基于粒計(jì)算的時(shí)間序列分析與建模方法研究
本文選題:粒計(jì)算 + 多粒度區(qū)間信息;; 參考:《大連理工大學(xué)》2015年博士論文
【摘要】:在當(dāng)今大數(shù)據(jù)時(shí)代,個(gè)體樣本數(shù)據(jù)不再是關(guān)注的焦點(diǎn),而對(duì)數(shù)據(jù)的理解和認(rèn)知要遠(yuǎn)比個(gè)體樣本數(shù)據(jù)重要。傳統(tǒng)的時(shí)間序列建模方法由于(1)其建模過程過分依賴于個(gè)體樣本數(shù)據(jù)使得所構(gòu)建的模型缺乏“可解釋性”;(2)所構(gòu)建的模型是以追求“數(shù)值”層面的“精確性”為目標(biāo),然而在大數(shù)據(jù)環(huán)境下,模型的精確性不是絕對(duì)必要的;(3)所構(gòu)建的模型的輸出是單一的數(shù)值數(shù)據(jù),這在大數(shù)據(jù)環(huán)境下很難為用戶所理解和認(rèn)知,因而,它已不能完全滿足當(dāng)今大數(shù)據(jù)時(shí)代背景下的時(shí)間序列分析和建模的實(shí)際應(yīng)用需要。作為當(dāng)前計(jì)算智能領(lǐng)域新興的、發(fā)展最快的信息處理范式之一,“粒計(jì)算”具有揭示人類處理復(fù)雜信息的粒化認(rèn)知機(jī)理的能力,它能夠?qū)⒕哂胁煌碚摶A(chǔ)的形式體系(如集合論、模糊集、粗糙集等)聯(lián)系到一起,形成一個(gè)統(tǒng)一的表示、描述、計(jì)算和處理信息粒的平臺(tái),這有可能誕生新的計(jì)算智能理論與方法。在這一背景下,本文從模擬人類處理復(fù)雜信息問題的;J(rèn)知機(jī)理出發(fā),借鑒模糊集理論思想和建模方法,緊緊圍繞基于粒計(jì)算的時(shí)間序列分析和建模的三個(gè)核心問題——時(shí)間序列的合理信息粒化、基于信息;臅r(shí)間序列分析與解釋和基于信息;臅r(shí)間序列建模,開展了研究,獲得的主要研究成果包括:(1)針對(duì)在時(shí)間序列信息;^程中,傳統(tǒng)的信息粒化方法只能對(duì)時(shí)間窗口上的數(shù)據(jù)在單一信息粒度水平下進(jìn)行信息;,這可能導(dǎo)致產(chǎn)生的信息粒無法捕獲相應(yīng)數(shù)據(jù)的本質(zhì)特征這一問題,提出了時(shí)間序列的多粒度區(qū)間信息粒化方法。所提出的粒化方法能夠在區(qū)間形式體系下,通過引入信息粒的合理性和特殊性概念,將時(shí)間序列在相應(yīng)時(shí)間窗口上信息粒的合理構(gòu)造問題轉(zhuǎn)換為一個(gè)受變量α∈[0,1]約束的區(qū)間信息粒邊界的優(yōu)化問題,而變量a則代表了對(duì)時(shí)間序列相應(yīng)時(shí)間窗口上的數(shù)據(jù)進(jìn)行信息;瘯r(shí)所使用的信息粒度水平。通過在不同的α取值下,對(duì)該優(yōu)化問題進(jìn)行求解,來誘導(dǎo)相應(yīng)α信息粒度水平下的區(qū)間信息粒,即可實(shí)現(xiàn)對(duì)時(shí)間序列同一時(shí)間窗口上所呈現(xiàn)數(shù)據(jù)的多粒度信息粒化。使用提出的多粒度區(qū)間信息粒化方法;瘮(shù)據(jù)時(shí),將產(chǎn)生一系列嵌套的區(qū)間信息粒,它們能夠被看成一個(gè)整體,即區(qū)間套信息粒,它代表了時(shí)間序列相應(yīng)時(shí)間窗口上所呈現(xiàn)的數(shù)據(jù)在不同信息粒度水平下進(jìn)行區(qū)間信息;慕Y(jié)果。(2)針對(duì)時(shí)間序列的粒化分析與解釋問題,提出了一種粒特征空間中具有“嵌套”矩形幾何結(jié)構(gòu)的“矩形套信息!钡木垲惙椒āT摲椒◤膸缀谓嵌,揭示了在粒特征空間中,由時(shí)間序列的幅值和它的一階差分序列分別經(jīng)過“多粒度區(qū)間信息;彼纬傻摹熬匦翁仔畔⒘!钡慕Y(jié)構(gòu)特征和它的表示方法,并借鑒模糊C-均值聚類的方法,利用矩形套信息粒的可分解和可合成特性,實(shí)現(xiàn)了對(duì)粒特征空間中與時(shí)間窗口相關(guān)的矩形套信息粒的聚類。更進(jìn)一步,考慮在粒特征空間中所形成的粒原型蘊(yùn)含著描述時(shí)間序列在相應(yīng)時(shí)間窗口上所呈現(xiàn)數(shù)據(jù)動(dòng)態(tài)特征的語義,這樣,可通過計(jì)算粒特征空間中與時(shí)間窗口相關(guān)的矩形套信息粒同這些粒原型之間的匹配程度來實(shí)現(xiàn)基于信息;臅r(shí)間序列分析與解釋。多組時(shí)間序列數(shù)據(jù)集上的實(shí)驗(yàn)結(jié)果表明,基于提出的矩形套信息粒的聚類方法去分析和解釋時(shí)間序列與人從;J(rèn)知機(jī)理出發(fā)去分析時(shí)間序列所獲得的結(jié)果完全一致。(3)提出了基于多粒度區(qū)間信息;臅r(shí)間序列層次化建模方法和兩個(gè)時(shí)間序列粒模型性能評(píng)價(jià)指標(biāo),實(shí)現(xiàn)了時(shí)間序列的;。所提出的;7椒◤娜祟愄幚韽(fù)雜信息問題的;J(rèn)知機(jī)理出發(fā),在考慮時(shí)間序列的幅值和它的一階差分序列的基礎(chǔ)上,充分借鑒了模糊建模的基本思想,通過“多粒度區(qū)間信息;眮韷嚎s時(shí)間序列規(guī)模,并將原始時(shí)間序列轉(zhuǎn)換為粒時(shí)間序列;通過對(duì)粒特征空間中的矩形套信息粒進(jìn)行聚類來獲得用于描述時(shí)間序列在相應(yīng)時(shí)間窗口上所呈現(xiàn)數(shù)據(jù)動(dòng)態(tài)特征的語義描述,從而將領(lǐng)域知識(shí)融入到建模過程中;通過挖掘時(shí)間序列相應(yīng)時(shí)間窗口在粒特征空間中形成的矩形套信息粒之間的動(dòng)態(tài)因果關(guān)系形成時(shí)間序列粒模型。相關(guān)的實(shí)驗(yàn)結(jié)果表明,依據(jù)本文提出的基于多粒度區(qū)間信息;臅r(shí)間序列層次化建模方法所構(gòu)建的模糊認(rèn)知圖時(shí)間序列粒模型具有良好的可解釋性,其輸出是一個(gè)具有語義描述的信息粒(區(qū)間),反映了時(shí)間序列在相應(yīng)時(shí)間窗口上數(shù)據(jù)的整體動(dòng)態(tài)特征(語義)和變化范圍(區(qū)間),這更容易被用戶理解和認(rèn)知,從而為用戶做出合理的決策提供有效的支撐。
[Abstract]:In today's large data age, individual sample data is no longer the focus of attention, and understanding and cognition of data is much more important than individual sample data. The traditional time series modeling method is due to (1) its modeling process is too dependent on individual sample data to make the model constructed without "interpretability"; (2) the model is constructed. In order to pursue the "accuracy" of the "numerical" level, the accuracy of the model is not absolutely necessary in the large data environment; (3) the output of the model is a single numerical data, which is difficult for the users to understand and cognate in the large data environment, because it can not fully meet the background of today's big data age. The time series analysis and the practical application of modeling are needed. As one of the emerging and fastest developing information processing paradigms in the field of computational intelligence, "granular computing" has the ability to reveal the granulation mechanism of human processing complex information. It can make the formal systems with different theoretical foundations (such as set theory, fuzzy set, rough set, etc.). To form a unified platform for representation, description, calculation and processing of information particles, it is possible to create a new theory and method of computing intelligence. In this context, this paper, starting from the simulation of the granular cognitive mechanism for dealing with complex information problems, draws on the theory of fuzzy sets and modeling methods, closely surrounding the particle based on particles. The three core issues of time series analysis and modeling, the rational information granulation of time series, time series analysis and interpretation based on information granulation and time series modeling based on information granulation, are carried out. The main achievements are as follows: (1) in the process of granulation of time series information, the traditional letter The granulation method can only grained information on a single information granularity level on the time window, which may lead to the problem that the generated information can not capture the essential characteristics of the corresponding data, and proposes a multi granularity interval information granulation method of time series. The proposed granulation method can be used in the interval form system. By introducing the concept of rationality and particularity of information particles, the rational construction of time series of information particles on the corresponding time window is converted into an optimization problem of the interval information particle boundary of a variable [0,1] constraint, while the variable a represents the use of the information granulation of the data on the corresponding time window. The level of information granularity. By solving the optimization problem under different alpha values to induce the interval information particles at the level of corresponding alpha information granularity, the multi granularity information of the data presented on the same time window can be realized. A series of nested interval information particles, which can be considered as a whole, that is, the interval set of information particles, which represents the result of the interval information granulation of the data presented on the corresponding time window at the level of different information granularity. (2) a particle feature space is proposed for the problem of the granulation analysis and interpretation of time series. The clustering method of "rectangle set of information particles" with "nested" rectangular geometric structure is used in this method to reveal the structural features of "rectangular set of information particles" formed by the "multi granularity interval information granulation" from the amplitude of time series and the first order difference sequence of its first order difference sequence in grain feature space from the geometric point of view. By using the method of fuzzy C- means clustering, and using the decomposition and synthesis characteristics of the rectangle set of information particles, the clustering of the rectangle set of information related to the time window in the granular feature space is realized. The semantics of the dynamic characteristics of the data are presented so that the time series analysis and interpretation based on the information granulation can be realized by calculating the matching degree of the rectangular set of information particles related to the time window in the grain feature space and the matching degree between the particles. The experimental results on the multi group time series data set show that the proposed rectangle information is based on the experimental results. The clustering method of grain is used to analyze and explain the time series and the results obtained from the analysis of time series from the granulated cognitive mechanism. (3) a hierarchical modeling method of time series based on multi granularity interval information granulation and the performance evaluation index of two time sequence grain models are proposed, and the granulation modeling of time series is realized. On the basis of the magnitude of time series and its first order difference sequence, the proposed granulation modeling method, based on the magnitude of time series and its first order difference sequence, fully draws on the basic idea of fuzzy modeling and compresses the scale of time series by "granulation of multi granularity interval information", and turns the original time series. It is replaced by a grain time sequence; a semantic description of the dynamic characteristics of the data used to describe the time series on the corresponding time window is obtained by clustering the rectangular set of information particles in the grain feature space, and the domain knowledge is incorporated into the modeling process, and the corresponding time window is formed in the granular feature space by mining the time sequence. The experimental results show that the time series model of fuzzy cognitive map based on the hierarchical modeling method of time series based on multi granularity interval information granulation proposed in this paper has good interpretability, and its output is a language. The information particle (interval) described in semantic description reflects the overall dynamic characteristics (semantics) and variation range (interval) of the time series of data on the corresponding time window, which is more easily understood and recognized by the user, thus providing effective support for the user to make a reasonable decision.
【學(xué)位授予單位】:大連理工大學(xué)
【學(xué)位級(jí)別】:博士
【學(xué)位授予年份】:2015
【分類號(hào)】:TP18;O211.61
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