A framework for classification with single feature kernel matrix

In this paper, we propose a novel classification framework using single feature kernel matrix. Different from the traditional kernel matrices which make use of the whole features of samples to build the kernel matrix, this research uses features of the same dimension of any two samples to build a sub-kernel matrix and sums up all the sub-kernel matrices to get the single feature kernel matrix. We also use single feature kernel matrix to build a new SVM classifier, and adapt SMO (Sequential Minimal Optimization) algorithm to solve the problem of SVM classifier. The results of the experiments on several artificial datasets and some challenging public cancer datasets display the classification performance of the algorithm. The comparisons between our algorithm and L₂-norm SVM on the cancer datasets demonstrate that the accuracy of our algorithm is higher, and the number of support vectors selected is fewer, indicating that our proposed framework is a more practical approach.     

基于可见光光谱高效鉴别玉米单倍体籽粒

单倍体技术已发展成为玉米遗传研究及现代玉米育种的重要技术之一,单倍体籽粒的鉴别筛选是其中的重要环节。目前单倍体籽粒主要是依赖于籽粒的R1-nj遗传标记通过人工肉眼观察颜色的有或无进行鉴别,费时费工。而且部分材料由于标记颜色很难从籽粒外部观察到,导致人工筛选准确率较低。基于可见光光谱分析建立玉米单倍体籽粒鉴别方法,探索利用可见光光谱鉴别玉米单倍体籽粒的可行性。同时,由于每季用于诱导单倍体的育种材料不尽相同,模型须能够鉴别未参加建模的材料的单倍体。本研究以9个遗传背景的单倍体和杂交籽粒共284粒作为试验材料,利用便携式紫外-可见光光纤光谱仪采集单个玉米籽粒的可见光漫透射光谱。光谱数据经平滑、矢量归一化预处理和主成分分析,基于支持向量机方法建立单倍体和杂交籽粒判别模型。每次选择1个背景的样本作为测试集,其余背景的样本作为建模集对模型进行交叉验证。模型交叉验证平均正确判别率达到92.06%。其中8次测试正确判别率在85%以上。结果表明利用可见光光谱分析建立玉米单倍体籽粒鉴别方法,并使模型可鉴别未参与建模材料的单倍体具有可行性。并且基于该方法有望建立玉米单倍体籽粒的自动化快速筛选系统,提高玉米单倍体育种效率。     

光谱特征波长的SPA选取和基于SVM的玉米颗粒霉变程度定性判别

利用波长范围在833～2 500 nm的傅里叶变换近红外光谱(Fourier transform near infrared spectroscopy, FT-NIR)对不同霉变程度的玉米颗粒进行检测区分。首先,为避免光谱数据首尾噪声影响,对比四种常见的预处理方法,最终选择移动平均平滑法对原始光谱数据进行预处理;然后为选出合适的样本集划分方法以提高模型预测性能,对常见的四种方法进行对比,最终利用SPXY(sample set partitioning based on joint x-y distance)法进行样本集划分;进一步为减少数据量,降低维度,使用连续投影算法(successive projections algorithm, SPA)提取出7个特征波长,分别为833,927,1 208,1 337,1 454,1 861和2 280 nm;最后,将七个特征波长数据作为输入,选取径向基函数(radial basis function, RBF)作为支持向量机(support vector machine, SVM)核函数,取参数C=7 760 469,γ=0.017 003建立判别模型。SVM模型对训练集和测试集的预测准确率分别达到97.78%和93.33%。另取不同品种的玉米颗粒,以同样的标准挑选样品组成独立验证集,所建立的判别模型对独立验证集的预测准确率达到91.11%。结果表明基于SPA和SVM能有效地对玉米颗粒霉变程度进行判别,所选取的7个特征波长为实现在线霉变玉米颗粒近红外检测提供了理论依据。     

3D MR image denoising using rough set and kernel PCA method

In this paper, we have presented a two stage method, using kernel principal component analysis (KPCA) and rough set theory (RST), for denoising volumetric MRI data. A rough set theory (RST) based clustering technique has been used for voxel based processing. The method groups similar voxels (3D cubes) using class and edge information derived from noisy input. Each clusters thus formed now represented via basis vector. These vectors now projected into kernel space and PCA is performed in the feature space. This work is motivated by idea that under Rician noise MRI data may be non-linear and kernel mapping will help to define linear separator between these clusters/basis vectors thus used for image denoising. We have further investigated various kernels for Rician noise for different noise levels. The best kernel is then selected on the performance basis over PSNR and structure similarity (SSIM) measures. The work has been compared with state-of-the-art methods under various measures for synthetic and real databases.     

Approximate Bayesian Computation for Discrete Spaces

Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.     

An interacting particle model with compact hierarchical structure

We present a model interacting particle system with a population of fixed size in which particles wander randomly in space, and pairs interact at a rate determined by a reaction kernel with finite range. The pairwise interaction randomly selects one of the particles (the victim) and instantly transfers it to the position of the other (the killer), thus maintaining the total number. The special feature of the model is that it possesses a closed hierarchical structure in which the statistical moments of the governing master equation lead to closed equations for the reduced distribution functions (the concentration, pair correlation function, and so on). In one spatial dimension, we show that persistent spatial correlations (clusters) arise in this model and we characterize the dynamics in terms of analytical properties of the pair correlation function. As the range of the reaction kernel is increased, the dynamics varies from an ensemble of largely independent random walkers at small range to tightly bound clusters with longer-range reaction kernels.     

高光谱最优波长选择及Fisher判别分析法判别玉米颗粒表面黄曲霉毒素

黄曲霉毒素是广泛存在于玉米中且具有剧毒的一种代谢产物,以美国农业部农业研究署(USDA-ARS) Toxicology and Mycotoxin Research Unit提供的2010年先锋玉米为研究对象,验证了高光谱成像技术对玉米中黄曲霉毒素检测的可行性。以甲醇为溶剂制备四种不同浓度的黄曲霉毒素溶液,并将其逐一滴在等量的4组共120粒玉米颗粒表面,以未处理的30粒洁净玉米作为一组对照样本,将大小、形状相似的150个样品随机分为训练集103个,验证集47个;对获取的400～1 000 nm波段范围内的高光谱图像,先进行标准正态变量变换(standard normal variate transformation, SNV)预处理,然后引入基于Fisher判别最小误判率的方法选择最优波长,并以所选波长作为Fisher判别分析法的输入建立判别模型,对玉米颗粒表面不同浓度的黄曲霉毒素进行识别,最后对模型判别正确率进行了验证。结果表明,选取四个最优波长(812.42, 873.00, 900.36和965.00 nm)时Fisher判别分析模型对训练集与验证集的准确率分别为87.4%和80.9%。该方法为含黄曲霉毒素玉米颗粒便携式检测仪器的开发,以及对田间霉变玉米自然代谢产生毒素的检测奠定了技术基础。     

Kernel-aligned multi-view canonical correlation analysis for image recognition

Existing kernel-based correlation analysis methods mainly adopt a single kernel in each view. However, only a single kernel is usually insufficient to characterize nonlinear distribution information of a view. To solve the problem, we transform each original feature vector into a 2-dimensional feature matrix by means of kernel alignment, and then propose a novel kernel-aligned multi-view canonical correlation analysis (KAMCCA) method on the basis of the feature matrices. Our proposed method can simultaneously employ multiple kernels to better capture the nonlinear distribution information of each view, so that correlation features learned by KAMCCA can have well discriminating power in real-world image recognition. Extensive experiments are designed on five real-world image datasets, including NIR face images, thermal face images, visible face images, handwritten digit images, and object images. Promising experimental results on the datasets have manifested the effectiveness of our proposed method.     

基于近红外高光谱成像技术的小麦不完善粒检测方法研究

小麦作为主要的粮食作物在我国农业生产、运输、食品加工等方面占有重要地位。不完善籽粒严重影响了小麦质量与粮食安全。不完善籽粒主要在生产、存储、包装等过程中产生，目前我国小麦质量检测多以人工分选为主，但存在人主观性较强，肉眼易疲劳，且费时费力等问题，因此，如何快速准确鉴别小麦不完善粒是现阶段提高生产率和保证粮食安全的重要问题。运用高光谱成像技术和特征波段选取方法提出一种快速有效的小麦不完善粒鉴别方法。利用近红外高光谱成像系统获得1 000粒小麦样本在862.9～1 704.2 nm共256个波段的高光谱反射图像，其中包括健康粒、生芽粒、霉变粒和赤霉粒各250粒，提取每个样本感兴趣区域的平均反射率光谱作为分类特征。本文首先对提取的全波段光谱信息进行窗口平滑、一阶导数差分、矢量归一化等数据预处理，将原始光谱数据的隐藏信号放大并消除随机误差；在预处理的基础上运用伪偏最小二乘(DPLS)和正交化线性判别分析(OLDA)对光谱进行特征提取，降低数据的冗余度；最后采用仿生模式识别(BPR)建立四类小麦的鉴别模型。实验结果表明，采用全波段光谱信息建立的小麦不完善粒鉴别模型的平均识别精度达到97.8%，分析结果可知，利用近红外高光谱成像技术的全波段光谱信息对小麦不完善粒鉴别是可行的。尽管全波段光谱信息取得了较好的鉴别效果，但高光谱成像设备较为昂贵，获取高光谱全波段光谱信息数据量较大，无法满足对现场设备运算速度的高要求，因此，采用连续投影算法(SPA)对全波段光谱数据进行特征波段的选择，使波段数量由256维降低到10维，从而提高系统的可行性和运算速度。采用选取的10个特征波段建立小麦不完善粒鉴别模型，实验结果表明10个特征波段的平均识别精度仅为83.2%，分析结果可知，尽管采用10个特征波段提高了系统实时性，但鉴别准确性较差。为达到与全波段特征基本相当的鉴别效果，利用光谱特征与图像特征结合的方法建立小麦不完善粒鉴别模型，将上述选取的10个特征波段的形态信息、纹理信息和光谱信息进行结合，实验结果表明，10个特征波段的光谱信息与图像信息结合使鉴别的平均识别精度达到94.2%，此识别效果与利用全波段光谱数据的识别效果基本相当。利用高光谱成像系统探索了小麦不完善粒鉴别的可行性，通过分析以上实验可知，基于近红外高光谱成像技术对小麦不完善粒检测具有良好的效果，在有效的提高运算速度的同时也保证了系统的鉴别精度，为后期小麦不完善粒快速检测设备的开发提供了有效的研究方向。     

A study of the spatial and temporal evolution of auto-ignition kernels using time-resolved tomographic OH-LIF

In this paper, the spatial and temporal evolution of auto-ignition kernels from methane jets propagating into a NO_x-vitiated, high-turbulence, hot air co-flow was studied by means of time-resolved tomographic laser-induced fluorescence of OH (Tomo OH-LIF). Measurements were performed using a burst dye laser system at 10 kHz for volumetric laser illumination and a multi-camera arrangement (8-views) for detection of the fluorescence signal. Auto-ignition kernels were detected three-dimensionally and tracked using a robust algorithm based on the intensity gradient of the volumetrically reconstructed signals. The size and location of the detected kernels were evaluated for operating conditions with different Reynolds numbers of the fuel jet. Results showed that auto-ignition randomly occurred with high probability in a well defined fairly axisymmetric radial region with strong fluctuations in the main direction of the flow. The increase of the Reynolds number of the fuel jet resulted in a radial spread of the location of auto-ignition events. The statistical evaluation of the orientation and growth of auto-ignition kernels with respect to the mean flow field showed that the kernels were oriented tangentially to the flow and temporally evolve towards this preferential direction as the ignition events progressed.     

On the Relation Between Orthogonal,Symplectic and Unitary Matrix Ensembles

For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations     

Local vertex corrections from exchange-correlation kernels with a discontinuity

The fundamental gap of an interacting many-electron system is given by the sum of the single-particle Kohn-Sham gap and the derivative discontinuity. The latter can be generated by advanced approximations to the exchange-correlation (XC) energy and is the key quantity to capture strong correlation with density functional theory (DFT). In this work we derive an expression for the derivative discontinuity in terms of the XC kernel of time-dependent density functional theory and demonstrate the crucial role of a discontinuity in the XC kernel itself. By relating approximate XC kernels to approximate local vertex corrections we then generate beyond-GW self-energies that include a discontinuity in the local vertex function. The quantitative importance of this result is illustrated with a numerical study of the local exchange vertex on model systems.     

An action function for a higher step Grushin operator

The purpose of this paper is to discuss how we can construct the heat kernel for (sub)-Laplacian in an explicit (integral) form in terms of a certain class of special functions. Of course, such cases will be highly limited. Here we only treat a typical operator, called Grushin operator. So, first we explain two methods to construct the heat kernel of a “step 2” Grushin operator. One is the eigenfunction expansion which leads to an integral form for the heat kernel, then we treat the formula by a method called, complex Hamilton–Jacobi method invented by Beals–Gaveau–Greiner. One of the main result in this paper is to construct an action function for a higher order oscillator. Until now, no explicit expression of the heat kernel for higher order cases have been given in an explicit form and we show a phenomenon that our action function will play a role toward the construction of the heat kernel of higher step Grushin operators.     

基于可见光谱和支持向量机的黄瓜叶部病害识别方法研究

以黄瓜叶部病害作为研究对象,基于可见光谱反射率差异识别黄瓜叶部病害,研究基于SVM的黄瓜叶部病害识别预测模型。采用小波变换进行数据预处理;选取Otsu、边缘分割法和K均值聚类三类分割方法进行病斑分割,比较错分率和运行时间,K均值聚类方法更适合黄瓜叶部病斑分割;提取纹理、颜色和形状特征参数,共15个特征参数;通过交叉验证选择最优参数c和g,对核函数参数进行优化处理,并通过比较线性核、多项式核、RBF核等不同核函数情况下SVM的正确识别率,确定RBF核SVM模式识别方法能够更精准地识别黄瓜叶部病害。并将基于SVM与另外两种常见的黄瓜叶部病害识别方法,BP神经网络和模糊聚类进行比较,结果表明,基于SVM的识别模型对霜霉病的正确识别率为95%,白粉病和褐斑病的正确识别率均为90%,平均诊断正确率为92%;该模式识别方法识别效果最佳,运行时间最短,为基于可见光谱的黄瓜病害识别模型提供参考。     

Free Fermions and the Classical Compact Groups

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.     

Convective motion and transfer of force by many-body hydrodynamic interaction

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. When the bodies are carried along by an incident flow without exerting forces or torques on the fluid then their translational and rotational velocities are linearly related to the incident flow velocity by convection kernels. In the absence of an incident flow, but with applied forces and torques, the force density acting on the fluid is linearly related to the forces and torques by transfer kernels. We show that the convection and transfer kernels are simply related by a symmetry relation. For freely moving bodies the force density exerted on the fluid is related to the incident flow by a convective friction kernel. We show that this kernel is symmetric.