本文關(guān)鍵詞： 主成分分析 模糊協(xié)方差矩陣 規(guī)則優(yōu)化 正定化　出處：《大連海事大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：模糊時間序列模型是數(shù)據(jù)預(yù)測分析研究領(lǐng)域中一個廣泛研究的課題,是為解決經(jīng)典時間序列分析方法不能處理模糊類問題應(yīng)運而生的。目前,模糊時間序列已被成功地應(yīng)用于股指預(yù)測、入學(xué)人數(shù)預(yù)測、溫度預(yù)測和航運指數(shù)預(yù)測等方面。為了進一步提高預(yù)測精度,學(xué)者提出了許多不同的模糊時間序列模型和預(yù)測方法,但其中多數(shù)方法都是圍繞論域的劃分和模糊規(guī)則的構(gòu)建方法兩方面做了不同程度的改進。在實際的預(yù)測過程中,模糊規(guī)則之間往往存在著相關(guān)性和冗余性,這不利于預(yù)測過程的簡化和預(yù)測精度的提高。因此,去除模糊規(guī)則之間的相關(guān)性和冗余性成為目前亟待解決的問題。針對如何去除規(guī)則間的相關(guān)性和冗余性的問題,本文基于主成分分析提出了一種模糊時間序列規(guī)則優(yōu)化算法。考慮到主成分分析只適用于協(xié)方差矩陣為正定的情況,本文從協(xié)方差矩陣正定和協(xié)方差矩陣非正定兩種不同的情況分別對算法進行了闡述和驗證。協(xié)方差矩陣正定時,首先構(gòu)建數(shù)據(jù)之間的模糊關(guān)系形成模糊規(guī)則,并將模糊規(guī)則用矩陣的形式表示,即構(gòu)建模糊關(guān)系矩陣;然后通過不同方法構(gòu)建模糊關(guān)系矩陣的模糊協(xié)方差矩陣;其次對模糊協(xié)方差矩陣進行主成分分析,提取模糊規(guī)則的主成分進而優(yōu)化模糊規(guī)則;最后根據(jù)優(yōu)化的模糊規(guī)則對亞馬遜股票的收盤價進行預(yù)測,驗證了算法的有效性。協(xié)方差矩陣非正定時,首先對非正定的協(xié)方差矩陣進行正定化,得到一個近似的正定相關(guān)矩陣代替原始協(xié)方差矩陣。其它步驟均與協(xié)方差矩陣正定時相同,最后通過對Alabama大學(xué)的入學(xué)人數(shù)進行預(yù)測,驗證了算法的有效性。本文將基于主成分分析的模糊時間序列優(yōu)化算法的應(yīng)用范圍進行了拓展,不僅使得算法同樣適用于協(xié)方差矩陣為非正定的情況,還提高了預(yù)測的精度;這充分說明新算法是有效的。
[Abstract]:Fuzzy time series model is a widely studied topic in the field of data prediction and analysis. Fuzzy time series have been successfully applied to the prediction of stock index, number of students, temperature and shipping index. In order to improve the prediction accuracy, many different fuzzy time series models and methods have been proposed. However, most of the methods are improved in different degrees around the division of the domain and the construction of fuzzy rules. In the actual prediction process, there is always correlation and redundancy between the fuzzy rules. This is not conducive to the simplification of prediction process and the improvement of prediction accuracy. Therefore, removing the correlation and redundancy between fuzzy rules is an urgent problem to be solved. In this paper, a fuzzy time series rule optimization algorithm based on principal component analysis (PCA) is proposed. In this paper, the algorithm is explained and verified from two different cases of covariance matrix positive definite and covariance matrix non-positive definite. When covariance matrix is positive definite, the fuzzy relation between data is first constructed to form fuzzy rules. The fuzzy rules are expressed in the form of matrix, that is, the fuzzy relation matrix is constructed, then the fuzzy covariance matrix of fuzzy relation matrix is constructed by different methods, and the principal component analysis of fuzzy covariance matrix is carried out. The main components of the fuzzy rules are extracted and the fuzzy rules are optimized. Finally, the closing price of Amazon stock is predicted according to the optimized fuzzy rules, and the validity of the algorithm is verified. When the covariance matrix is not positive definite, The nonpositive definite covariance matrix is transformed into positive definite matrix, and an approximate positive definite correlation matrix is obtained instead of the original covariance matrix. The other steps are the same as the positive timing of the covariance matrix. Finally, the number of students enrolled in Alabama University is predicted. The validity of the algorithm is verified. In this paper, the application scope of fuzzy time series optimization algorithm based on principal component analysis is extended, which not only makes the algorithm suitable for covariance matrix with non-positive definite, but also improves the precision of prediction. This fully shows that the new algorithm is effective.
【學(xué)位授予單位】：大連海事大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O159

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