Blind source separation by weighted K-means clustering

Blind separation of sparse sources （BSSS） is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x（t） with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.

基于改进的Weighted K-Means聚类的外卖员接单区域划分问题研究

外卖行业蓬勃发展,人们对于外卖服务质量的要求也不断提升。因外卖员接单区域基本固定,合理划分外卖员负责区域并分配每个区域外卖员人数成为提升效率的关键。本项目基于查询算法模型,分析上海市2017年某时段的外卖数据,试图得到一个对于外卖接单区域的较为合理的划分标准并给出该划分。K-Means是一种常见的划分聚类算法,是在集中式系统框架无法对海量数据进行处理分析的基础上提出的。然而对于有权重的二维点集无法使用K-Means聚类算法,因此研究一种改进的Weighted K-Means算法显得尤为必要。本项目定义带权质心和带权距离,提出了新的Weighted K-Means算法,并使用改进前后的两种方法处理上海市外卖接单信息,给出合理可行的外卖员接单区域划分。对比两种方法的结果,改进的Weighted K-Means不仅方法可行,区域划分表现也更优秀。与此同时,使用该方法对外卖接单区域进行新的划分,有助于优化现有外卖模式、提升外卖效率以及顾客满意度。

基于kernel K-means算法的城市交通客流量分析

基于核函数这种基于统计学习理论的方法,介绍了kernel K-means算法的基本原理与步骤,与传统的K-means算法进行了对比分析,无论是运算速度还是算法有效性,kernel K-means算法都优于传统的K-means算法,并应用于实际的城市交通客流量数据分析实验,结果验证了方法的有效性,为城市交通规律分析、城市规划与交通政策的制定提供了依据。

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L^q , L^p )~α (R^n) Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.

Commutators of Weighted Lipschitz Functions and Multilinear Singular Integrals with Non-Smooth Kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.

LKAW: A Robust Watermarking Method Based on Large Kernel Convolution and Adaptive Weight Assignment

Robust watermarking requires finding invariant features under multiple attacks to ensure correct extraction.Deep learning has extremely powerful in extracting features,and watermarking algorithms based on deep learning have attracted widespread attention.Most existing methods use 3×3 small kernel convolution to extract image features and embed the watermarking.However,the effective perception fields for small kernel convolution are extremely confined,so the pixels that each watermarking can affect are restricted,thus limiting the performance of the watermarking.To address these problems,we propose a watermarking network based on large kernel convolution and adaptive weight assignment for loss functions.It uses large-kernel depth-wise convolution to extract features for learning large-scale image information and subsequently projects the watermarking into a highdimensional space by 1×1 convolution to achieve adaptability in the channel dimension.Subsequently,the modification of the embedded watermarking on the cover image is extended to more pixels.Because the magnitude and convergence rates of each loss function are different,an adaptive loss weight assignment strategy is proposed to make theweights participate in the network training together and adjust theweight dynamically.Further,a high-frequency wavelet loss is proposed,by which the watermarking is restricted to only the low-frequency wavelet sub-bands,thereby enhancing the robustness of watermarking against image compression.The experimental results show that the peak signal-to-noise ratio(PSNR)of the encoded image reaches 40.12,the structural similarity(SSIM)reaches 0.9721,and the watermarking has good robustness against various types of noise.

Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces

Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.

Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces

Let T be the singular integral operator with variable kernel, T＊ be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator D^γ on the weighted Morrey spaces.

The cytosolic isoform of triosephosphate isomerase,ZmTPI4,is required for kernel development and starch synthesis in maize(Zea mays L.)

Triosephosphate isomerase(TPI)is an enzyme that functions in plant energy production,accumulation,and conversion.To understand its function in maize,we characterized a maize TPI mutant,zmtpi4.In comparison to the wild type,zmtpi4 mutants showed altered ear development,reduced kernel weight and starch content,modified starch granule morphology,and altered amylose and amylopectin content.Protein,ATP,and pyruvate contents were reduced,indicating ZmTPI4 was involved in glycolysis.Although subcellular localization confirmed ZmTPI4 as a cytosolic rather than a plastid isoform of TPI,the zmtpi4 mutant showed reduced leaf size and chlorophyll content.Overexpression of ZmTPI4 in Arabidopsis led to enlarged leaves and increased seed weight,suggesting a positive regulatory role of ZmTPI4 in kernel weight and starch content.We conclude that ZmTPI4 functions in maize kernel development,starch synthesis,glycolysis,and photosynthesis.

Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space

Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 ＋ T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space.

Weighted estimates for strongly singular integral operators with rough kernels

The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.

基于函数型数据分析和k-means算法的电力用户分类（英文）

为了对大量电力用户的稀疏、不规律的日耗电量数据进行特征分析,并对用户进行分类,文章提出一种函数性数据聚类分析方法。首先,应用kernel方法将离散的电量数据还原成连续曲线;然后,受Sobolev空间距离的启发,定义了新的函数距离,用于k-means算法进行聚类。以某城市10 000户居民538天的实际用电数据进行实验,得到了用户在不同距离和聚类个数下的聚类原型。实验结果显示,由于选取的用户主要是城市居民,其用电模式比较相似:大高峰时段主要在6—9月,小高峰时段主要在1—2月,日消耗波动较小。而不同用户类别的主要区别体现在用电量的范围上:低耗电用户整体低于13 k W?h/天,高耗电用户接近100 k W?h/天。

求解大规模谱聚类的近似加权核k-means算法

谱聚类将聚类问题转化成图划分问题,是一种基于代数图论的聚类方法.在求解图划分目标函数时,一般利用Rayleigh熵的性质,通过计算Laplacian矩阵的特征向量将原始数据点映射到一个低维的特征空间中,再进行聚类.然而在谱聚类过程中,存储相似矩阵的空间复杂度是O(n2),对Laplacian矩阵特征分解的时间复杂度一般为O(n3),这样的复杂度在处理大规模数据时是无法接受的.理论证明,Normalized Cut图聚类与加权核k-means都等价于矩阵迹的最大化问题.因此,可以用加权核k-means算法来优化Normalized Cut的目标函数,这就避免了对Laplacian矩阵特征分解.不过,加权核k-means算法需要计算核矩阵,其空间复杂度依然是O(n2).为了应对这一挑战,提出近似加权核k-means算法,仅使用核矩阵的一部分来求解大数据的谱聚类问题.理论分析和实验对比表明,近似加权核k-means的聚类表现与加权核k-means算法是相似的,但是极大地减小了时间和空间复杂性.

一种基于抽样改进加权核K-means的大数据谱聚类算法

经典谱聚类将数据聚类转化为加权图划分问题,在分析Normalized Cut目标函数与加权核K-means函数等价基础上,设计了一种基于抽样改进加权核K-means算法的大规模数据谱聚类算法。算法通过Leaders进行初始聚类预处理,以控制后续随机抽样的数据规模及对原始数据类别的覆盖,通过抽样子集内加权核K-means迭代优化,避免Laplacian矩阵特征分解的大量资源占用,从而以部分核矩阵的使用避免全部核矩的时间、空间复杂度。试验结果表明,改进算法在保持与经典算法相近聚类精度基础上,大幅提高了聚类效率。

一种基于D^2权重的核k-means聚类算法

核k-means算法是标准k-means算法的扩展,提高了k-means聚类中对非线性不可分数据的聚类效果.传统核k-means算法的初始中心是随机选取的,导致出现聚类时间较慢、聚类性能低等问题.文中提出了一种基于D2权重的核k-means算法,它根据点对簇内距离的贡献,选取对其贡献最大的点为簇中心,然后在核空间内进行相应的聚类.在UCI数据集上进行实验,实验结果表明,新算法相对于传统的核k-means算法,可以有效地缩短聚类时间,并提高聚类的质量,新算法性能优于传统的核K-means算法.

Maize kernel weight responses to sowing dateassociated variation in weather conditions

Variation in weather conditions during grain filling has substantial effects on maize kernel weight(KW). The objective of this work was to characterize variation in KW with sowing date-associated weather conditions and examine the relationship between KW, grain filling parameters, and weather factors. Maize was sown on eight sowing dates(SD) at 15–20-day intervals from mid-March to mid-July during 2012 and 2013 in the North China Plain. With sowing date delay, KW increased initially and later declined, and the greatest KW was obtained at SD6 in both years. The increased KW at SD6 was attributed mainly to kernel growth rate(Gmean), and effective grain-filling period(P). Variations in temperature and radiation were the primary factors that influenced KW and grain-filling parameters. When the effective cumulative temperature(AT) and radiation(Ra)during grain filling were 950 °C and 1005.4 MJ m-2, respectively, P and KW were greatest. High temperatures(daily maximum temperature [Tmax] > 30.2 °C) during grain filling under early sowing conditions, or low temperatures(daily minimum temperature [Tmin] < 20.7 °C) under late sowing conditions combined with high diurnal temperature range(Tmax-min> 7.1 °C) decreased kernel growth rate and ultimately final KW. When sowing was performed from May 25 through June 27, higher KW and yield of maize were obtained. We conclude that variations in environmental conditions(temperature and radiation) during grain filling markedly affect growth rate and duration of grain filling and eventually affect kernel weight and yield of maize.

优化加权核K-means聚类初始中心点的SLIC算法

超像素是近年来快速发展的一种图像预处理技术,被广泛应用于计算机视觉领域。简单线性迭代聚类(simple linear iterative clustering,SLIC)算法是其中的一种图像预处理技术框架,该算法根据像素的颜色和距离特征进行聚类来实现良好的分割结果。然而,SLIC算法尚存在一些问题。基于优化加权核K-means聚类初始中心点,提出一种新的SLIC算法(WKK-SLIC算法)。算法基于图像像素之间的颜色相似性和空间相似性度量,采用超像素分割的归一化割公式,使用核函数来近似相似性度量。算法将像素值和坐标映射到高维特征空间中,通过对该特征空间中的每个点赋予适当的权重,使加权K均值和归一化割的目标函数的优化在数学上等价。从而通过在所提出的特征空间中迭代地应用简单的K-means聚类来优化归一化割的目标函数。在WKK-SLIC算法中,采用密度敏感的相似性度量计算空间像素点的密度,启发式地生成K-means聚类的初始中心以达到稳定的聚类结果。实验结果表明,WKK-SLIC算法在评估超像素分割的几个标准上优于SLIC算法。

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.

Weighted boundedness of some integral operators on weighted λ-central Morrey space

In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given.

An Improved Kernel K-Mean Cluster Method and Its Application in Fault Diagnosis of Roller Bearing

For the kernel K-mean cluster method is run in an implicit feature space, the initial and iterative cluster centers cannot be defined explicitly. Against the deficiency of the initial cluster centers selected in the original space discretionarily in the existing methods, this paper proposes a new method for ensuring the clustering center that virtual clustering centers are defined in the feature space by the original classification as the initial cluster centers and the iteration clustering centers are ensured by the further virtual classification. The improved method is used for fault diagnosis of roller bearing that achieves a good cluster and diagnosis result, which demonstrates the effectiveness of the proposed method.