Cooperative Sensor Anomaly Detection Using Global Information

Sensor networks are deployed in many application areas nowadays ranging from environment monitoring, industrial monitoring, and agriculture monitoring to military battlefield sensing. The accuracy of sensor readings is without a doubt one of the most important measures to evaluate the quality of a sensor and its network. Therefore, this work is motivated to propose approaches that can detect and repair erroneous (i.e., dirty) data caused by inevitable system problems involving various hardware and software components of sensor networks. As information about a single event of interest in a sensor network is usually reflected in multiple measurement points, the inconsistency among multiple sensor measurements serves as an indicator for data quality problem. The focus of this paper is thus to study methods that can effectively detect and identify erroneous data among inconsistent observations based on the inherent structure of various sensor measurement series from a group of sensors. Particularly, we present three models to characterize the inherent data structures among sensor measurement traces and then apply these models individually to guide the error detection of a sensor network. First, we propose a multivariate Gaussian model which explores the correlated data changes of a group of sensors. Second, we present a Principal Component Analysis (PCA) model which captures the sparse geometric relationship among sensors in a network. The PCA model is motivated by the fact that not all sensor networks have clustered sensor deployment and clear data correlation structure. Further, if the sensor data show non-linear characteristic, a traditional PCA model can not capture the data attributes properly. Therefore, we propose a third model which utilizes kernel functions to map the original data into a high dimensional feature space and then apply PCA model on the mapped linearized data. All these three models serve the purpose of capturing the underlying phenomenon of a sensor network from its global view, and then guide the error detection to discover any anomaly observations. We conducted simulations for each of the proposed models, and evaluated the performance by deriving the Receiver Operating Characteristic (ROC) curves.     

HIV模型的统计诊断

描述HIV的数学模型是一组非线性常微分方程,其中包括CD4+T细胞再感染率和死亡率,HIV病毒死亡率等多个重要未知参数,准确估计这些参数有助于正确了解患者病情发展,以采用个人化治疗方案.针对此模型已提出多个参数估计方法,包括基于数值解的非线性最小二乘,截面似然及两步估计.另一方面,由于客观因素影响,各观测数据对于参数估计的影响大小不同,找出对参数估计影响大的观测值,进一步分析其原因具有重要意义.基于HIV模型的两步估计,构造了用于影响分析的非参数Cook型统计量,并给出其大样本分布.通过模拟数据和临床数据分析发现:(1)所构造统计量可以检测中度以上偏移.(2)相对于内点,边界点对HIV模型的参数估计影响更大.基于以上结论,建议对HIV模型进行参数估计时,对边界点应加以格外关注.提出的方法也可以推广到其他线性常微分方程模型的统计诊断问题中.     

再生核空间W_2~1(R)中的分段投影插值

本文在具有再生核的空间W_2~1(R)中讨论分段插值问题,给出W_2~1(R)的再生核的解析式,并构造一个分段插值公式。     

正定Lipschitz核的本征值

设 G 是 R~d 中闭单位正方体,正定对称核 K(x,y)在 G×G 上满足α阶的 Lipschitz条件。本文证明,由 K(x,y)生成的积分算子 K 的本征值渐近为 O(1/(n~(1+α/d)))。     

用镜像法计算再生磁头线圈中的输出电压

本文用镜像法分析再生过程中,从施加在记录磁介质上的记录磁化强度析出的磁通和耦合到再生磁头的磁通,根据两种回路磁阻不同的影响计算出交链于再生磁头线圈中的磁通.由此可求得,当具有模拟信号的记录磁介质进入再生磁头的前部空间时所产生的再生电压.计算结果表明,再生电压的幅值中包含着许多重要的记录损失参数.     

加权Herz空间上的粗糙算子

研究了粗糙算子在加权Ｈｅｒｚ空间上的有界性质。     

递归方法在窗宽选择上的应用

在未知总体分布的情形下,给出密度核估计中选择窗宽的一个新方法,并在选取高斯核的情形下,推导出计算窗宽的递归公式。最后通过与理论窗宽值比较,说明使用该递归方法选择最优窗宽是非常有效的一个途径。     

基于最小二乘支持向量机对偶优化问题的核偏最小二乘

提出了一种基于对偶优化的核最小二乘(KPLS)方法,把KPLS用最小二乘支持向量机的形式表示.推导了KPLS对偶优化形式的公式,且使其具有最小二乘支持向量机的风格.在初始空间中构造优化问题,应用核技术在特征空间中解对偶问题,这种解与非线性的KPLS具有相似性.实验验证了这种方法的效果,表明了该方法的有效性和优越性.     

基于核主元分析法和支持向量机的人耳识别

对人耳识别中若干关键问题进行了研究. 介绍了两种人耳图像归一化处理的方法,即基于外耳轮廓长轴的线标记法和基于外耳轮廓起始点的点标记法,并对这两种方法进行了对比. 在分析现有人耳识别方法不足的基础上,提出利用核主元分析法提取人耳图像的代数特征,再利用支持向量机分类模型进行人耳识别. 在带有角度、光照变化的北京科技大学人耳图像库上得到的识别率为98.7%,表明了该识别方法的有效性以及利用人耳图像进行身份识别的可行性.     

以{ei}i^n=1为正交基的再生核Hilbert空间

再生核Hilbert空间首先是一个Hilbert空间,再生核方法(RKHS method)为研究Hilbert空间提供了一个有力的数学工具,核函数具有许多优良的性质,可以通过这些性质来刻画整个Hilbert空间。笔者主要研究了以{ei}in=1为正交基的再生核Hilbert空间H中的核函数的一些性质,并通过这些性质简要的描述了Hilbert空间H与它的核函数之间的关系。