Adaptive multiple subtraction using a constrained L1-norm method with lateral continuity

The Lt-norm method is one of the widely used matching filters for adaptive multiple subtraction. When the primaries and multiples are mixed together, the L1-norm method might damage the primaries, leading to poor lateral continuity. In this paper, we propose a constrained L1-norm method for adaptive multiple subtraction by introducing the lateral continuity constraint for the estimated primaries. We measure the lateral continuity using prediction-error filters （PEF）. We illustrate our method with the synthetic Pluto dataset. The results show that the constrained L1-norm method can simultaneously attenuate the multiples and preserve the primaries.

A NEURAL-BASED NONLINEAR L_1-NORM OPTIMIZATION ALGORITHM FOR DIAGNOSIS OF NETWORKS*

Based on exact penalty function, a new neural network for solving the L1-norm optimization problem is proposed. In comparison with Kennedy and Chua’s network(1988), it has better properties.Based on Bandler’s fault location method(1982), a new nonlinearly constrained L1-norm problem is developed. It can be solved with less computing time through only one optimization processing. The proposed neural network can be used to solve the analog diagnosis L1 problem. The validity of the proposed neural networks and the fault location L1 method are illustrated by extensive computer simulations.

ZONAL SPHERICAL POLYNOMIALS WITH MINIMAL L_1-NORM

Radial functions have become a useful tool in numerical mathematics. On the sphere they have to be identified with the zonal functions. We investigate zonal polynomials with mass concentration at the pole, in the sense of their L1-norm is attaining the minimum value. Such polynomials satisfy a complicated system of nonlinear e-quations (algebraic if the space dimension is odd, only) and also a singular differential equation of third order. The exact order of decay of the minimum value with respect to the polynomial degree is determined. By our results we can prove that some nodal systems on the sphere, which are defined by a minimum-property, are providing fundamental matrices which are diagonal-dominant or bounded with respect to the ∞-norm, at least, as the polynomial degree tends to infinity.

L_1范数支持向量机在代谢组学中的应用

代谢组学是关于生物体内源性代谢物质的整体及其变化规律的科学,也是一个数据密集型的研究领域,由此使得模式识别在代谢数据处理中有重要作用.L1范数支持向量机(L1-Norm Support Vector Machines,L1-norm SVMs)作为在模式识别领域中准确、稳健的方法,在代谢组学中的应用较少.该文应用L1-norm SVM方法对小鼠感染血吸虫后的代谢数据进行了分析,分析结果显示L1-norm SVM在聚类与特征选择方面具有优势,并表明它在代谢组学领域的应用有着潜力和前景.

基于L^(1)范数的全变分地震信号反褶积优化算法

基于借范数最优化的思想,提出一种基于L^(1)范数的全变分地震信号反褶积优化算法。该算法基于L^(1)范数全变分理论构建地震信号重建模型,同时将其转化为符合迭代与交替最小化的求解形式,通过交替方向乘子法设计地震信号的反褶积优化算法。该算法无需考虑反褶积使用的限制条件,可以在含噪声的情况下有效恢复地震信号,同时提高地震信号的分辨率和信噪比。使用该算法对合成信号和野外采集地震数据进行实验,结果表明:该算法提高了子波的主频,拓宽了有效频带,即使在信号受到较重噪声污染时,也可以获得较好的处理结果。

Bearings Intelligent Fault Diagnosis by 1-D Adder Neural Networks

Integrated with sensors,processors,and radio frequency(RF)communication modules,intelligent bearing could achieve the autonomous perception and autonomous decision-making,guarantying the safety and reliability during their use.However,because of the resource limitations of the end device,processors in the intelligent bearing are unable to carry the computational load of deep learning models like convolutional neural network(CNN),which involves a great amount of multiplicative operations.To minimize the computation cost of the conventional CNN,based on the idea of AdderNet,a 1-D adder neural network with a wide first-layer kernel(WAddNN)suitable for bearing fault diagnosis is proposed in this paper.The proposed method uses the l1-norm distance between filters and input features as the output response,thus making the whole network almost free of multiplicative operations.The whole model takes the original signal as the input,uses a wide kernel in the first adder layer to extract features and suppress the high frequency noise,and then uses two layers of small kernels for nonlinear mapping.Through experimental comparison with CNN models of the same structure,WAddNN is able to achieve a similar accuracy as CNN models with significantly reduced computational cost.The proposed model provides a new fault diagnosis method for intelligent bearings with limited resources.

基于Curvelet变换的稀疏反褶积

常规反褶积方法通常需要假设地层反射系数是稀疏的,然后再利用L1范数反褶积求得稀疏的反射系数来提高分辨率,但常规反褶积方法在提高分辨率的同时降低了信噪比,并且反褶积后同相轴的连续性会变差。针对上述问题,提出了基于Curvelet变换的反褶积方法。Curvelet变换对多维信号具有最好的稀疏表示,能获得最优的非线性逼近,因而可利用Curvelet变换来表示地震反射信号,将其引入到L1范数反褶积后,可利用稀疏的Curvelet系数来描述反射系数,从而无需地层反射信号是稀疏的假设。根据有效信号和随机噪声在Curvelet域中的分布特点,可通过阈值法来压制噪声提高信噪比,并且利用Curvelet变换对地震信号进行多维表示,可实现多维反褶积保持同相轴的连续性。最后,给出了一种阈值循环迭代算法来计算L1范数反褶积问题。研究结果表明,基于Curvelet变换的稀疏反褶积方法在提高地震分辨率的同时能有效地压制随机噪声,并保持同相轴的连续性。

基于0-1规划的规则中文文件碎片自动拼接技术

为了实现规则中文文件碎片的拼接,研究了规则碎片文件中汉字文本的特征,提出了文件碎片中文本行信息的提取方法,定义了基于L1-norm的碎片边界差异度概念,建立了基于0-1规划的文件碎片拼接模型,并运用聚类分析降低了算法复杂度.与现有同类算法相比,本文的算法无需使用人工干预即可完成正确拼接.

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

Joint 2D DOA and Doppler frequency estimation for L-shaped array using compressive sensing

A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.

Statistical Classification Using the Maximum Function

The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.

Association RuleMining Frequent-Pattern-Based Intrusion Detection in Network

In the network security system,intrusion detection plays a significant role.The network security system detects the malicious actions in the network and also conforms the availability,integrity and confidentiality of data informa-tion resources.Intrusion identification system can easily detect the false positive alerts.If large number of false positive alerts are created then it makes intrusion detection system as difficult to differentiate the false positive alerts from genuine attacks.Many research works have been done.The issues in the existing algo-rithms are more memory space and need more time to execute the transactions of records.This paper proposes a novel framework of network security Intrusion Detection System(IDS)using Modified Frequent Pattern(MFP-Tree)via K-means algorithm.The accuracy rate of Modified Frequent Pattern Tree(MFPT)-K means method infinding the various attacks are Normal 94.89%,for DoS based attack 98.34%,for User to Root(U2R)attacks got 96.73%,Remote to Local(R2L)got 95.89%and Probe attack got 92.67%and is optimal when it is compared with other existing algorithms of K-Means and APRIORI.

Blind Deblurring Based on L_0 Norm from Salient Edges

Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.

L_1-norm packings from function fields

In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L1-norm which is analogous to the Hamming distance in coding theory. Two constructions with reasonable parameters are obtained, by using some results from a function field including divisor class group, narrow ray class group, and so on. We also present some asymptotic results of the two packings.

ROBUST NONPARAMETRIC REGRESSION BASED ON L_1-NORM AND B-SPLINES

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ASYMPTOTICS OF THE “MINIMUM L_1-NORM”ESTIMATES IN A PARTLY LINEAR MODEL

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Learning robust principal components from L1-norm maximization

Principal component analysis(PCA) is fundamental in many pattern recognition applications.Much research has been performed to minimize the reconstruction error in L1-norm based reconstruction error minimization(L1-PCA-REM) since conventional L2-norm based PCA(L2-PCA) is sensitive to outliers.Recently,the variance maximization formulation of PCA with L1-norm(L1-PCA-VM) has been proposed,where new greedy and nongreedy solutions are developed.Armed with the gradient ascent perspective for optimization,we show that the L1-PCA-VM formulation is problematic in learning principal components and that only a greedy solution can achieve robustness motivation,which are verified by experiments on synthetic and real-world datasets.

Asymptotics of the“Minimum L_1-Norm”Estimates in Nonparametric Regression Models

Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m（m≥0）times continuously differentiable and its ruth derivative,g0（m）,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L1- norm estimator of go is proposed.Under some regularity conditions including that the random errors are independent but not necessarily have a common distribution,it is proved that the rates of convergence of the piecewise polynomial L1-norm estimator are o(n-2（m+γ）+1/m+γ-1/δalmost surely and o(n-2（m+γ）+1/m+γ-δ)in probability,which can arbitrarily approach the optimal rates of convergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））.

EQUIVALENCE BETWEEN NONNEGATIVE SOLUTIONS TO PARTIAL SPARSE AND WEIGHTED l_1-NORM MINIMIZATIONS

Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.

基于特征选择和点互信息剪枝的产品属性提取方法

产品属性的自动抽取是情感分析中的重要研究内容.文中提出一种基于特征选择和词频及点互信息剪枝的产品属性提取方法.首先引入在分类任务中常用的l1-norm正则化(Lasso)方法,将产品属性抽取问题转换为分类中的特征选择问题,利用Lasso生成稀疏模型的特性,将模型中少量的特征作为产品特征属性候选集.然后根据候选特征属性集中的特征属性在文本中出现的频率进行排序并剪枝.最后经过进一步合并和点互信息剪枝处理,得到最终的产品属性集.在中文产品评论集上的实验证实文中方法的有效性.