Expanding the Spectral Envelope

谱包络的概念最近被引入，作为定性值时间序列的频域分析和标度的一般统计方法。在开发该技术的过程中，还出现了许多其他有趣的扩展。本研究涉及到基本概念在各个方向的延伸。第一个扩展涉及匹配两个分类序列，以发现它们是否包含相似的模式，并受到两个DNA序列匹配问题的激励。该方法建立在定义光谱包络线所使用的思想之上，并着重于测量两个分类时间序列之间相似性的所谓相干包络线。该方法基于快速傅里叶变换，计算简单，速度快，适用于长序列。在另一个方向上，将该技术扩展到定性空间数据的分析。激发这个项目的应用程序是在计算机视觉中具有潜在用途的自动图像检索和模式识别。具体来说，这一部分的研究将侧重于通过最优缩放和波数谱包络分析分类随机场。由于频谱包络方法的许多应用都是在平稳性和同质性假设不现实的情况下进行的，因此本研究将探讨基于小波的分析相对于动态傅立叶分析的好处。本研究的另一个扩展是将该概念应用于实验设计中收集的实值时间序列的分析，其中主要关注的是是否有任何以及有多少共同循环分量。这个问题是由医学和行为科学中的许多应用所引起的。最近引入了一种称为光谱包络的统计概念，作为研究长序列字母或符号（如代码）模式的一般方法。这种方法最著名的应用是生物技术，特别是DNA分析。在发展这个概念的过程中，许多其他的实际扩展变得明显。本研究涉及到基本概念在各个方向的延伸。第一个扩展涉及匹配两个非数字序列，以发现它们是否包含相似的模式，其动机是在两个不同的遗传密码中寻找相似性的生物技术问题。另一个方向是将该技术扩展到定性空间数据（如图像），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发挥作用。此外，用于匹配序列的方法可以应用于计算机视觉和机器人技术，其中的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纳入当前的医学应用，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.