Feature subset selection based on mahalanobis distance: a statistical rough set method

In order to select effective feature subsets for pattern classification, a novel statistics rough set method is presented based on generalized attribute reduction. Unlike classical reduction approaches, the objects in universe of discourse are signs of training sample sets and values of attributes are taken as statistical parameters. The binary relation and discernibility matrix for the reduction are induced by distance function. Furthermore, based on the monotony of the distance function defined by Mahalanobis distance, the effective feature subsets are obtained as generalized attribute reducts. Experiment result shows that the classification performance can be improved by using the selected feature subsets.

Method of Monitoring Wearing and Breakage States of Cutting Tools Based on Mahalanobis Distance Features

The Mahalanobis distance features proposed by P.C.Mahalanobis, an Indian statistician, can be used in an automatic on-line cutting tool condition monitoring process based on digital image processing. In this paper, a new method of obtaining Mahalanobis distance features from a tool image is proposed. The key of calculating Mahalanobis distance is appropriately dividing the object into several component sets. Firstly, a technique is proposed that can automatically divide the component groups for calculating Mahalanobis distance based on the gray level of wearing or breakage regions in a tool image. The wearing region can be divided into high gray level component group and the tool-blade into low one. Then, the relation between Mahalanobis distance features of component groups and tool conditions is investigated. The results indicate that the high brightness region on the flank surface of the turning tool will change with its abrasion change and if the tool is heavily abraded, the area of high brightness will increase apparently. The Mahalanobis distance features of high gray level component group are related with wearing state of tool and low gray level component group correlated with breakage of tool. The experimental results show that the abrasion of the tool’s flank surface affected the Mahalanobis distances of high brightness component of the tool and the pixels of high brightness component set. Compared with the changes of them, we found that the Mahalanobis distance of high brightness component of the tool was more sensitive to the abrasion of cutting tool than the area of high brightness component set of the tool. Here we found that the relative changing rate of the area of high brightness component set was not quite obvious and it was ranging from 2% to 15%, while the relative changing rate of the Mahalanobis distance in table 1 ranges from 13.9% to 47%. It is 3 times higher than the changing rate of the area.

Outlier Detection Based on Robust Mahalanobis Distance and Its Application

Classical Mahalanobis distance is used as a method of detecting outliers, and is affected by outliers. Some robust Mahalanobis distance is proposed via the fast MCD estimator. However, the bias of the MCD estimator increases significantly as the dimension increases. In this paper, we propose the improved Mahalanobis distance based on a more robust Rocke estimator under high-dimensional data. The results of numerical simulation and empirical analysis show that our proposed method can better detect the outliers in the data than the above two methods when there are outliers in the data and the dimensions of data are very high.

Improved Relative-transformation Principal Component Analysis Based on Mahalanobis Distance and Its Application for Fault Detection

主要部件分析(PCA ) 广泛地在过程工业被使用了，它能维持最大的差错察觉率。尽管许多问题在 PCA 被处理了，一些必要问题仍然保持未解决。这研究以下列方法为差错察觉性能改进 PCA。第一，一个相对转变计划基于 Mahalanobis 距离(MD ) 被介绍消除数据的尺寸的效果而不是无尺寸的标准化，并且改进精确性和差错察觉的即时性能。理论推导证明那相对转变能直接基于 MD 消除尺寸的效果并且在结果显示出的相对空间，分析和模拟给 PCA 的合理解释它的优势和有效性。第二，一个改进摆平的预言错误(SPE ) 统计数值被给改进标准化 PCA 的差错察觉表演，它能使标准化基于 PCA 的差错察觉方法成为对实际工业过程合适的更多。最后，二个改进方法被联合更有效地检测差错。建议方法被使用在热连续滚动过程检测 looper 系统的单个差错和多差错，模拟结果以易感知，精确性和差错察觉的即时性能为差错察觉性能表明这些改进的有效性。

An improved Mahalanobis distance-based colour segmentation method for rural building recognition

Aiming at the rapid identification of rural buildings in complex environments from high-spatialresolution images, an improved Mahalanobis distance colour segmentation method(IMDCSM) is proposed and realised in Red, Green and Blue(RGB) space. Vector sets of a lower discrete degree are obtained by filtering the colour vector sets of the building samples, and a standard ellipsoid equation can be constructed based on these vector sets. The threshold of interested colour range can be flexibly and intuitively selected by changing the shape and size of this ellipsoid. Then, according to the relationship between the location of the image pixel colour vector and the ellipsoid, all building information can be extracted quickly. To verify the effectiveness of the proposed method, unmanned aerial vehicle(UAV) images of two areas in the suburbs of Chengdu city and Deyang city were utilised as experimental data for image segmentation, and the existing colour segmentation method based on the Mahalanobis distance was selected as an indicator to assess the effectiveness of this method. The experimental results demonstrate that the completeness and correctness of this method reached 95% and 83.0%, respectively, values that are higher than those of the Mahalanobis distance colour segmentation method(MDCSM). In general, this method is suitable for the rapid extraction of rural building information, and provides a new threshold selection method for classification.

新纠缠辅助量子MDS码的构造

纠缠辅助量子纠错码是经典量子纠错码的推广,通过在接收者和发送者双方预先共享纠缠态的方式实现量子通信.由于预先共享纠缠态会造成额外的费用,如何构造具有较小预先共享纠缠态的纠缠辅助量子纠错码是一个有趣的问题.本文给出了有限域Fq2上一类负循环码是厄米特对偶包含码的充分条件,通过研究其分圆陪集的结构性质,确定了不同数目的预先共享纠缠态的存在条件,并结合纠缠辅助量子纠错码的构造方法,构造了一些新的具有较小预先共享纠缠态的纠缠辅助量子Maximum-Distance-Separable(MDS)码.

基于MD-PCA-BP模型的露天矿山爆破振动速度预测

为解决露天矿山爆破复杂场地地质条件的爆破振动预测问题,提出了一种基于马氏距离判别(MD)和主成分分析(PCA)的改进BP神经网络预测模型,即MD-PCA-BP模型。结合内蒙古长滩露天矿爆破振动监测数结果,利用马氏距离判别法剔除监测数据的离群值,并采用主成分分析法对爆破振动影响因素进行降维处理得到3个主成分因子,计算各主成分因子的得分,最终通过BP神经网络构建爆破振动与主成分得分的非线性关系,建立了基于MD-PCA-BP的爆破振动预测模型。结果表明:基于MD-PCA-BP模型建立的爆破振动速度预测模型预测结果与实测值的拟合度达到0.94,预测模型具有较高的预测精度;将预测结果与萨道夫斯基经验公式、2个改进的高程经验公式、MD-BP模型、PCA-BP模型以及BP模型进行比较,MD-PCA-BP模型的预测误差大部分在10%以内,相较于经验公式和未改进的BP预测模型具有更高的可靠度和准确度。基于MD-PCA-BP的爆破振动预测模型在复杂地形的爆破振动速度预测方面表现出了良好的预测效果,对复杂地形的爆破振动预测具有一定的参考作用。

基于2个不相交子集的MDS自对偶码构造

最大距离可分(maximum distance separable, MDS)自对偶码是一类最优线性码,在通信、数据存储和区组设计等领域有着广泛的应用,构造MDS自对偶码是当前编码理论研究的一个热点问题。文章基于有限域及其乘法群的2个不相交子集,利用广义Reed-Solomon(RS)码构造了几类新的MDS自对偶码;得到的MDS自对偶码具有灵活的长度。

基于CNN-MD的军用电站健康状态评估方法

基于健康状态评估的军用电站预先维修对提高其可靠性、安全性有着重要意义,采用基于CNN-MD的评估方法,对军用电站健康状态进行评估。建立卷积神经网络(convolutional netural network,CNN)军用电站健康状态识别模型,通过采用不同的状态样本训练模型,可使模型识别和输出健康状态类别;再引入马氏距离(Mahlanobis distance,MD)算法,计算不同状态下样本与健康样本的MD距离,并将其归一化为健康指数,即可进一步量化军用电站健康评价结果。以某型军用电站人工模拟不同健康状态的工况获取实验数据,通过模型能对正常、退化和注意三种状态进行有效区分,并得到量化评价健康指数0.6为正常状态的临界阈值,0.6以下为退化以下状态的具体量化评估值,验证了所方法的有效性。该方法通过CNN和MD结合,可实现军用电站健康状态定性与定量评估目的,为开展预先维修提供依据。

基于Mahalanobis距离的运动意识分类研究

提出基于Mahalanobis距离判别式算法的意识任务分类方法。对被测试者想象左右手运动时脑电信号的mu节律能量变化进行在线动态分析,提取EEG(C3,C4)两个通道的mu节律能量作为特征向量,用Mahalanobis距离判别式算法对左右手运动想象脑电模式进行分类,实验结果表明,正确识别率可达87.86%。

一种基于Mahalanobis距离的增量聚类算法

经典的模糊c均值聚类算法对非球型或椭球型分布的数据集进行聚类效果较差。将经典的模糊c均值聚类中的欧氏距离用Mahalanobis距离替代,利用Mahalanobis距离的优点,将其用于增量学习中,提出一种基于马氏距离的模糊增量聚类学习算法。实验结果表明该算法能较有效地解决模糊聚类方法中的缺陷,提高了训练精度。

中国区域技术创新能力:基于Mahalanobis距离的聚类优化实证研究

针对中国区域技术创新能力最新实证研究在聚类方法和结果方面的一些不足,基于样本间Mahalanobis距离,结合所研究问题的背景情况和统计理论,选择ward聚类方法实施聚类,基于聚类结构的稳定性和敏感性准则,通过观察Dendrogram图,得到聚类数量的可能取值区间,然后求解Pseudo-F最大值来确定最优聚类数量。

利用Mahalanobis距离的SAR图像溢油识别

利用合成孔径雷达(SAR)可在日夜及全天候条件下进行高分辨率溢油监测的优点,提出了一种基于特征向量的SAR图像溢油识别方法。在暗区边界确定的SAR图像中进行量算,得到特征向量,并采用Mahalanobis距离对目标物进行识别。经实验验证,选取的特征值数量合理,且对于判定是否为溢油效果明显;利用Mahalanobis距离进行判别,算法清晰,且准确率达到96%以上;与其他溢油判定方法相比,附加条件较少,且利于在计算机上编程实现。

利用Mahalanobis距离进行人脸表情的识别

提出了利用Mahalanobis距离进行人脸表情识别的方法．首先将待分类的图像样本集进行坐 标变换,使得变换以后类间离散度尽可能大而类内离散度尽可能小,即使变换以后的Fisher准则函数 取得极大值,在新的坐标下求每个待分类样本到各类均值向量的Mahalanobis距离,从而将待分类的 样本归到Mahalanobis距离最小的类中去,通过实验得到了平均80．25％的识别率．

Mahalanobis距离在多元随机变量线性变换中的定理

根据多元统计分析中Mahalanobis距离的计算理论,对其计算性质进行了讨论和研究,证明了多元随机变量在经过可逆线性变换后,其Mahalanobis距离的计算数值不变这一重要性质.并通过实际问题说明了此性质在多元统计分析,特别是在距离判别分析中的作用.

基于马田系统的Mahalanobis距离选择

主要讨论Euclidean距离的局限性,提出Mahalanobis距离的一个结论,给出Mahalanobis距离计算步骤,并结合实例加以说明。

基于VMD-MD的油气管道泄漏信号去噪方法

针对油气管道泄漏检测时,采集的泄漏信号会受到噪声信号干扰而影响监测精度的问题,提出变分模态分解(VMD)和马氏距离(MD)相结合的去噪方法。该方法首先利用VMD分解信号,得到多个模态分量,再依次计算出各模态分量概率密度与原采集信号间概率密度的马氏距离来区分有效模态分量和含噪模态分量,最后选择有效模态分量进行重构,从而达到信号去噪目的。与其他去噪方法在仿真模拟信号试验和实际管道泄漏信号试验中进行对比,该方法的输出信噪比是最高的,为46.7740 dB,而均方误差是最低的,为5.1972×10^(-7),表明该方法在去噪效果方面具有一定的优越性,为后续油气管道的泄漏识别奠定了良好的基础。

一种基于Mahalanobis距离和主成分分析的电子鼻信号预处理方法

针对样本集中的少数异常样本便可导致网络的稳定性下降甚至失效的问题。该文提出了基于马氏距离异常检测的PCA-RBF（Principal Component Analysis-Radial Basis Function）网络模型,将粗糙样本集经异常检验后进行PCA-RBF网络的识别。实验证明该方法能够克服异常样本的干扰,提高了网络的稳定性和识别能力。

基于VMD-MD的输电铁塔螺栓松动检测方法

针对输电铁塔局部螺栓松动,给出了一种基于变分模态分解(VMD)与马氏距离(MD)相结合的检测方法。首先,对脉冲激振下的输电铁塔振动响应信号进行VMD分解,并通过互相关指数重构信号,提取关键频段信息;其次,对重构信号提取故障敏感特征构成特征向量,利用MD对工况进行判别,针对现场实验随机性强的特点,采用随机抽取的方法重构测试集,有效提高了判别效果;最后,利用本文提出的方法对铁塔局部测点敏感度进行分析,为现场铁塔局部螺栓松动检测做出探索。

结合Mahalanobis距离的SUSAN彩色边缘检测方法研究

针对HSI颜色空间在图像处理和分析方面更加符合人眼的视觉特性,提出了一种结合Mahalanobis距离的SUSAN彩色图像边缘检测方法.该方法首先将彩色图像从RGB空间转换到HSI空间,然后以H、S、I为变量计算空间中两种颜色的色差距离,结合SUSAN算子对边缘进行检测.实验结果表明:此方法可以有效地检测彩色图像的边缘.在保留图像边缘方面,性能优于传统的彩色边缘检测方法.