假設二元反應曲線為簡單線性羅吉斯迴歸模型(Simple Linear Logistic Regression Model)，在樣本數為偶數的前題下，所謂的最佳D型設計(D-Optimal Design)是直接將半數的樣本點配置在第17.6個百分位數，而另一半則配置在第82.4個百分位數。很遺憾的是，這兩個位置在參數未知的情況下是無法決定的，因此逐次實驗設計法(Sequential Experimental Designs)在應用上就有其必要性。在大樣本的情況下，本文所探討的逐次實驗設計法在理論上具有良好的漸近最佳D型性質(Asymptotic D-Optimality)。尤其重要的是，這些特性並不會因為起始階段的配置不盡理想而消失，影響的只是收斂的快慢而已。但是在實際應用上，這些大樣本的理想性質卻不是我們關注的焦點。實驗步驟收斂速度的快慢，在小樣本的考慮下有決定性的重要性。基於這樣的考量，本文將提出三種起始階段設計的方法並透過模擬比較它們之間的優劣性。 / The D-optimal design is well known to be a two-point design for the simple linear logistic regression function model. Specif-ically , one half of the design points are allocated at the 17.6- th percentile, and the other half at the 82.4-th percentile. Since the locations of the two design points depend on the unknown parameters, the actual 2-locations can not be obtained. In order to dilemma, a sequential design is somehow necessary in practice. Sequential designs disscused in this context have some good properties that would not disappear even the initial stgae is not good enough under large sample size. The speed of converges of the sequential designs is influenced by the initial stage imposed under small sample size. Based on this, three initial stages will be provided in this study and will be compared through simulation conducted by C++ language.

線性迴歸模型中共線性的問題是導致模型不適當的重大原因之一。共線性 的存在不止會影響到參數的估計，使參數的變異變大，還會妨礙我們評估 自變數對模型重要性的能力，甚至會使我們忽略或去除掉重要的自變數。 而變異膨脹因子是診斷線性迴歸模型共線性問題時常用而有效的方法之一 ，但它只是考慮單一自變數的情況。本文則對於模型同時加入一組自變數 時影響原模型共線性的問題，先推導出廣義的判定係數，再利用它推導出 變異膨脹矩陣。再應用這個變異膨脹矩陣發展出六個準則，使得變異膨脹 矩陣有一個單一的指標來對模型的共線性做診斷。最後並以一個例子以實 際的數據，用六個準則對不同的模型做診斷，並嘗試找出各準則的指標。

隨著網路的發達,各式各樣的資訊和商品也在網路上充斥著,使用者尋找資訊或是上網購物時,有的網站有推薦系統(recommender system)能提供使用者相關資訊或商品。若推薦系統能夠讓消費者所搜尋的相關資訊或商品能夠符合他們的習性時,便能讓消費者增加對系統的信賴程度,因此系統是否能準確預測出使用者的偏好就成為一個重要的課題。本研究使用兩筆資料,並以相關研究的三篇文獻進行分析和比較。這三篇文獻分別為IRT模型法(IRT model-based method)、相關係數法(correlation-coefficient method)、以及矩陣分解法(matrix factorization)。 在經過一連串的實證分析後,歸納出以下結論: 1. 模型法在預測方面雖然精確度不如其他兩種方法來的好,但是模型有解釋變數之間的關係以及預測機率的圖表展示,因此這個方法仍有存在的價值。 2. 相關係數法容易因為評分稀疏性的問題而無法預測,建議可以搭配內容式推薦系統的運作方式協助推薦。 3. 矩陣分解法在預測上雖然比IRT模型法還好，但分量的數字只是一個最佳化的結果，實際上無法解釋這些分量和數字的意義。 / With the growth of the internet, websites are full of a variety of information and products. When users find the information or surf the internet to shopping, some websites provide users recommender system to find with which related. Hence, whether the recommender system can predict the users' preference is an important topic. This study used two data,which are "Mondo" and "MovieLens", and we used three related references to analyze and compare them. The three references are following: IRT model-based method, Correlation-coefficient method, and Matrix factorization. After the data analysis, we get the following conclusions: 1. IRT model-based method is worse then other methods in predicting, but it can explain the relationship of variables and display the graph of predicting probabilities. Hence this method still has it's value. 2. Correlation-coefficient method is hard to predict because of sparsity. We can connect it with content filtering approach. 3. Although matrix factorization is better then IRT model-based method in predicting, the vectors is a result of optimization. It may be hard to explain the meaning of the vectors.

基礎矩陣在影像處理是非常重要的參數，舉凡不同影像間對應點之計算、座標系統轉換、乃至重建物體三維模型等問題，都有賴於基礎矩陣之精確與否。本論文中，我們提出一個機制，透過粒子群最佳化的觀念來求取基礎矩陣，我們的方法不但能提高基礎矩陣的精確度，同時能降低計算成本。 我們從多視角影像出發，以SIFT取得大量對應點資料後，從中選取8點進行粒子群最佳化。取樣時，我們透過分群與隨機挑選以避免選取共平面之點。然後利用最小平方中值表來估算初始評估值，並遵循粒子群最佳化演算法，以最小疊代次數為收斂準則，計算出最佳之基礎矩陣。 實作中我們以不同的物體模型為標的，以粒子群最佳化與最小平方中值法兩者結果比較。實驗結果顯示，疊代次數相同的實驗，粒子群最佳化演算法估測基礎矩陣所需的時間，約為最小平方中值法來估測所需時間的八分之一，同時粒子群最佳化演算法估測出來的基礎矩陣之平均誤差值也優於最小平方中值法所估測出來的結果。 / Fundamental matrix is a very important parameter in image processing. In corresponding point determination, coordinate system conversion, as well as three-dimensional model reconstruction, etc., fundamental matrix always plays an important role. Hence, obtaining an accurate fundamental matrix becomes one of the most important issues in image processing. In this paper, we present a mechanism that uses the concept of Particle Swarm Optimization (PSO) to find fundamental matrix. Our approach not only can improve the accuracy of the fundamental matrix but also can reduce computation costs. After using Scale-Invariant Feature Transform (SIFT) to get a large number of corresponding points from the multi-view images, we choose a set of eight corresponding points, based on the image resolutions, grouping principles, together with random sampling, as our initial starting points for PSO. Least Median of Squares (LMedS) is used in estimating the initial fitness value as well as the minimal number of iterations in PSO. The fundamental matrix can then be computed using the PSO algorithm. We use different objects to illustrate our mechanism and compare the results obtained by using PSO and using LMedS. The experimental results show that, if we use the same number of iterations in the experiments, the fundamental matrix computed by the PSO method have better estimated average error than that computed by the LMedS method. Also, the PSO method takes about one-eighth of the time required for the LMedS method in these computations.

電腦視覺三維建模的精確度，仰賴影像中對應點的準確性。以前的研究大多採取兩張影像，透過極線轉換(epipolar transfer)取得影像間基礎矩陣(fundamental matrix)的關係，然後進行比對或過濾不良的對應點以求取精確的對應點。然極線轉換存在退化的問題，如何避免此退化問題以及降低兩張影像之間轉換錯誤的累積，成為求取精確三維建模中極待解決的課題。 本論文中，我們提出一套機制，透過三焦張量(trifocal tensor)的觀念來過濾影像間不良的對應點，提高整體對應點的準確度，從而能計算較精確的投影矩陣進行三維建模。我們由多視角影像出發，先透過Bundler求取對應點，然後採用三焦張量過濾Bundler產生的對應點，並輔以最小中值平方法(LMedS)提升選點之準確率，再透過權重以及重複過濾等機制來調節並過濾對應點，從而取得精確度較高的對應點組合，最後求取投影矩陣進行電腦視覺中的各項應用。 實作中，我們測詴了三組資料，包含一組以3ds Max自行建置的資料與兩組網路中取得的資料。我們先從三張影像驗證三焦張量的幾何特性與其過濾對應點的可行性，再將此方法延伸至多張影像，同樣也能證實透過三焦張量確實能提升對應點的準確度，甚至可以過濾出輸入資料中較不符合彼此間幾何性的影像。 / The accuracy of 3D model constructions in computer vision depends on the accuracy of the corresponding points extracted from the images. Previous studies in this area mostly use two images and compute the fundamental matrix through the use of the epipolar geometry and then proceed for corresponding point matching and filtering out the outliers in order to get accurate corresponding points. However, the epipoler transform suffers from the degenerate problems and, also, the accumulated conversion errors during the corresponding matches both will degrade the model accuracy. Solving these problems become crucial in reconstructing accurate 3D models from multiple images. In this thesis, we proposed a mechanism to obtain accurate corresponding points for 3D model reconstruction from multiple images. The concept of trifocal tensor is used to remove the outliers in order to improve the overall accuracy of the corresponding points. We first use Bundler to search the corresponding points in the feature points extracted from multiple view images. Then we use trifocal tensor to determine and remove the outliers in the corresponding points generated by Bundler. LMedS is used in these processes to improve the accuracy of the selected points. One can also improve the accuracy of the corresponding points through the use of weighting function as well as repeated filtering mechanism. With these high precision corresponding points, we can compute more accurate fundamental matrix in order to reconstruct the 3D models and other applications in computer vision. We have tested three sets of data, one of that is self-constructed data using the 3ds Max and the other two are downloaded from the internet. We started by demonstrating the geometric properties of trifocal tensor associated with three images and showed that it can be used to filter out the bad corresponding points. Then, we successfully extended this mechanism to more images and successfully improved the accuracy of the corresponding points among these images.

策略聯盟在管理理論與實務上都是重要且常被提及的議題，但因組織進入策略聯盟後績效提升的成果不一致，以致廣受學者與經理人之質疑與討論。近期研究顯示，策略聯盟是否能提升績效與組織學習或改變有關。本研究以組織慣性觀點檢視在策略聯盟過程中組織慣性之所在、展現與成因，以及透過策略聯盟如何化解組織慣性，達成焦點組織跟隨策略意圖而來的組織改變。 Hannan與Freeman(1984)據組織生態學提出的組織慣性觀點認為，組織為使利害關係人持續投入資源，須達到當責性(accountability)與穩定性(reliability)的要求，如此將令組織在重複產出下產生慣性(inertia)。組織慣性具有效率、低成本及自動化等功能以因應穩定的環境，但當環境變遷時，組織慣性則將成為組織因應環境的絆腳石與組織改變的障礙。據此，本研究目的有二：一、希望透過聯盟雙造（多方）受訪者的觀點，探討焦點組織的組織慣性所在與展現。二、如何透過組織間的策略聯盟化解焦點組織的組織慣性，達成焦點組織策略改變之目的，找出策略聯盟成員廠商與領導廠商的條件及化解組織慣性的機制。 組織慣性引自物理學的慣性概念，本研究利用跨領域理論之借用，嘗試與當前的聯盟研究對話，透過質性紮根的研究方式，訪談紡織產業中參與策略聯盟之廠商，以變革事件為分析單位，探索廠商參與策略聯盟過程中出現的組織慣性及其化解方式，並就本研究之發現與相關組織理論對話。 本研究核心問題為：一、組織慣性成因；二、組織慣性之化解；三、策略聯盟如何化解組織慣性。理論貢獻包括：一、提出組織內各單位、各層級無法同步改變是組織慣性之成因。二、若可使組織內部達成同步改變，則可化解組織慣性；透過認知、誘因、資源與能力的互補提升等三種機制可影響各個個體的決策與行動。三、策略聯盟可透過對象的選擇，以鏡像脈絡與聯盟倡導人途徑造成焦點組織同步改變，化解其組織慣性。實務意涵為提供具有組織慣性的組織改變的可行途徑，以及策略聯盟夥伴的選取與聯盟化解組織慣性之機制。 / Strategic alliances are a popular practical strategy in the management field and represent an important area of academic research. The outcomes of organizations that have joined strategic alliances have been inconsistent, however, so strategic alliance is still a black box for management scholars and managers. Recent studies have shown that the performance of strategic alliances is related to the process of organizational learning or changes in the focal organizations. This research is based on the organizational inertia perspective, which analyzes the organizational inertia of a focal organization in the process of strategic alliance through the Management Matrix (Seetoo, 2005). This matrix shows the locations, causes, and presentations of the organizational inertia. Overcoming organizational inertia through strategic alliances may allow organizations to achieve expected changes in strategic intent. Organizational inertia was originally a concept from physics. In this study, we have borrowed from multiple theories in an attempt to dialogue with the current research on strategic alliances. According to organizational ecological theory, organizational inertia emerges when an organization wants its stakeholders to continue to input their resources into the organization, and ,in turn, the organization must provide output that meets the stakeholders’ requirements regarding accountability and reliability. After repeated production and documentation, the organization acquires inertia (Hannan & Freeman, 1984). In a stable environment, an organization with inertia is efficient, low-cost, and automated. When the environment is changing, however, organizational inertia will become an obstacle for organizations in their ability to respond to external changes. This study has several purposes, First, through the interviewees, who are key persons in dyadic (or multiple) partnerships in strategic alliances, we aim to investigate the locations, causes, and presentations of the focal organizations’ organizational inertia. Second, in order to analyze the process of overcoming the focal organizations’ inertia in a strategic alliance context, we aim to identify the routes, mechanisms, and characteristics of the strategic alliance partner that aid in overcoming the focal organization’s inertia. Through qualitative interviews with the participating organizations, all of which have joined strategic alliances in the textile industry, our analysis focuses on the events surrounding strategic change. We explore the presentations and overcoming of the focal organizations’ inertia in the strategic alliance process. The findings of this study are brought into the conversation through dialogue with relevant organization theory. From the analysis of the qualitative data from multiple resources, we put forward the following three propositions: First, the focal organization’s lack of coherence and synchronous change are the cause of the organizational inertia. Second, if coherence and synchronous change can be reached within the organization, organizational inertia can be resolved. Third, a strategic alliance can help the focal organization to achieve the coherent and synchronous change to overcome its organizational inertia. This study makes several theoretical contributions. First, we find that the focal organizations inability to enact coherent, synchronous change is the main cause of organizational inertia. Second, if synchronous change can be reached within the organization, this can resolve organizational inertia; offering new information to influence cognition, incentives, resources, and capabilities are complementary enhancement mechanisms that can affect individuals’ decisions and actions. Third, strategic alliance through the selection of an alliance partner, a mirroring context, and an alliance champion can improve the focal organizations’ ability to access synchronous change to overcome its organizational inertia. When the partners in the strategic alliance have high reputation and capability, they will accomplish these mechanisms more easily. For the coherence of multiple decision makers, one partner of the strategic alliance must mirror the focal organization to obtain a better result in overcoming focal organizational inertia. Other, there needs to be a champion in the multiple strategic alliance who can to persuade people to alter their cognition, plan incentive allocation, integrate the organizations’ capabilities and resources, and so on. The practical implications of this research are that it provides a viable way to overcome organizational inertia, as well as selecting strategic alliance partners and the mechanisms and routes of strategic alliances.

近幾年來，華語流行音樂的發展越來越多元，而大眾所接收到的資訊是流行音樂當中的組成元素”曲與詞”，兩者分別具有賦予人類感知的功能，使人能夠深刻體會音樂作品當中所表答的內容與意境。然而，作曲與作詞都是屬於專業的創作藝術，作詞者通常在填詞時，會先對樂曲當中的結構進行粗略的分析，找出整首曲子的曲式，而針對可以填詞的部份，再進行更細部的分析將詞填入最適當的位置。流行音樂當中，曲與詞存在著密不可分的關係，瞭解歌曲結構不僅能降低填詞的門檻，亦能夠明白曲子的骨架與脈絡;在音樂教育與音樂檢索方面亦有幫助。 本研究的目標為，使用者輸入流行音樂歌曲，系統會自動分析出曲子的『曲式結構』。方法主要分成三個部分，分別為主旋律擷取、歌句分段與音樂曲式結構擷取。首先，我們利用Support Vector Machine以學習之方式建立模型後，擷取出符號音樂中之主旋律。第二步驟我們以”歌句”為單位，對主旋律進行分段，對於分段之結果建構出Self-Similarity Matrix矩陣。最後再利用Non-Negative Matrix Factorization針對不同特徵值矩陣進行分解並建立第二層之Self-Similarity Matrix矩陣，以歧異度之方式找出曲式邊界。 我們針對分段方式對歌曲結構之影響進行分析與觀察。實驗數據顯示，事先將歌曲以歌句單位分段之效果較未分段佳，而歌句分段之評測結果F-Score為0.82;將音樂中以不同特徵值建構之自相似度矩進行Non-Negative Matrix Factorization後，另一空間中之基底特徵更能有效地分辨出不同的歌曲結構，其F-Score為0.71。 / Music structure analysis is helpful for music information retrieval, music education and alignment between lyrics and music. This thesis investigates the techniques of music structure analysis for Chinese popular music. Our work is to analyze music form automatically by three steps, main melody finding, sentence discovery, and music form discovery. First, we extract main melody based on learning from user-labeled sample using support vector machine. Then, the boundary of music sentence is detected by two-way classification using support vector machine. To discover the music form, the sentence-based Self-Similarity Matrix is constructed for each music feature. Non-negative Matrix Factorization is employed to extract the new features and to construct the second level Self-Similarity Matrix. The checkerboard kernel correlation is utilized to find music form boundaries on the second level Self-Similarity Matrix. Experiments on eighty Chinese popular music are performed for performance evaluation of the proposed approaches. For the main melody finding, our proposed learning-based approach is better than existing methods. The proposed approaches achieve 82% F-score for sentence discovery while 71% F-score for music form discovery.

管理學應是一門解決企業或是組織問題的的學問。當實務界在組織經營發生問題時，管理學嘗試從經濟學、社會學、心理學、政治學這些已經發展百年的學科當中，淬取對實務界有幫助的理論或是架構，並提出解決方案；同時藉由實際將理論或是架構運用於實務界的經驗，檢討並改進理論的正確以及完整性。 照理來說，管理學因為位於居中整合的角色，以及能夠解決實務界在經營管理上的問題，應該廣為一般社會大眾所理解並採用。然而實際情況卻是在理論部分，大家眾說紛紜，並且經常被具有深厚實務經驗的人士嘲諷為紙上談兵。在實務界的部分，管理方面相關的專業或是技能，卻又多靠經驗傳承，缺少系統性的知識架構，讓相關經驗的實用性受到一定程度的限制。 有鑑於此，司徒達賢（2005）提出「管理就是整合」之核心觀念，強調「管理」不只在學術上扮演著整合的角色，管理者在實際的管理行為上，做得也就是整合的動作。司徒達賢並嘗試融合各家學說，以「管理矩陣」為架構，將管理者的整合行為加以編碼、解碼，讓讀者可以更深入的去觀察一個管理者如何去思考策略、觀察環境、權衡得知利害、以至於最後進行整合的動作。 透過「管理矩陣」為分析架構的方式，不只為管理學上的「整合化」、「科學化」邁進一大步，其中由管理矩陣所衍生出來的其他創新觀點，如「整合的棋局觀點」、「六大管理元素之陰陽表裡」，更是提供讀者許多不同且實用的思考角度。 本研究以整合的核心觀念為出發，以《鹿鼎記》為分析文本，透過管理矩陣分析法的解說並且實際操作，希望讓組織各階層的成員能夠更瞭解，管理者在組織或是跨組織當中，進行整合的整個過程以及其背後所代表的涵意。另外更深入討論關於「整合的棋局觀點」、「六大管理元素之陰陽表裡」兩項管理議題，讓管理者重新思考「整合」與「被整合」之間的關係，以及懂得調和管理元素的陰陽，並且讓組織成員能夠將上述觀念，實際運用於個人所負責的組織創價流程中。

現今許多網路商店或電子商務將產品銷售給消費者的過程中，皆使用推薦系統的幫助來提高銷售量。如亞馬遜公司(Amazon)、Netflix，深入了解顧客的使用習慣，建構專屬的推薦系統並進行個性化的推薦商品給每一位顧客。 推薦系統應用的技術分為協同過濾和內容過濾兩大類，本研究旨在探討協同過濾推薦系統中潛在因子模型方法，利用矩陣分解法找出評分矩陣。在Koren等人(2009)中，將矩陣分解法的演算法大致分為兩種，隨機梯度下降法(Stochastic gradient descent)與交替最小平方法(Alternating least squares)。本研究主要研究目的有三項，一為比較交替最小平方法與隨機梯度下降法的預測能力，二為兩種矩陣分解演算法在加入偏誤項後的表現，三為先完成交替最小平方法與隨機梯度下降法，以其預測值對原始資料之遺失值進行資料插補，再利用奇異值分解法對完整資料做矩陣分解，觀察其前後方法的差異。 研究結果顯示，隨機梯度下降法所需的運算時間比交替最小平方法所需的運算時間少。另外，完成兩種矩陣分解演算法後，將預測值插補遺失值，進行奇異值分解的結果也顯示預測能力有提升。 / Recommender system has been largely used by Internet companies such Amazon and Netflix to make recommendations for Internet users. Techniques for recommender systems can be divided into content filtering approach and collaborative filtering approach. Matrix factorization is a popular method for collaborative filtering approach. It minimizes the object function through stochastic gradient descent and alternating least squares. This thesis has three goals. First, we compare the alternating least squares method and stochastic gradient descent method. Secondly, we compare the performance of matrix factorization method with and without the bias term. Thirdly, we combine singular value decomposition and matrix factorization. As expected, we found the stochastic gradient descent takes less time than the alternating least squares method, and the the matrix factorization method with bias term gives more accurate prediction. We also found that combining singular value decomposition with matrix factorization can improve the predictive accuracy.

給定聯合分配，可以容易地導出對應的條件分配。反之，給定條件分配的資訊，是否能導出對應的聯合分配呢？例如根據O. Paul et al.（1963，1968）對造成心血管疾病因素之追蹤研究，可得出咖啡量、吸菸量及是否有心血管疾病三者間的條件機率模型資料，是否能找到對應的聯合機率模型，以便可以更深入地研究三者之關係，是一個重要的議題。在選定參考點下，Chen（2010）提出以勝算比法找條件密度函數相容的充要條件，以及在相容性成立時，如何求得聯合分配。在二維中，當兩正值條件機率矩陣不相容時，郭俊佑（2013）以幾何平均法修正勝算比矩陣，並導出近似聯合分配，同時利用幾何平均法之特性，提出最佳參考點之選擇法則。本研究以二維的勝算比法為基礎，探討三維離散的相容性問題，獲得下列幾項結果：一、證明了三個三維條件機率矩陣相容的充要條件就是兩兩相容。二、當三維條件機率矩陣不相容時，利用幾何平均法導出近似聯合分配。三、利用兩兩相容的充要條件，導出三維條件機率矩陣相容的充要條件，並證明該充要條件與Chen的結果一致。四、在幾何平均法下，提出最少點法，有效率地找出最佳參考點，以產生總誤差最小的近似聯合分配。五、設計出程式檢驗三維條件機率矩陣是否相容，並找出最佳參考點，同時比較最少點法與窮舉法之間效率的差異。 / Given a joint distribution, we can easily derive the corresponding fully conditional distributions. Conversely, given fully conditional distributions, can we find out the corresponding joint distribution? For example, according to a longitudinal study of coronary heart disease risk factors by O. Paul et al. (1963, 1968), we obtain conditional probability model data among coffee intake, the number of cigarettes smoked and whether he/she has coronary heart disease or not. Whether we can find out the corresponding joint distribution is an important issue as the joint distribution may be used to do further analyses. Chen (2010) used odds ratio method to find a necessary and sufficient condition for their compatibility and also gave the corresponding joint distribution for compatible situations. When two positive discrete conditional distributions in two dimensions are incompatible, Kuo (2013) used a geometric mean method to modify odds ratio matrices and derived an approximate joint distribution. Kuo also provided a rule to find the best reference point when the geometric mean method is used. In this research, based on odds ratio method in two dimensions, we discuss their compatibility problems and obtain the following results on three-dimensional discrete cases. Firstly, we prove that a necessary and sufficient condition for the compatibility of three conditional probability matrices in three dimensions is pairwise compatible. Secondly, we extend Kuo’s method on two-dimensional cases to derive three-dimensional approximate joint distributions for incompatible situations. Thirdly, we derive a necessary and sufficient condition for the compatibility of three conditional probability matrices in three dimensions in terms of pairwise compatibility and also prove that this condition is consistent with Chen’s results. Fourthly, we provide a minimum-points method to efficiently find the best reference point and yield an approximate joint distribution such that total error is the smallest. Fifthly, we design a computer program to run three-dimensional discrete conditional probability matrices problems for compatibility and also compare the efficiency between minimum-points method and exhausting method.