非平穩資料的時間序列分析:層級切割法及其運用

在這個研究中，分成兩大部分。第一部份主要是提出一套新的分析方法，稱為層級切割法(Hierarchical Segmentation) ，尤其在處理非穩定性的時間序列資料。層級切割法主要的想法，是利用編碼的方式，對資料進行分類 (clustering)。經過三層的編碼後，我們很輕易的將連續的資料，依據其本身所表現的特性，切割成數段。在最上層的編碼裡，代碼相同的區段，表示他們具有相似的特性。這樣的分析方法，尤其在連續資料中，對於模式(pattern)或是某一特別區段的辨識(identifying)上，是一個非常有用的工具。對於分析方法的理論發展上，也不需要像傳統時間序列對於資料需要有穩定性的假設，是一個很值得期待的方法。我們也將這個方法實際應用在不同領域的分析上。在此論文中，我們探討了在生物方面，有關生物時鐘、豆象產卵行走的軌跡的問題；在心理學方面，探討夫妻之間情緒的變化和之間的相互影響。在生物時鐘方面，每一個時間點，對於生物而言都是一個相位(phase) 。找出穩定且可靠的相位(phase) 來定義每天活動的起始或是結束是一個研究的關鍵。利用層級切割法，我們很成功的找出每天起始的相位，並進一步探討週期的變化，活動的波形(waveform) ，和因著外來刺激而產生的相位移動(phase shift) ，並發展出一套架構相位反應曲線(phase response curve, PRC) 的方法。我們也透過模擬的方式來比較HS 和Onset 這兩個方法的優劣。結果發現，HS 相對於Onset 具又較佳的穩定性，亦即從活動的波形的角度而言，HS 其所得到的相位標誌能標示出固定的相位。在豆象產卵行為方面，主要是利用層級切割法，找出豆象行走軌跡的模式，並探討在三種不同的資源環境下，豆象是否改變其行為反應。發現豆象在豐富的資源環境行走軌跡呈現較簡單的模式且偏好近距離的搜尋。隨著資源使用的耗竭，其行走軌跡出現愈多的長距離的搜尋。在夫妻情緒資料的分析上，透過層級切割，將情緒變動較大的期間區分出來，經由chi-square 檢定，發現不論在正、負面情緒上，夫妻之間具有一致性 (coherent)的情緒反應。經由HS 的方式，我們將資料切割成三段。並且利用模擬的方式，證實這樣的分斷，更能幫助我們解釋情緒變動的相互影響。最後運用了 stochastic small-world network (SSWN)，動態影片，以其更能捕捉夫妻之間情緒的互動。第二部分是對於灰色蟑螂其階級的不穩定性的探討。我們發展了兩個指標，分別用來量化在一個族群中階層制度的不穩定性和其競爭的程度。我們發現不穩定性和族群內的個體數目具有高度的相關，而競爭的程度與階層的不穩定具有高度的正相關。亦即，在一族群中，若其階層制度越不穩定，表示族群內競爭程度就越激烈。

關鍵字

層級切割法；生物時鐘；行走軌跡；夫妻情緒相互影響；階層制度

並列摘要

There are two parts in this dissertation. First is that we propose a new method, Hierarchical Segmentation (HS), to analyze non-stationary time series data. The main idea of HS is to divide a series of data into several segments according to the characteristics of data through three level coding. At the upper level, there resemble each other if they have the same codewords. So, it is useful in identifying patterns or special segments with appropriate coding. Here, we apply HS in three different fields: circadian rhythm, moving trajectory and the emotional interaction of couples. In circadian rhythm study, a phase represents each time point for the experiment duration. It is crucial to decide robust and reliable markers as the onset or offset points for the daily activity. We define the onset phase markers via HS; furthermore, we discuss the variation of periods, waveform, and the phase shift inducing by the outside stimulation and develop a new approach in constructing phase response curve (PRC). We compare HS and Onset methods via simulation. It reveals that HS is more robust than Onset; in other words, the phase markers inducing by HS can mark the benchmark in waveform. In the study of oviposition behavior, we explore the moving trajectory of bean weevil and try to find out the moving patterns via HS. We are interested in exploring that if subject changes her moving pattern under three different resource environments. It reveals that the moving patterns is simpler and local search preferred in rich patch than in half and poor. With resource consumed, the moving patterns are increased into lots of long walk. In the couple data analysis, we divide the segments of highly emotional response. After examining with chi-square test, we find that there is coherence situation in both positive and negative emotion. We separate the series data into three segments, and we prove that the approach is helpful in catching the interaction patterns. Finally, we use stochastic small-world network (SSWN) and dynamic movie to represent the dyadic dynamic interactions. The other part is to explore the unstable hierarchy formation in cockroach, Nauphoeta cinerea. We develop two indices to quantify the degree of unstable and the competitive pressure in a group. It reveals that the degree of unstableness is highly related with group size, and there is highly positive relation between unstableness and competitive pressure. In other words, within a group, the more unstable a hierarchy formation is, the stronger the competition appears.

並列關鍵字

hierarchical segmentation ； circadian rhythm ； moving trajectory ； small-world dyadic dynamic interactions ； hierarchy fornation

參考文獻

chapter 1

Aschoff, J. (1960) Exogenous and endogenous components in circadian rhythms. In

Cold Spring Harbor Symposium on Quantitative Biology: Biological Clocks, J.

Aschoff Eds. pp. 11-28. the Biological Laboratory Cold Spring Harbor, New

Aschoff, J. (1965) Circadian rhythm in man. Science 148, 1427-1432.

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非平穩資料的時間序列分析:層級切割法及其運用

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