N/A / In the previous academic studies, there are different views on the pros and cons for diversified firms and focus firms. On the other hand, most of previous works show that going to globalization is quite a definite trend and able to generate values for its shareholders. Both topics are especially critical for contemporary multi-business multinational firms, of which GE is a very typical example. In this study, we intend to conduct comprehensive analysis of the business and financial strategy that GE uses to grab deeper understanding of how a globally diversified company should leverage its competitive advantages to pursue growth and great performance. We also provide our views on some of the potential issues for firms like GE and recommend some measures to be done to make those companies more financially sound. From the result of our case study, we primarily conclude that diversification is good if the company can leverage the power of its various businesses and use the resources of one business to support the others in a reasonable manner. It is also crucial that the diversified firm should do its best to maintain its transparency to the outsiders to remove their concerns about information asymmetry. Furthermore, from the case of GE, it is also suggested that globalization should do a company with the scale like GE’s more good than harm. Going globally is actually an inevitable direction for most of the companies in the future.

設H是一個實數正交的矩陣，我們要求它的特徵值以及特徵向量。H可以表示成Schur參數的形式。根據Ammar，Gragg及Reichel的論文，我們把H的特徵問題轉換成兩個元素由Schur參數決定的二對角矩陣的奇異值(奇異向量)的問題。我們用這個方法寫成程式並且與CLAPACK的程式比較準確度及速度。最後列出一些數值的結果作為結論。 / Let H be an orthogonal Hessenberg matrix whose eigenvalues, and possibly eigenvectors, are to be determined. Then H can be represented in Schur parametric form [2]. Following Ammar, Gragg, and Reichel's paper [1], we compute the eigenproblem of H by finding the singular values (and vectors) of two bidiagonal matrices whose elements are explicitly known functions of the Schur parameters. We compare the accuracy and speed of our programs using the method described aboved with those in CLAPACK. Numerical results conclude this thesis.

傳統的主成分分析(principal component analysis)法，只能分析二式二向的資料(2-mode 2-way data)，若是要處裡三向三式的資料(3-mode 3-way data)或是更多維的資料，則必須用其它的方法。例如將某一向資料取平均數，再做分析。此法雖然可行，但卻忽略三向資料間可能潛藏的相關性。且社會科學的研究日趨複雜，三向資料也就更常見到，而我們可能也對三向資料間彼此的關聯感到興趣。因此在1960、1970年代，學者開始研究將主成分分析的模型加以擴展成適合分析三向資料的模型。本文除了介紹三向資料主成分分析所使用的Tucker3模型及其參數估計法外，也以28家股票上市公司為實例，探討資本結構影響因素於五年間（1989~1993年）在不同公司群組間的變化情形。

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.

奇異值分解(singular valve decomposition)是一個重要且被廣為運用的矩陣分解方法，其具備許多良好性質，包括低階近似理論(low rank approximation)。在現今大數據(big data)的年代，人們接收到的資訊數量龐大且形式多元。相較於文字型態的資料，影像資料可以提供更多的資訊，因此影像資料扮演舉足輕重的角色。影像資料的儲存比文字資料更為複雜，若能運用影像壓縮的技術，減少影像資料中較不重要的資訊，降低影像的儲存空間，便能大幅提升影像處理工作的效率。另一方面，有時影像在被存取的過程中遭到雜訊汙染，產生模糊影像，此模糊的影像被稱為退化影像(image degradation)。近年來奇異值分解常被用於解決影像處理問題，對於影像資料也有充分的解釋能力。本文考慮將奇異值分解應用在影像壓縮與去除雜訊上，以奇異值累積比重作為選取奇異值的準則，並透過模擬實驗來評估此方法的效果。 / Singular value decomposition (SVD) is a robust and reliable matrix decomposition method. It has many attractive properties, such as the low rank approximation. In the era of big data, numerous data are generated rapidly. Offering attractive visual effect and important information, image becomes a common and useful type of data. Recently, SVD has been utilized in several image process and analysis problems. This research focuses on the problems of image compression and image denoise for restoration. We propose to apply the SVD method to capture the main signal image subspace for an efficient image compression, and to screen out the noise image subspace for image restoration. Simulations are conducted to investigate the proposed method. We find that the SVD method has satisfactory results for image compression. However, in image denoising, the performance of the SVD method varies depending on the original image, the noise added and the threshold used.

獼猴桃源出於中國，卻成就於紐西蘭，並有了「奇異果」此一新名稱。而且，來自中國大陸的奇異果，價格比其本土的獼猴桃高出數倍，兩者於口感、外型等其他方面，亦存在明顯差距；如何使中國獼猴桃轉變為奇異果，是本論文的研究重心。在此目標下，本論文分為「紐西蘭奇異果」與「中國大陸獼猴桃」兩部分，以文獻閱讀、資料搜尋、田野調查、專家訪談等方式，先從紐西蘭出發，研究促成奇異果產業形成的關鍵因素，再將此關鍵因素提供中國大陸獼猴桃發展參考，最後得出結論與建議。本論文發現，在形塑產業的過程中，「政府」在法律保障、制度規劃、外部產業環境的營造上，扮演著重要角色，因此本論文之立場選擇，係以「中國大陸獼猴桃盛產區政府」之角度，借鏡紐西蘭的發展經驗，在政策規劃的思維下，為獼猴桃尋找建設性的出路，並以此作為結論與建議。 紐西蘭提供的經驗，包括制訂專法規範奇異果產業、立法保護單一出口機制、建立誘因機制、打造產業群聚、以資料庫進行科學化管理、重視品種研究，以及政府為扶植紐西蘭奇異果產業所做的其他措施。而中國大陸獼猴桃產業尚處於發展初階，加上各地方獼猴桃的適生度不同，經營集中度低，資源難以匯聚，使獼猴桃一直無法有效商品化。但由於獼猴桃栽種面積與產量皆為世界第一，近年來更開發出多元食用與藥用等用途，再加上中國大陸法制建設逐步完善，投資風險降低，若以紐西蘭奇異果產業的經驗為借鏡，調整措施並加強整合，獼猴桃發展前景仍值得期待。 有鑑於此，本研究以「公私協力八卦模型」作為結論，並建議中國大陸首先應擇定試點集中經營之區域，以便日後將商品化經驗複製於其他省份。在試點經營措施上，本論文建議以平台為依托進行整合；針對獼猴桃制訂相關法規，促使能夠引領產業整體發展的龍頭集團形成；建立誘因機制，讓龍頭集團的經營利潤回饋果農；並在品種培育、收購標準、資料庫管理等方式下，逐步形成標準化生產，再加上獼猴桃基金的保險機制，讓中國大陸獼猴桃逐步從產業化邁向商品化。 / Mihoutao originated from China but thrived in New Zealand under the name of “kiwifruit”; however, the price of kiwifruit is vastly higher than that of Mihoutao, and their taste and shape are of evident differences. As such, this thesis seeks to answer the question of “how to turn mihoutao into kiwifruit” by looking into the management and operation of New Zealand kiwifruit industry and providing lessons from such experience to the commercialization of China mihoutao. This thesis adopts methodologies of material reading, data collecting, field works, and expert interviewing to reach the final conclusions and suggestions, and it is discovered that the government plays a key role in the process of agriculture industrialization. Therefore, the proposed suggestions are for “the government of China mihoutao province” to echo with my topic. This thesis concludes with “Eight-trigram Model” to express the partnership with public and private sectors. Furthermore, it suggests China to construct the mihoutao commercialization mechanism on the regional basis as an experiment, which can be later duplicated in other provinces. More specifically about the measures, referring to New Zealand kiwifruit industry’s policies, mihoutao regulations, leading corporation, incentives, plant cultivation, scientific management via database, mihoutao fund are recommended. With all these policies in order, it is believed that a more institutionalized and commercialized mihoutao industry will be gradually shaped, and the Chinese “mihoutao” will also be commercialized as “kiwifruit” eventually.