustrate the advantage of the proposed method.

Magnet-assisted assembly of 1-dimensional hollow PtCo nanomaterials on an electrode surface

In this work, rapid and controllable confinement of one-dimensional (1D) hollow PtCo nanomaterials on an indium tin oxide (ITO) electrode surface was simply realized via magnetic attraction. The successful assembly was verified by scanning electron microscopy (SEM) and cyclic voltammetry, which showed that a longer exposure time of the electrode to the suspension of these 1D hollow nanomaterials (magnetic suspension) led to a larger amount of attached 1D hollow PtCo nanomaterials.

Carbon Nanotube/Silica Coaxial Nanocable as a Three-Dimensional Support for Loading Diverse Ultra-High-Density Metal Nanostructures: Facile Preparation and Use as Enhanced Materials for Electrochemical Devices and SERS

In this paper, we have reported a very simple strategy (combined sonication with sol-gel techniques) for synthesizing well-defined silica-coated carbon nanotube (CNT) coaxial nanocable without prior CNT functionalization. After functionalization with NH2 group, the CNT/silica coaxial nanocable has been employed as a three-dimensional support for loading ultra-high-density metal or hybrid nanoparticles (NPs) such as gold NPs, Au/Pt hybrid NPs, Pt hollow NPs, and Au/Ag core/shell NPs. Most importantly, it is found that the ultra-high-density Au/Pt NPs supported on coaxial nanocables (UASCN) could be used as enhanced materials for constructing electrochemical devices with high performance. Four model probe molecules (O-2, CH3OH, H2O2, and NH2NH2) have been investigated on UASCN-modified glassy carbon electrode (GCE). It was observed that the present UASCN exhibited high electrocatalytic activity toward diverse molecules and was a promising electrocatalyst for constructing electrochemical devices with high performance. For instance, the detection limit for H2O2 with a signal-to-noise ratio of 3 was found to be 0.3 mu M, which was lower than certain enzyme-based biosensors.

A general route to prepare one- and three-dimensional carbon nanotube/metal nanoparticle composite nanostructures

Adsorption of polyethyleneimine (PEI)-metal ion complexes onto the surfaces of carbon nanotubes (CNTs) and subsequent reduction of the metal ion leads to the fabrication of one-dimensional CNT/metal nanoparticle (CNT/M NP) heterogeneous nanostructures. Alternating adsorption of PEI-metal ion complexes and CNTs on substrates results in the formation of multilayered CNT films. After exposing the films to NaBH4, three-dimensional CNT composite films embedded with metal nanoparticles (NPs) are obtained. UV-visible spectroscopy, scanning electron microscopy, and X-ray photoelectron spectroscopy are used to characterize the film assembly. The resulting (CNT/M NP)(n) films inherit the properties from both the metal NPs and CNTs that exhibit unique performance in surface-enhanced Raman scattering (SERS) and electrocatalytic activities to the reduction of O-2; as a result, they are more attractive compared to (CNT/polyelectrolyte)(n) and (NP/polyelectrolyte)(n) films because of their multifunctionality.

Self-assembly of ionic liquids-stabilized Pt nanoparticles into two-dimensional patterned nanostructures at the air-water interface

In this paper, we demonstrate the self-assembly of ionic liquids (ILs)-stabilized Pt nanoparticles into two-dimensional (2D) patterned nanostructures at the air-water interface under ambient conditions. Here, ILs are not used as solvents but as mediators by virtue of their pronounced self-organization ability in synthesis of self-assembled, highly organized hybrid Pt nanostructures. It is also found that the morphologies of the 2D patterned nanostructures are directly connected with the quantities of ILs. Due to the special structures of ILs-stabilized Pt nanoparticles, 2D patterned Pt nanostructures can be formed through the pi-pi stack interactions and hydrogen bonds. The resulting 2D patterned Pt nanostructures exhibit good electrocatalytic activity toward oxygen reduction.

Alternate assemblies of polyelectrolyte functionalized carbon nanotubes and platinum nanoparticles as tunable electrocatalysts for dioxygen reduction

A novel method based on electrostatic layer-by-layer self-assembly (LBL) technique for alternate assemblies of polyelectrolyte functionalized multi-walled carbon nanotubes (MWNTs) and platinum nanoparticles (PtNPs) is proposed. The shortened MWNTs can be functionalized with positively charged poly(diallyldimethylammonium chloride) (PDDA) based on electrostatic interaction. Through electrostatic layer-by-layer assembly, the positively charged PDDA functionalized MWNTs (PDWNTs) and negatively charged citrate-stabilized PtNPs were alternately assembled on a 3-mercaptopropanesulfonic sodium (NIPS) modified gold electrode and also on other negatively charged surface, e.g. quartz slide and indium-tin-oxide (ITO) plate, directly forming the three-dimensional (3D) nanostructured materials. This is a very general and powerful technique for the assembling three-dimensional nanostructured materials containing carbon nanotubes (CNTs) and nanoparticles. Thus prepared multilayer films were characterized by ultraviolet-visiblenear-infrared spectroscopy (UV-vis-NIR), scanning electron microscopy (SEM) and cyclic voltammetry (CV). Regular growth of the mutilayer films is monitored by UV-vis-NIR.

Two- and three-dimensional Au nanoparticle/CoTMPyP self-assembled nanotructured materials: Film structure, tunable electrocatalytic activity, and plasmonic properties

Two- and three-dimensional Au nanoparticle/[tetrakis(N-methylpyridyl)porphyrinato]cobalt (CoTMPyP) nanostructured materials were prepared by "bottom-up" self-assembly. The electrocatalytic and plasmonic properties of the Au nanoparticle/CoTMPyP self-assembled nanostructured materials (abbreviated as Au/CoTMPyP SANMs) are tunable by controlled self-assembly of the An nanoparticles and CoTMPyP on indium tin oxide (ITO) electrode. The electrocatalytic activity of the Au/CoTMPyP SANMs can be tuned in two ways. One way is that citrate-stabilized An nanoparticles are positioned first on ITO surface with tunable number density, and then positively charged CoTMPyP ions are planted selectively on these gold sites. The other way is that An nanoparticles and CoTMPyP are deposited by virtue of layer-by-layer assembly, which can also tune the amount of the as-deposited electrocatalysts. FE-SEM studies showed that three-dimensional SANMs grow in the lateral expansion mode, and thermal annealing resulted in both surface diffusion of nanoparticles and atomic rearrangement to generate larger gold nanostructures with predominant (I 11) facets.

Hydrothermal synthesis and crystal structure of a sulfur-bridged binuclear copper(II) coordination polymer generated by a spontaneous reduction

A simultaneous reduction SO42- to S2- by 2,5-pyridinedicarboxylate under hydrothermal conditions produced a new binuclear copper(II) coordination polymer [CuS(4,4'-bipy)](n) (4,4-bipy = 4,4'-bipyridine) (1). Single crystal X-ray analysis revealed that compound I consisted of sulfur-bridged binuclear copper(II) units with Cu-Cu bonding which were combined with 4,4-bipy to generate a three-dimensional network constructed from mutual interpenetration of two-dimensional (6,3) nets. Crystal data for 1:C10H8CuN2S, tetragonal 14(1)/acd, a = 14.0686(5) Angstrom, b = 14.0686(5) Angstrom, c = 38.759(2) Angstrom, Z = 32. Other characterizations by elemental analysis, IR, EPR and TGA analysis were also described in this paper.