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Decision-making with heterogeneous sensors - a copula based approach.

机译：使用异构传感器进行决策-一种基于copula的方法。

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摘要

Statistical decision making has wide ranging applications, from communications and signal processing to econometrics and finance. In contrast to the classical one source - one receiver paradigm, several applications have been identified in the recent past that require acquiring data from multiple sources or sensors. Information from the multiple sensors are transmitted to a remotely located receiver known as the fusion center which makes a global decision. Past work has largely focused on fusion of information from homogeneous sensors. This dissertation extends the formulation to the case when the local sensors may possess disparate sensing modalities. Both the theoretical and practical aspects of multimodal signal processing are considered.;The first and foremost challenge is to 'adequately' model the joint statistics of such heterogeneous sensors. We propose the use of copula theory for this purpose. Copula models are general descriptors of dependence. They provide a way to characterize the nonlinear functional relationships between the multiple modalities, which are otherwise difficult to formalize. The important problem of selecting the 'best' copula function from a given set of valid copula densities is addressed, especially in the context of binary hypothesis testing problems. Both, the training-testing paradigm, where a training set is assumed to be available for learning the copula models prior to system deployment, as well as generalized likelihood ratio test (GLRT) based fusion rule for the online selection and estimation of copula parameters are considered. The developed theory is corroborated with extensive computer simulations as well as results on real-world data.;Sensor observations (or features extracted thereof) are most often quantized before their transmission to the fusion center for bandwidth and power conservation. A detection scheme is proposed for this problem assuming unifom scalar quantizers at each sensor. The designed rule is applicable for both binary and multibit local sensor decisions. An alternative suboptimal but computationally efficient fusion rule is also designed which involves injecting a deliberate disturbance to the local sensor decisions before fusion. The rule is based on Widrow's statistical theory of quantization. Addition of controlled noise helps to linearize the higly nonlinear quantization process thus resulting in computational savings. It is shown that although the introduction of external noise does cause a reduction in the received signal to noise ratio, the proposed approach can be highly accurate when the input signals have bandlimited characteristic functions, and the number of quantization levels is large.;The problem of quantifying neural synchrony using copula functions is also investigated. It has been widely accepted that multiple simultaneously recorded electroencephalographic signals exhibit nonlinear and non-Gaussian statistics. While the existing and popular measures such as correlation coefficient, corr-entropy coefficient, coh-entropy and mutual information are limited to being bivariate and hence applicable only to pairs of channels, measures such as Granger causality, even though multivariate, fail to account for any nonlinear inter-channel dependence. The application of copula theory helps alleviate both these limitations. The problem of distinguishing patients with mild cognitive impairment from the age-matched control subjects is also considered. Results show that the copula derived synchrony measures when used in conjunction with other synchrony measures improve the detection of Alzheimer's disease onset.
机译：统计决策具有广泛的应用，从通信和信号处理到计量经济学和金融。与经典的一种来源-一种接收器范例相反，最近已经发现了几种需要从多个来源或传感器获取数据的应用。来自多个传感器的信息被传输到位于远端的接收器，该接收器被称为融合中心，该中心做出全局决策。过去的工作主要集中在融合来自同类传感器的信息。本文将公式扩展到本地传感器可能具有不同的传感方式的情况。考虑了多模态信号处理的理论和实践方面。第一个也是最重要的挑战是“充分地”建模此类异构传感器的联合统计数据。我们建议为此使用copula理论。 Copula模型是依赖性的一般描述。它们提供了表征多种模态之间非线性函数关系的方法，而这些方法否则很难形式化。解决了从给定的有效copula密度集中选择“最佳” copula函数的重要问题，尤其是在二元假设检验问题的情况下。训练测试范式（其中假设训练集可用于在系统部署之前学习copula模型）以及用于在线选择和估计copula参数的基于广义似然比测试（GLRT）的融合规则都是这两种方法。考虑过的。发达的理论与广泛的计算机模拟以及真实数据的结果得到了证实。传感器观测（或其提取的特征）最经常在传输到融合中心进行带宽和功率节省之前进行量化。针对每个传感器的统一标量量化器，提出了针对该问题的检测方案。设计的规则适用于二进制和多位本地传感器决策。还设计了另一种次优但计算效率高的融合规则，该规则涉及在融合之前向本地传感器决策注入故意干扰。该规则基于Widrow的量化统计理论。受控噪声的添加有助于线性化非线性非线性量化过程，从而节省了计算量。结果表明，尽管外部噪声的引入确实会导致接收信噪比的降低，但是当输入信号具有带宽受限的特征函数，并且量化级的数量很大时，所提出的方法仍可以是高精度的。还研究了使用copula函数量化神经同步性的方法。多个同时记录的脑电信号表现出非线性和非高斯统计已被广泛接受。尽管现有和流行的度量（例如相关系数，corr-熵系数，coh熵和互信息）仅限于双变量，因此仅适用于通道对，但Granger因果关系等度量即使是多元变量也无法解释任何非线性的通道间依赖性。 copula理论的应用有助于减轻这两个限制。还考虑了将轻度认知障碍患者与年龄匹配的对照对象区分开的问题。结果表明，与其他同步措施结合使用时，由copula得出的同步措施可改善阿尔茨海默氏病发作的检测。

著录项

  • 作者

    Iyengar, Satish Giridhar.;

  • 作者单位

    Syracuse University.;

  • 授予单位 Syracuse University.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2011
  • 页码 157 p.
  • 总页数 157
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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