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.

High-temperature AlN interlayer for crack-free AlGaN growth on GaN

This paper presents a study of the transformation of high-temperature AlN (HT-AlN) interlayer (IL) and its effect on the strain relaxation of Al0.25Ga0.75N/HT-AlN/GaN. The HT-AlN IL capped with Al0.25Ga0.75N transforms into AlGaN IL in which the Al composition increases with the HT-AlN IL thickness while the total Ga content keeps nearly constant. During the HT-AlN IL growth on GaN, the tensile stress is relieved through the formation of V trenches. The filling up of the V trenches by the subsequent Al0.25Ga0.75N growth is identified as the Ga source for the IL transformation, whose effect is very different from a direct growth of HT-AlGaN IL. The a-type dislocations generated during the advancement of V trenches and their filling up propagate into the Al0.25Ga0.75N overlayer. The a-type dislocation density increases dramatically with the IL thickness, which greatly enhances the strain relaxation of Al0.25Ga0.75N. (c) 2008 American Institute of Physics.

Does an enhanced yellow luminescence imply a reduction of electron mobility in n-type GaN?

It is studied whether there is any regular relationship between the yellow luminescence band and electron mobility of n-type GaN. For a series of GaN samples grown with the same Si doping, it is found that the electron mobility decreases with an increase of relative intensity of yellow luminescence, accompanied by an increase of edge dislocation density. Further research indicates that it is acceptors introduced by edge dislocations which lead to the concomitant changes of yellow luminescence and electron mobility. Similar changes are induced by Si doping in the n-type GaN samples with relatively low edge dislocation density. However, the relationship between the yellow luminescence and electron mobility of n-type GaN is not a simple one. A light Si doping may simultaneously increase yellow luminescence and electron mobility when Si doping plays a dominant role in reducing the carrier scattering. This means that even the intensity of yellow luminescence is often used as an indicator of material quality for GaN, it does not have any monotonous correlation with the electron mobility of GaN. (c) 2007 American Institute of Physics.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

Reduction of tensile stress in GaN grown on Si(111) by inserting a low-temperature AlN interlayer

This study describes the growth of a low-temperature AlN interlayer for crack-free GaN growth on Si(111). It is demonstrated that, in addition to the lower growth temperature, growth of the AlN interlayer under Al-rich conditions is a critical factor for crack-free GaN growth on Si(111) substrates. The effect of the AlN interlayer thickness and NH3/TMA1 ratios on the lattice constants of subsequently grown high temperature GaN was investigated by X-ray triple crystal diffraction. The results show that the elimination of micro-cracks is related to the reduction of the tensile stress in the GaN epitaxial layers. This was also coincident with a greater number of pits formed in the AlN interlayer grown under Al rich conditions. It is proposed that these pits act as centers for the generation of misfit dislocations, which in turn leads to the reduction of tensile stress. (C) 2004 Elsevier B.V. All rights reserved.

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.

Manifold covering theory in biomimetic pattern recognition

We describe a new model which is based on the concept of cognizing theory. The method identifies subsets of the data which are embedded in arbitrary oriented lower dimensional space. We definite manifold covering in biomimetic pattern recognition, and study its property. Furthermore, we propose this manifold covering algorithm based on Biomimetic Pattern Recognition. At last, the experimental results for face recognition demonstrates that the correct rejection rate of the test samples excluded in the classes of training samples is very high and effective.

Stress reduction in GaN films on (111) silicon-on-insulator substrate grown by metal-organic chemical vapor deposition

The GaN film was grown on the (111) silicon-on-insulator (SOI) substrate by metal-organic chemical vapor deposition and then annealed in the deposition chamber. A multiple beam optical stress sensor was used for the in-situ stress measurement, and X-ray diffraction (XRD) and Raman spectroscopy were used for the characterization of GaN film. Comparing the characterization results of the GaN films on the bulk silicon and SOI substrates, we can see that the Raman spectra show the 3.0 cm(-1) frequency shift of E-2(TO), and the full width at half maximum of XRD rocking curves for GaN (0002) decrease from 954 arc see to 472 are sec. The results show that the SOI substrates can reduce the tensile stress in the GaN film and improve the crystalline quality. The annealing process is helpful for the stress reduction of the GaN film. The SOI substrate with the thin top silicon film is more effective than the thick top silicon film SOI substrate for the stress reduction. (C) 2007 Elsevier B.V. All rights reserved.

Influence of N doping on the Rashba coefficient, semiconductor-metal transition, and electron effective mass in InSb1-xNx nanowires: Ten-band k center dot p model

The electronic structures of InSb1-xNx nanowires are investigated using the ten-band k center dot p method. It is found that nitrogen increases the Rashba coefficient of the nanowires dramatically. For thick nanowires, the Rashba coefficient may increase by more than 20 times. The semiconductor-metal transition occurs more easily in InSb1-xNx nanowires than in InSb nanowires. The electronic structure of InSb1-xNx nanowires is very different from that of the bulk material. For fixed x the bulk material is a semimetal, while the nanowires are metal-like. In InSb1-xNx bulk material and thick nanowires, an interesting decrease of electron effective mass is observed near k=0 which is induced by the nitrogen, but this phenomenon disappears in thin nanowires.

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.

Origin and elimination of spurious solutions of the eight-band k center dot p theory

The origin of spurious solutions in the eight-band envelope function model is examined and it is shown that spurious solutions arise from the additional spurious degeneracies caused by the unphysical bowing of the conduction bands calculated within the eight-band k center dot p model. We propose two approaches to eliminate these spurious solutions. Using the first approach, the wave vector cutoff method, we demonstrate the origin and elimination of spurious solutions in a transparent way without modifying the original Hamiltonian. Through the second approach, we introduce some freedom in modifying the Hamiltonian. The comparison between the results from the various modified Hamiltonians suggests that the wave vector cutoff method can give accurate enough description to the final results.

Study on the oxygen concentration reduction in heavily Sb-doped silicon

It was determined that oxygen concentration in heavily Sb-doped silicon was about 40% lower than that in the lightly doped Czochralski grown silicon and decreased with increasing content of Sb by means of coincident elastic recoil detection analysis. Through thermodynamic calculation, the oxygen loss by evaporation from the free surface of melt is only due to the formation of SiO, and Sb2O3 evaporation can be neglected. The basic reason for oxygen concentration reduction in heavily Sb-doped CZSi was that oxygen solubility decreased when element Sb with larger radius doped degenerately into silicon crystal. (C) 1999 Elsevier Science B.V. All rights reserved.

Color center conversion by femtosecond pulse laser irradiation in LiF : F-2 crystals

We report the observation of intense spontaneous emission of green light from LiF:F-2:F-3(+) centers in active channel waveguides generated in lithium fluoride crystals by near-infrared femtosecond laser radiation. While irradiating the crystal at room temperature with 405 nm light from a laser diode, yellow and green emission was seen by the naked eye. Stripe waveguides were fabricated by translating the crystal along the irradiated laser pulse, and their guiding properties and fluorescence spectra at 540 nm demonstrated. This single-step process inducing a waveguide structure offers a good prospect for the development of a waveguide laser in bulk LiF crystals.