HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction

Most methods for dimensionality reduction are based on either tensor representation or local geometry learning. However, the tensor-based methods severely rely on the assumption of global and multilinear structures in high-dimensional data; and the manifold learning methods suffer from the out-of-sample problem. In this paper, bridging the tensor decomposition and manifold learning, we propose a novel method, called Hypergraph Regularized Nonnegative Tensor Factorization (HyperNTF). HyperNTF can preserve nonnegativity in tensor factorization, and uncover the higher-order relationship among the nearest neighborhoods. Clustering analysis with HyperNTF has low computation and storage costs. The experiments on four synthetic data show a desirable property of hypergraph in uncovering the high-order correlation to unfold the curved manifolds. Moreover, the numerical experiments on six real datasets suggest that HyperNTF robustly outperforms state-of-the-art algorithms in clustering analysis.Comment: 12 pages, 6 figures, 9 table

HSIC Regularized LTSA

Hilbert-Schmidt Independence Criterion (HSIC) measures statistical independence between two random variables. However, instead of measuring the statistical independence between two random variables directly, HSIC first transforms two random variables into two Reproducing Kernel Hilbert Spaces (RKHS) respectively and then measures the kernelled random variables by using Hilbert-Schmidt (HS) operators between the two RKHS. Since HSIC was first proposed around 2005, HSIC has found wide applications in machine learning. In this paper, a HSIC regularized Local Tangent Space Alignment algorithm (HSIC-LTSA) is proposed. LTSA is a well-known dimensionality reduction algorithm for local homeomorphism preservation. In HSIC-LTSA, behind the objective function of LTSA, HSIC between high-dimensional and dimension-reduced data is added as a regularization term. The proposed HSIC-LTSA has two contributions. First, HSIC-LTSA implements local homeomorphism preservation and global statistical correlation during dimensionality reduction. Secondly, HSIC-LTSA proposes a new way to apply HSIC: HSIC is used as a regularization term to be added to other machine learning algorithms. The experimental results presented in this paper show that HSIC-LTSA can achieve better performance than the original LTSA

A Multikernel-Like Learning Algorithm Based on Data Probability Distribution

In the machine learning based on kernel tricks, people often put one variable of a kernel function on the given samples to produce the basic functions of a solution space of learning problem. If the collection of the given samples deviates from the data distribution, the solution space spanned by these basic functions will also deviate from the real solution space of learning problem. In this paper a multikernel-like learning algorithm based on data probability distribution (MKDPD) is proposed, in which the parameters of a kernel function are locally adjusted according to the data probability distribution, and thus produces different kernel functions. These different kernel functions will generate different Reproducing Kernel Hilbert Spaces (RKHS). The direct sum of the subspaces of these RKHS constitutes the solution space of learning problem. Furthermore, based on the proposed MKDPD algorithm, a new algorithm for labeling new coming data is proposed, in which the basic functions are retrained according to the new coming data, while the coefficients of the retrained basic functions remained unchanged to label the new coming data. The experimental results presented in this paper show the effectiveness of the proposed algorithms

Generation of femtosecond γ-ray bursts stimulated by laser-driven hosing evolution

The promising ability of a plasma wiggler based on laser wakefield acceleration to produce betatron X-rays with photon energies of a few keV to hundreds of keV and a peak brilliance of 1022-1023 photons/s/mm2 /mrad2 /0.1%BW has been demonstrated, providing an alternative to large-scale synchrotron light sources. Most methods for generating betatron radiation are based on two typical approaches, one relying on an inherent transverse focusing electrostatic field, which induces transverse oscillation, and the other relying on the electron beam catching up with the rear part of the laser pulse, which results in strong electron resonance. Here, we present a new regime of betatron γ-ray radiation generated by stimulating a large-amplitude transverse oscillation of a continuously injected electron bunch through the hosing of the bubble induced by the carrier envelope phase (CEP) effect of the self-steepened laser pulse. Our method increases the critical photon energy to the MeV level, according to the results of particle-in-cell (PIC) simulations. The highly collimated, energetic and femtosecond γ-ray bursts that are produced in this way may provide an interesting potential means of exploring nuclear physics in table top photo nuclear reactions

Directional enhancement of selected high-order-harmonics from intense laser irradiated blazed grating targets

Relativistically intense laser solid target interaction has been proved to be a promising way to generate high-order harmonics, which can be used to diagnose ultrafast phenomena. However, their emission direction and spectra still lack tunability. Based upon two-dimensional particle-in-cell simulations, we show that directional enhancement of selected high-order-harmonics can be realized using blazed grating targets. Such targets can select harmonics with frequencies being integer times of the grating frequency. Meanwhile, the radiation intensity and emission area of the harmonics are increased. The emission direction is controlled by tailoring the local blazed structure. Theoretical and electron dynamics analysis for harmonics generation, selection and directional enhancement from the interaction between multi-cycle laser and grating target are carried out. These studies will benefit the generation and application of laser plasma-based high order harmonics

Control of laser light by a plasma immersed in a tunable strong magnetic field

The interaction between laser light and an underdense plasma immersed in a spatio-temporally tunable magnetic field is studied analytically and numerically. The transversely nonuniform magnetic field can serve as a magnetic channel, which can act on laser propagation in a similar way to the density channel. The envelope equation for laser intensity evolution is derived, which contains the effects of magnetic channel and relativistic self-focusing. Due to the magnetic field applied, the critical laser power for relativistic self-focusing can be significantly reduced. Theory and particle-in-cell simulations show that a weakly relativistic laser pulse can propagate with a nearly constant peak intensity along the magnetic channel for a distance much longer than its Rayleigh length. By setting the magnetic field tunable in both space and time, the simulation further shows that the magnetized plasma can then act as a lens of varying focal length to control the movement of laser focal spot, decoupling the laser group velocity from the light speed c in vacuum

A two-dimensional angular-resolved proton spectrometer

We present a novel design of two-dimensional (2D) angular-resolved spectrometer for full beam characterization of ultrashort intense laser driven proton sources. A rotated 2D pinhole array was employed, as selective entrance before a pair of parallel permanent magnets, to sample the full proton beam into discrete beamlets. The proton beamlets are subsequently dispersed without overlapping onto a planar detector. Representative experimental result of protons generated from femtosecond intense laser interaction with thin foil target is presented

Ultrahigh-charge electron beams from laser-irradiated solid surface

Compact acceleration of a tightly collimated relativistic electron beam with high charge from a laser–plasma interaction has many unique applications. However, currently the well-known schemes, including laser wakefield acceleration from gases and vacuum laser acceleration from solids, often produce electron beams either with low charge or with large divergence angles. In this work, we report the generation of highly collimated electron beams with a divergence angle of a few degrees, nonthermal spectra peaked at the megaelectronvolt level, and extremely high charge (∼100 nC) via a powerful subpicosecond laser pulse interacting with a solid target in grazing incidence. Particle-in-cell simulations illustrate a direct laser acceleration scenario, in which the self-filamentation is triggered in a large-scale near–critical-density plasma and electron bunches are accelerated periodically and collimated by the ultraintense electromagnetic field. The energy density of such electron beams in high-Z materials reaches to ∼1012 J/m3, making it a promising tool to drive warm or even hot dense matter states