本研究的主要目的是檢視倒傳導神經網路是否具有人類在分類學習上所呈現出來的學習效應 — 競爭學習、遮蔽效應與不相關線索的影響。在實驗中，我們採用兩種倒傳導神經網路，來測試激發函數是否會影響倒傳導神經網路的學習。此兩種倒傳導神經網路分別採用sigmoid激發函數與hyperbolic-tangent激發函數。實驗結果顯示，以sigmoid為激發函數與以hyperbolic-tangent為激發函數的倒傳導神經網路都具有這三個學習效應。還有，以sigmoid為激發函數的倒傳導神經網路所呈現出來的學習效應比以hyperbolic-tangent為激發函數的倒傳導神經網路來得顯著。本研究的次要目的在於瞭解有效性（使用性）與敏感度分析的數值是否有對應關係。實驗結果顯示，線索A與線索B的敏感度分析數值差異可以反映出線索A與線索B的有效性差異。然而，敏感度分析數值卻無法準確地顯示線索的有效性數值。 / The main objective of this research is to examine whether back propagation neural networks (BP) have the learning effects found in human category learning — competitive learning, overshadowing and the deleterious of an irrelevant cue. Two kinds of BP, BP with sigmoid activation function and BP with hyperbolic-tangent activation function, are investigated to see if the activation function will make BP behave differently. According to the results of our experiments, these three learning effects are demonstrated both in BP with sigmoid and BP with hyperbolic-tangent, but they seems more significant in BP with sigmoid than in BP with hyperbolic-tangent. The second objective of our research is to see if there is a correspondence between the validity (the utilization) and the value of sensitivity analysis, R. From the results of our experiments, we observe that the difference between values of sensitivity analysis with respect to Cue A and Cue B reflects the difference of the validities between Cue A and Cue B. However, the value of sensitivity analysis does not show exactly what validity a cue is.

為了瞭解影響演化性神經網路（ENT）預測表現的四項重要的機制：輸入資料性質、訓練樣本大小、網路搜尋密度以及控制模型複雜度，進而找出能使ENT充分發揮效果的組合。在本論文中首先設計ENT在模擬資料上的實驗，探討上述四項機制個別對預測表現的影響，再依照實驗結果的建議，設計能讓ENT發揮功效的組合，並以實際金融高頻率資料：香港恆生指數在一九九八年十二月報酬率為標的，探討模擬資料的結果在實際金融資料需要調整的部份。實驗結果顯示，當輸入資料經過線性過濾後，搭配大樣本訓練、高搜尋強度與適當地模型複雜度控制，會是能讓神經網路提高預測能力的組合。在實際金融資料的實驗當中同時發現，資料中偶而出現特別高或特別低的變化，會對ENT的預測表現有相當程度的影響。 / In this thesis, Evolutionary Neural Trees (ENTs) are applied to forecast the artificial data generated by financial and chaos models — iid random, linear process (Auto Regressive-Moving Average；ARMA), nonlinear processes (AutoRegressive Conditional Heteroskedasticity；ARCH, General AutoRegressive Conditional Heteroskedasticity；GARCH, Bilinear), mixed linear and nonlinear process (AR and GARCH). Experiments of the artificial data were conducted to understand the characteristics of ENTs mechanism. – data pre-processing procedures, search intensity, sample size and complexity regularization. From the experiment results of artificial data, the combination of pure linear or nonlinear time series, large sample size, intensive search and simple neural trees are suggested for the parameters setting of ENTs. And for the sake of computational burden, we have a trade-off between search intensity and sample size. Ten experiments are designed for ENTs modeling on the high-frequency stock returns of Heng Sheng stock index on December, 1998, in order to have an efficient combination of the factors of ENTs. The results show that ENTs would perform more efficiently if data are pre-processed by a linear filter, for ENTs will concentrate on searching in the space of nonlinear signals. Also, as is well demonstrated in this study, the infrequent bursts (outliers) appearing in the data set can be very disturbing for the ENTs modeling.

本篇論文旨在分析神經網路學習績效，並提出一套學習演算法，結合倒傳遞網路(BP)與理解神經網路(RN)，命名為RNBP，這套學習演算法將與傳統的BP做比較，以兩個不同的財務金融領域的應用，一個是選擇權上Black-Scholes訂價模式的模擬，一個是金融交換上利率的預測。主要績效的評估準則是以學習的效率與模擬、預測的準確度為依據。 此外，本論文的另一個重點是提出一套對於神經網路系統進一步分析的方法與工具，敏感度分析(Sensitivity Analysis)與滯留區(Dead Region)分析，藉以瞭解神經網路系統是否具有效地良好學習或被一般化的能力，從神經網路的角度來說，這也是BP與RNBP的另一個績效比較標準。本研究的結果顯示RNBP在預測準確度上較BP為優良，但是在學習效率與預測能力的穩定性上並沒有呈現一致性的結論；此外，敏感度分析與滯留區分析的結果也幫助神經網路在應用領域上有更深入的瞭解。 在過去，神經網路的應用者往往忽略了進一步瞭解神經網路的重要性與可行性，本論文的貢獻在於藉由分析神經網路所學習的知識，幫助應用者進一步瞭解神經網路表達的訊息在應用領域上所隱含的實質意義。 / The study attempts to analyze the learning performance of neural networks in applications, and propose a new learning procedure for the layered feedforward neural network systems, named KNBP, which binds RN and BP learning algorithms. Two artificial neural networks, BP and KNBP, here are both applied to two financial fields, the simulation of Black-Scholes pricing model for the call options and the midrates forecasting in financial swaps. The explicit performance comparison between the two artificial neural network systems is mainly based on two criteria, which are learning efficiency and forecasting effectiveness. Then we propound a mathematical methodology of sensitivity analysis and the dead regions to deeply explore inside the network structures to see whether the models of ANNS are actually well trained or valid, and thus setup an alternative comparable criterion. The results from this study show that RNBP performs better than BP in forecasting effectiveness, but RNBP obtains neither a consistent learning efficiency in cases nor a stable forecasting ability. Furthermore, the sensitivity analysis and the dead region analysis provide a deeper view of the ANNs in the applied fields. In the past, most studies applying neural networks ignored the importance that it is feasible and advantageous to obtain more useful information via analyzing neural networks. The purpose of the research is to help further understanding to the information discovery resulted from neural networks in practical applications.

此篇論文，主要是討論遞迴式神經網路。在文中，我們將架構一個單層的神經網路結構。並利用三種不同的學習法則來套用此架構。我們也做了圓軌跡和圖形８的模擬，以及討論了此架構的收斂性。 / Our task in this paper is to discuss the Recurrent Neural Network. We construct a singal layer neural network and apply three different learning rules to simulate circular trajectory and figure eight. Also, we present the proof of convergence.

學界間廣泛地認為一般金融資產報酬具有的特性是:線型不可預測性,條件 異質變異數,非條件尖峰態 ... 等特性o 固然金融資產報酬具有線型不可 預測之特性,可是並不能否決其間可能有非線型依存關係的存在o目前大部 份經濟計量分析方法中的模式建構問題均是在假設模式的結構訊息已知的 條件下求解,然若真實體系的結構訊息未知或不明朗時,貿然地假設為某種 特定的模式結構,則可能又難於避免模式設定錯誤的困擾,因而對於真實體 系行為的描述亦將可能是誤導且不合理的,這意味著:除非該特定的模式結 構正是真實體系的表徵, 否則無論該特定模式的結構特性多完美,均難以 建構一令人信服的數理化模式來表徵真實體系之行為o 不幸地,此一問題 在高度非線型的動態隨機體系中尤其嚴重, 甚至是否存在一 ``真實'' 模式來據以表徵體系之行為,亦是相當值得懷疑, 故考慮一種無需特定結 構訊息假設的無母數方法或函數逼近法實屬必要o 類神經網路中的倒傳遞 網路模式即是符合此種特性的方法之一o然而學界間仍無法確定的是金融 資產報酬序列資料所產生的 ARCH 效果本身是否為真實序列資料產生機制 特性之顯現, 還是應歸咎於被忽略掉條件均數方面之非線性所衍生模式設 定錯誤情況下的代用模式, 並不得而知;另一方面, ARCH 模式的顯著成就 及其價值亦不能予以輕易地漠視, 因此, 試圖將 ARCH 模式所能提供的攸 關訊息納入倒傳遞網路模式的考量之中而形成倒傳遞網路-自迴歸條件異 質變異數 (BPN-ARCH) 模式以增進樣本外預測能力的精度便是本論文最 主要的嘗試重點與目的o

本研究主要應用基於總體經驗模態分解法(EEMD)之倒傳遞類神經網路(BPNN)預測兩種不同的非線性時間序列數據，包括政大逐時用電量以及逐日歷史黃金價格。透過EEMD，這兩種資料會分別被拆解為數條具有不同物理意義的本徵模態函數(IMF)，而這讓我們可以將這些IMF視為各種影響資料的重要因子，並且可將拆解過後的IMF放入倒傳遞類神經網路中做訓練。 另外在本文中，我們也採用移動視窗法作為預測過程中的策略，另外也應用內插法和外插法於逐時用電量的預測。內插法主要是用於補點以及讓我們的數據變平滑，外插法則可以在某個範圍內準確預測後續的趨勢，此兩種方法皆對提升預測準確度占有重要的影響。 利用本文的方法，可在預測的結果上得到不錯的準確性，但為了進一步提升精確度，我們利用多次預測的結果加總平均，然後和只做一次預測的結果比較，結果發現多次加總平均後的精確度的確大幅提升，這是因為倒傳遞類神經網路訓練過程中其目標為尋找最小誤差函數的關係所致。 / In this paper, we applied the Ensemble Empirical Mode Decomposition (EEMD) based Back-propagation Neural Network (BPNN) learning paradigm to two different topics for forecasting: the hourly electricity consumption in NCCU and the historical daily gold price. The two data series are both non-linear and non-stationary. By applying EEMD, they were decomposed into a finite, small number of meaningful Intrinsic Mode Functions (IMFs). Depending on the physical meaning of IMFs, they can be regarded as important variables which are input into BPNN for training. We also use moving-window method in the prediction process. In addition, cubic spline interpolation as well as extrapolation as our strategy is applied to electricity consumption forecasting, these two methods are used for smoothing the data and finding local trend to improve accuracy of results. The prediction results using our methods and strategy resulted in good accuracy. However, for further accuracy, we used the ensemble average method, and compared the results with the data produced without applying the ensemble average method. By using the ensemble average, the outcome was more precise with a smaller error, it results from the procedure of finding minimum error function in the BPNN training.

在這份研究中，我們提出一個類分散式神經網路框架，此框架為高頻交易系統研究下之子專案。在系統中，我們透過資料探勘程序發掘財務時間序列中的模式，其中所採用的資料探勘演算法之一即為類神經網路。我們實作一個在分散式平台上訓練類神經網路的框架。我們採用Apache Spark來建立底層的運算叢集，因為它提供高效能的記憶體內運算（in-memory computing）。我們分析一些分散式後向傳導演算法（特別是用來預測財務時間序列的），加以調整，並將其用於我們的框架。我們提供了許多細部的選項，讓使用者在進行類神經網路建模時有很高的彈性。 / In this research, we introduce a distributed framework of artificial neural network (ANN) as a subproject under the research of a high-frequency trading (HFT) system. In the system, ANNs are used in the data mining process for identifying patterns in financial time series. We implement a framework for training ANNs on a distributed computing platform. We adopt Apache Spark to build the base computing cluster because it is capable of high performance in-memory computing. We investigate a number of distributed backpropagation algorithms and techniques, especially ones for time series prediction, and incorporate them into our framework with some modifications. With various options for the details, we provide the user with flexibility in neural network modeling.

Black-Scholes選擇權定價模型是各種選擇定價的開山始祖，無論在理論或實務上均獲致許多的便利及好評，美中不足的是，這種既定模型下結構化參數的估計問題，在真實體系的結構訊息未知或是不明朗時，或是模式錯誤，亦或政治結構或金融環境不知時，該模型在實證資料的評價上會面臨價格偏誤的窘境。是故，許多的數值演算法（numerical algorithms）便因應而生，這些方法一則源於對此基本模型的修正，一則是屬於逼近的數值解。 評價選擇權的方法雖不一而足，然所有的這些理論或模型可分為二大類即模型驅動的理論（model-drive approach）及資料驅動的理論（data-driven approach）。前者是建構在許多重要的假設，當這些假設成立時，則選擇權的價格可用如Black-Scholes偏微分方程來表示，而後再用數值解法求算出，許多的數值方法即屬於此類的範疇；而資料驅動的理論（data-driven approach），其理論的特色是它的有效性（validity）不像前者是依其假設，職是之故，他在處理現實世界的財務資料時更顯見其具有極大的彈性。這些以計算智慧（computation intelligence）為主的財務計量方法，如人工神經網路（ANNs），遺傳演算法（GAs），遺傳規劃（GP）已在財務工程（financial engineering）領域上萌芽，並有日趨蓬勃的態勢，而將機器學習技術（machine learning techniques）應用在衍生性商品的定價，應是目前財務應用上最複雜及困難，亦是最富挑戰性的問題。 本文除了對現有文獻的整理評析外，在人工神經網路方面，除用於S&P 500的實證外，並用於台灣剛推行不久的認購構證評價之實證研究；而遺傳規劃在計算智慧發展的領域中，算是較年輕的一員，但發展卻相當的快速，雖目前在經濟及財務上已有一些文獻，但就目前所知的二篇文獻選擇權定價理論的文獻中，仍是試圖學習Black-Scholes選擇權定價模型，而本文則提出修正模型，使之成為完全以資料驅動的模型，應用於S&P 500實證，亦證實可行。最後，本文結合計算智慧中的遺傳演算法（ genetic algorithms）及數學上的加權殘差法（weight-residual method）來建構一條除二項式定價模型，人工神經網路定價模型，遺傳規劃定價模型等資料驅動模型之外的另一種具適應性學習能力的選擇權定價模式。 / The option pricing development rapid in recent years. However, the recent rapid development of theory and the application can be traced to the pathbreaking paper by Fischer Black and Myron Scholes(1973). In that pioneer paper, they provided the first explicit general equilibrium solution to the option pricing problem for simple calls and puts and formed a basis for the contingent claim asset pricing and many subsequent academic studies. Although the Black-Scholes option pricing model has enjoyed tremendous success both in practice and research, Nevertheless, it produce biased price estimates. So, many numerical algorithms have advanced to modify the basic model. I classified these traditional numerical algorithms and computational intelligence methods into two categories. Namely, the model-driven approach and the data-driven approach. The model-driven approach is built on several major assumptions. When these assumption hold, the option price usually can be described as a partial differential equation such as the Black-Scholes formula and can be solved numerically. Several numerical methods can be regarded as a member of this category. There are the Galerkin method, finite-difference method, Monte-Carlo method, etc. Another is the data-driven approach. The validity of this approach does not rests on the assumptions usually made for the model-driven one, and hence has a great flexibility in handling real world financial data. Artificial neural networks, genetic algorithms and genetic programming are a member of this approach. In my dissertation, I take a literature review about option pricing. I use artificial neural networks in S & P 500 index option and Taiwan stock call warrant pricing empirical study. On the other hand, genetic programming development rapid in recent three years, I modified the past model and contruct a data-driven genetic programming model. andThen, I usd it to S & P 500 index option empirical study. In the last, I combined genetic algorithms and weight-residual method to develop a option pricing model.

協同規劃、預測與再補貨(Collaborative Planning, Forecasting and Replenishment; CPFR)，是目前供應鏈管理下重要的討論議題；台灣近年來由於加入WTO與製造業外移使競爭壓力加劇，全球運籌需求提升，使廠商間的合作更加密切，且近年來企業資訊環境與基礎建設逐漸成熟，有助於協同商務之發展。在CPFR流程與供應鏈協同作業環境下，一個供需雙方協同且績效良好的銷售預測具有關鍵的重要性，是管理決策與協同合作時的重要依據；但是多數的企業並沒有一個結構化、有系統化的預測流程及方法，進行多點且不同方法之預測，這樣的銷售預測較無穩定的品質，亦較難提供管理者合理的數據解釋。 在CPFR流程下，強調買賣雙方透過完整、即時資訊的交流，進行短期、單一銷售預測，以提供雙方後續訂單預測、訂單補貨等決策的依據。本研究利用演算法（類神經網路和演化策略法）找出更適合混合性預測架構的解釋變數，再以較適合於實數解之演化策略法於修改黃蘭禎（2004）的三階段之預測模型架構，最後採用實驗方法，進行模型績效驗證。 / Collaborative Planning, forecasting and replenishment (CPFR) is an important issue of supply chain management currently. Because of the severer competition resulted from entrance into WTO and industry integration, cooperation between Taiwanese companies becomes more intensely; enterprises’ information environment and foundation construction attain to maturity also boost the development of collaboration business. In CPRF process and supply chain operation environment, it is critical that a good performance sale forecasting collaborated by both supplier and buyer sides, and it is also the basis of policy decision and collaboration. However, the majority of the companies lack for a structural and systematical forecasting process to proceed with a multi-points forecasting with different methods. This kind of sale forecasting is less of stable quality and is harder to provide the managers a reasonable statistics explanation. Under the CPRF process, both buyers and sellers are able to obtain the short-term and single sale forecasting by real time information communication. Furthermore, the follow-up order forecasting and replenishment strategy decision can be also established through this process. This research finds the variables that are more suitable to the mixed structure by usage of the algorithms, ANN and Evolution Strategy. And this research uses Evolution Strategy that is more suitable to real question to improve the mixed structure of Huang (2004). In the end, experimentation is adopted in order to verify the performance of the model.

增長層級式自我組織映射網路(GHSOM)屬於一種非監督式類神經網路，為自我組織映射網路(SOM)的延伸，擅長於對樣本分群，以輔助分析樣本族群裡的共同特徵，並且可以透過族群間存在的空間關係假設來建立分類器，進而辨別出異常的資料。 因此本研究提出一個創新的對偶方法(即為一個建立決策支援系統架構的方法)分別對舞弊與非舞弊樣本分群，首先兩類別之群組會被配對，即辨識某一特定無弊群體的非舞弊群體對照組，針對這些配對族群，套用基於不同空間假設所設立的分類規則以檢測舞弊與非舞弊群體中是否有存在某種程度的空間關係，此外並對於舞弊樣本的分群結果加入特徵萃取機制。分類績效最好的分類規則會被用來偵測受測樣本是否有舞弊的嫌疑，萃取機制的結果則會用來標示有舞弊嫌疑之受測樣本的舞弊行為特徵以及相關的輸入變數，以做為後續的決策輔助。 更明確地說，本研究分別透過非舞弊樣本與舞弊樣本建立一個非舞弊GHSOM樹以及舞弊GHSOM樹，且針對每一對GHSOM群組建立分類規則，其相應的非舞弊/舞弊為中心規則會適應性地依循決策者的風險偏好最佳化調整規則界線，整體而言較優的規則會被決定為分類規則。非舞弊為中心的規則象徵絕大多數的舞弊樣本傾向分布於非舞弊樣本的周圍，而舞弊為中心的規則象徵絕大多數的非舞弊樣本傾向分布於舞弊樣本的周圍。 此外本研究加入了一個特徵萃取機制來發掘舞弊樣本分群結果中各群組之樣本資料的共同特質，其包含輸入變數的特徵以及舞弊行為模式，這些資訊將能輔助決策者(如資本提供者)評估受測樣本的誠實性，輔助決策者從分析結果裡做出更進一步的分析來達到審慎的信用決策。 本研究將所提出的方法套用至財報舞弊領域(屬於財務舞弊偵測的子領域)進行實證，實驗結果證實樣本之間存在特定的空間關係，且相較於其他方法如SVM、SOM+LDA和GHSOM+LDA皆具有更佳的分類績效。因此顯示本研究所提出的機制可輔助驗證財務相關數據的可靠性。此外，根據SOM的特質，即任何受測樣本歸類到某特定族群時，該族群訓練樣本的舞弊行為特徵將可以代表此受測樣本的特徵推論。這樣的原則可以用來協助判斷受測樣本的可靠性，並可供持續累積成一個舞弊知識庫，做為進一步分析以及制定相關信用決策的參考。本研究所提出之基於對偶方法的決策支援系統架構可以被套用到其他使用財務數據為資料來源的財務舞弊偵測情境中，作為輔助決策的基礎。 / The Growing Hierarchical Self-Organizing Map (GHSOM) is extended from the Self-Organizing Map (SOM). The GHSOM’s unsupervised learning nature such as the adaptive group size as well as the hierarchy structure renders its availability to discover the statistical salient features from the clustered groups, and could be used to set up a classifier for distinguishing abnormal data from regular ones based on spatial relationships between them. Therefore, this study utilizes the advantage of the GHSOM and pioneers a novel dual approach (i.e., a proposal of a DSS architecture) with two GHSOMs, which starts from identifying the counterparts within the clustered groups. Then, the classification rules are formed based on a certain spatial hypothesis, and a feature extraction mechanism is applied to extract features from the fraud clustered groups. The dominant classification rule is adapted to identify suspected samples, and the results of feature extraction mechanism are used to pinpoint their relevant input variables and potential fraud activities for further decision aid. Specifically, for the financial fraud detection (FFD) domain, a non-fraud (fraud) GHSOM tree is constructed via clustering the non-fraud (fraud) samples, and a non-fraud-central (fraud-central) rule is then tuned via inputting all the training samples to determine the optimal discrimination boundary within each leaf node of the non-fraud (fraud) GHSOM tree. The optimization renders an adjustable and effective rule for classifying fraud and non-fraud samples. Following the implementation of the DSS architecture based on the proposed dual approach, the decision makers can objectively set their weightings of type I and type II errors. The classification rule that dominates another is adopted for analyzing samples. The dominance of the non-fraud-central rule leads to an implication that most of fraud samples cluster around the non-fraud counterpart, meanwhile the dominance of fraud-central rule leads to an implication that most of non-fraud samples cluster around the fraud counterpart. Besides, a feature extraction mechanism is developed to uncover the regularity of input variables and fraud categories based on the training samples of each leaf node of a fraud GHSOM tree. The feature extraction mechanism involves extracting the variable features and fraud patterns to explore the characteristics of fraud samples within the same leaf node. Thus can help decision makers such as the capital providers evaluate the integrity of the investigated samples, and facilitate further analysis to reach prudent credit decisions. The experimental results of detecting fraudulent financial reporting (FFR), a sub-field of FFD, confirm the spatial relationship among fraud and non-fraud samples. The outcomes given by the implemented DSS architecture based on the proposed dual approach have better classification performance than the SVM, SOM+LDA, GHSOM+LDA, SOM, BPNN and DT methods, and therefore show its applicability to evaluate the reliability of the financial numbers based decisions. Besides, following the SOM theories, the extracted relevant input variables and the fraud categories from the GHSOM are applicable to all samples classified into the same leaf nodes. This principle makes that the extracted pre-warning signal can be applied to assess the reliability of the investigated samples and to form a knowledge base for further analysis to reach a prudent decision. The DSS architecture based on the proposed dual approach could be applied to other FFD scenarios that rely on financial numbers as a basis for decision making.