本研究之樣本取自1991年7月1日至2010年3月之月資料，探討各總體經濟變數包括：利率、匯率(美元對新台幣)、M1B、出口、GDP、領先指標綜合指數與大陸及美國兩股市，對台股指數之影響。實證結果顯示，道瓊工業指數為影響台股加權指數最具代表性與領先的指標，大陸股市則非如一般所預期對台股指數變動有重要解釋能力。且道瓊工業指數、利率、M1b、GDP對台股具有領先的單向因果關係。 在衝擊反應函數及變異數分解中，除了道瓊工業指數為判斷台股指數變動最重要因素外，利率與貨幣供給則扮演著解釋台股變動另一重要的角色，利率調升對台股指數之影響為先正後負，當利率調升前，投資者會事先反應，但調升後便會開始調節，反而對台股造成負向影響；而GDP及出口在變異數分解中占台股變異數比例是相對次高的比重，說明台股的變動反應了經濟的基本面因素，台股的變動亦會受其影響，惟此二項變數屬於落後指標，只能用在事後分析。而(美元兌新台幣)匯率及領先指標綜合指數則對台股變動無顯著解釋能力。

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.

本文有兩個研究目標，第一個是比較政大用電量與氣溫之間的相關性，第二則是分析影響黃金價格波動的因素。本文使用到的研究方法有希爾柏特黃轉換（HHT）與一些統計值。 　　本研究使用的分析數據如下：政大逐時用電量、台北逐時氣溫以及倫敦金屬交易所（London Metal Exchange）的月平均黃金價格。透過經驗模態分解法（EMD），我們可以將分析數據拆解成數個互相獨立的分量，再藉由統計值選出較重要的分量並分析其意義。逐時用電量的重要分量為日分量、週分量與趨勢；逐時氣溫的重要分量為日分量與趨勢；月平均黃金價格的重要分量則是低頻分量與趨勢。 藉由這些重要分量，我們可以更加了解原始數據震盪的特性，並且選出合理的平均週期將所有的分量分組，做更進一步的分析。逐時用電量與逐時氣溫分成高頻、中頻、低頻與趨勢四組，其中低頻與趨勢相加的組合具有最高的相關性。月平均黃金價格則是分為高頻、低頻與趨勢三組，其中高頻表現出供需以及突發事件等短週期因素，低頻與歷史上對經濟有重大影響的事件相對應，趨勢則是反應出通貨膨脹的現象。 / There are two main separated researched purposes in this thesis. First one is comparing the correlation between electricity consumption and temperature in NCCU. Another one is analyzing the properties of gold price volatility. The methods used in the study are Hilbert-Huang transform (HHT) and some statistical measures. 　　The following original data: hourly electricity consumption in NCCU, hourly temperature in Taipei, and the LME monthly gold prices are decomposed into several components by empirical mode decomposition (EMD). We can ascertain the significant components and analyze their meanings or properties by statistical measures. The significant components of each data are shown as follows: daily component, weekly component and residue for hourly electricity consumption; daily component and residue for hourly temperature; low frequency components and residue for the LME monthly gold prices. 　　We can understand more properties about these data according to the significant components, and dividing the components into several terms based on reasonable mean period. The components of hourly electricity consumption and hourly temperature are divided into high, mid, low frequency terms and trends, and the composition of low frequency terms and trends have the highest correlation between them. The components of LME monthly gold prices are divided into high, low frequency term and trend. High frequency term reveals the supply-demand and abrupt events. The low frequency term represents the significant events affecting economy seriously, and trend shows the inflation in the long run.

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.

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第23回名古屋大学年代測定総合研究センターシンポジウム平成22(2010)年度報告

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.

金融市場常常受到政治、經濟與社會環境等因素所影響，所得到價格為眾多變數交互作用的結果，包含了許多雜訊。本文引進一套數據處理方法「整體經驗模態分解」(Ensemble Empirical Mode Decomposition，EEMD)來分析「期貨市場」以及「預測市場」。第一個實證利用EEMD處理台股期貨，分析對台股指數的解釋能力，並同時與原始台股期貨預測台股指數，比較預測結果；第二個實證利用EEMD來分析預測市場，判別是否能有效的消除雜訊，準確預測選舉結果。 第一個實證結果發現，EEMD能有效地過濾期貨市場的雜訊，另外，在最後到期日前十二天或者是前九天，以週期為6.5日經EEMD處理的台股期貨對台股指數的預測較原始台股期貨預測準確；第二個實證結果指出，直接利用EEMD處理預測市場得到的長期趨勢「剩餘訊號」(Residue)來預測選舉並無優於原始預測市場，主因為預測市場參與者不只在乎長期趨勢，亦在乎短期事件的衝擊，故直接利用剩餘訊號預測選舉結果會有所失真，而將剩餘訊號由低頻率之「本質模態函數」(Intrinsic Modes Function，IMF)合併至週期為6日與12日的IMF，得到了EEMD週趨勢價格，分成選前一天和選前十天的資料並與原始預測市場以及民調預測做比較，從不同的準則來看，發現以EEMD週趨勢價格來做選舉預測，準確度較原始預測市場與民調預測的結果更好。根據中選會2012年初選前對選罷法做成的解釋，未來事件交易所在選前十日亦須停止交易，我們可將EEMD運用在日後的選舉預測，把預測市場的合約價格以EEMD處理，應可提高選舉預測的準確度。 / The financial markets are usually affected by political, economic and social environment factors, and thus the volatilities of asset prices in these markets are subject to a lot of noises and shocks. To filter out noises and quantify shocks, this paper applies a data processing method, Ensemble Empirical Mode Decomposition (EEMD), and demonstrates its improved prediction to the futures and election prediction markets. While the first empirical application shows that the EEMD effectively filters out the noises in the futures market, the second one indicates that the Taiwanese election prediction using EEMD “residue” is not as accurate as that by original data from the prediction market. The reason why the residue cannot serve as a good predictor is that the market participants consider not only the long-term trend, but also shocks, especially those right before the elections. We then attempt to predict the election outcomes by the week trend series processed by EEMD. The prediction by the week EEMD trend series turns out to be more accurate than that by the poll and original prediction market. Based on this study, we can apply the EEMD to the next election prediction and improve its accuracy.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20196号 / 理博第4281号 / 新制||理||1615(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 馬場 正昭, 教授 寺嶋 正秀, 教授 松本 吉泰 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21101号 / 工博第4465号 / 新制||工||1694(附属図書館) / 京都大学大学院工学研究科原子核工学専攻 / (主査)教授 高木 郁二, 教授 佐々木 隆之, 准教授 土田 秀次 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM