應用可適時序之動態階層自我組織網路圖於股市時間序列分群上之研究

Abstract

自我組織網路圖 (Self-Organizing Maps, SOM) 在類神經網路的非監督式學習類別中，一直是個強而有力的分支，特別擅長於將高維度的資料映射在較低維度的空間上。在探索式資料分析或叢集分析的應用裡，由於自我組織網路圖本身非監督式學習的特性，特別適合分群的資料，因此極適合用來作為分群方法。然而，當輸入的資料依時序而變，或是整體的環境為動態時，自我組織網路圖便由於其必須事先決定網路拓樸、大小，以及將外部環境視為靜態的假設等等限制，必定要有所改變，才更能適用。因此，本研究試圖藉由提出可適時序之動態階層自我組織網路圖，來解答以上的難題。本模型的階層狀架構可依據所預期資料呈現的細節程度，動態地決定網路的拓樸與大小；同時，該架構下的每個單獨自我組織網路圖，皆可由目前網路的狀態與當下輸入的樣本，以更新網路每單元的獨立學習參數（學習率與鄰近集合），進而可適應動態環境。接下來，本研究利用叢集分析，以五種不同的修改後自我組織網路圖模型做為分群方法，企圖在輸入的各種不同組合之股價資料中，尋找其線圖相似者。隨後並透過計算每次不同分群結果的分群效度，以驗證各種不同變數與分群結果之效度間的關係。最後，本研究以應用可適時序之動態階層自我組織網路，其確實可顯著地改善股市時間序列之分群效度做為總結。

The Self-Organizing Map (SOM), along with its variants, is quite popular in the unsupervised learning category in Artificial Neural Networks (ANN) for transforming high-dimensional data into an output map space of much lower dimension. For applications of Exploratory Data Analysis (EDA) or Cluster Analysis, SOM has been served as an excellent clustering method since the learning process is unsupervised and samples are unlabeled. However, if the input data is time-variant or the external environment is dynamic, some improvements must be done due to the limitations of static map topology and the assumption of static, stationary environment. These all limited the performance of SOM as a clustering method. Consequently, this thesis solves the above-mentioned difficulties by the introducing of the Growing Time Adaptive Dynamic Hierarchical Self-Organizing Maps. The hierarchical architecture of growing maps is capable of adjusting the topology according to the specified degree of detail level of data representation automatically. Besides, each map follows a time-adaptive learning process to adapt to the dynamic environment by updating independent learning rate and neighborhood sets parameters of each neuron based on the current map status and the randomly picked sample at a given time. The purpose is to discover similar stock price trends. Thereupon, Cluster Analysis is performed on the five top capitalization-weighted stocks of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX). Moreover, the relationship between various variables and the cluster validity indices will be verified as well. At last this thesis concludes that clustering of stock time series using the proposed Growing Time-Adaptive Dynamic Hierarchical Self-Organizing Maps can improve the cluster validity considerably in stock time series.