Expanding the Spectral Envelope

Stoffer DMS-9703720谱包络的概念是最近被引入的一种用于定性值时间序列的频域分析和尺度的通用统计方法。在开发这项技术的过程中，许多其他有趣的扩展变得显而易见。本研究涉及基本概念在不同方向上的延伸。第一个扩展涉及匹配两个分类序列，以努力发现它们是否包含相似的模式，并由两个DNA序列的匹配问题驱动。该方法建立在定义谱包络时所用的思想基础上，并集中在可以被称为相干包络的东西上，用于度量两个分类时间序列之间的相似性。该方法基于快速傅里叶变换，具有计算简单、速度快、适用于长序列的特点。另一方面，将该技术扩展到定性空间数据的分析。推动这一项目的应用程序是自动图像检索和模式识别，可能在计算机视觉中使用。具体地说，这一部分的研究将集中在通过最优尺度和波数谱包络来分析分类随机场。由于谱包络方法的许多应用都是平稳性和齐性假设不现实的情况，因此本研究将探索基于小波的分析相对于动态傅立叶分析的优势。这项研究的另一个扩展是将这一概念应用于在实验设计中收集的实值时间序列的分析，其中主要感兴趣的是是否有以及有多少具有共同的循环分量。这个问题是由医学和行为科学中的大量应用引起的。最近引入了一个称为谱包络的统计概念，作为研究长序列字母或符号(如代码)中的模式的一般方法。这种方法最广为人知的应用是在生物技术中，特别是在DNA分析中。在发展这一概念的过程中，许多其他实际扩展变得明显。本研究涉及基本概念在不同方向上的延伸。第一个扩展涉及匹配两个非数字序列，以努力发现它们是否包含相似的模式，并受到在两个原本不同的遗传密码中寻找相似性的生物技术问题的推动。另一个方向是将该技术扩展到定性空间数据(如图像)，并应用于自动图像检索、自动模式识别和计算机视觉。这项研究将对机器人和自动化技术产生影响，这些技术将在工业制造过程中有用。此外，序列匹配中使用的方法可以应用于计算机视觉和机器人领域，在这些领域，问题是自动快速对齐从不同相机角度拍摄的同一场景的两张照片。此外，这项研究将侧重于如何将这项新技术融入当前的医学应用中，例如了解压力情况下生物节律的变化。

Stoffer DMS-9703720 The concept of the spectral envelope was recently introduced as a general statistical method for the frequency domain analysis and scaling of qualitative-valued time series. In the process of developing the technology, many other interesting extensions became evident. This research involves the extension of the fundamental concept in various directions. The first extension involves matching two categorical sequences in an effort to discover whether they contain similar patterns and is motivated by the problem of matching of two DNA sequences. The approach builds on the ideas used in defining the spectral envelope and focuses on what could be called coherency envelopes for measuring the similarity between two categorical time series. Estimation is based on the fast Fourier transform so that the methods are computationally simple and fast, and can be applied to long sequences. In another direction, the technology is extended to the analysis of qualitative spatial data. The applications that motivate this project are automated image retrieval and pattern recognition with potential use in computer vision. Specifically, this part of the research will focus on the analysis of categorical random fields via optimal scaling and the wave number spectral envelope. Since many of the applications where the spectral envelope methodology has been an asset are situations where the assumptions of stationarity and homogeneity are not realistic, this research will explore the benefits of wavelet-based analysis over dynamic Fourier analysis. Another extension of this research is to apply the concept to the analysis of real-valued time series collected in an experimental design where the primary interest is whether any, and how many, have common cyclic components. This problem is motivated by numerous applications in the medical and behavioral sciences. A statistical concept called the spectral envelope was recently introduced as a general method to study patterns in long seq uences of letters or symbols (such as codes). The most well known application of this methodology is in biotechnology, specifically in the analysis of DNA. In the process of developing the concept, many other practical extensions became evident. This research involves the extension of the fundamental concept in various directions. The first extension involves matching two non-numeric sequences in an effort to discover whether they contain similar patterns and is motivated by the biotechnical problem of finding similarities in two otherwise different genetic codes. Another direction is to extend the technology to qualitative spatial data (such as images) with applications in automated image retrieval, automated pattern recognition, and computer vision. This research will have an impact on robotics and automation technologies that will be useful, for example, in industrial manufacturing processes. Moreover, the methodology used in matching sequences could have applications in computer vision and robotics where the problem is to automatically and quickly align two pictures of the same scene taken from different camera angles. In addition, this research will focus on ways to incorporate this new technology into current medical applications such as understanding changes in biorythms in stressful situations.