本文選題：多維時(shí)間序列 + 相似性度量��； 參考：《浙江大學(xué)》2017年碩士論文

【摘要】：多維時(shí)間序列是現(xiàn)實(shí)中廣泛存在的一種數(shù)據(jù)類型,因而對(duì)多維時(shí)間序列的分析和數(shù)據(jù)挖掘有著重要的意義。相似性度量作為多維時(shí)間序列分析的關(guān)鍵之一,現(xiàn)有的方法存在諸多不足。本文提出一種計(jì)算多維時(shí)間序列相似度的方法,將衡量單維時(shí)間序列相似度的DTW擴(kuò)展至多維時(shí)間序列,并結(jié)合度量學(xué)習(xí)算法LMNN,進(jìn)而得到對(duì)多維時(shí)間序列更好的相似性度量效果。本文主要的研究工作如下:(1)DTW是計(jì)算單維時(shí)間序列相似度的常用方法,其主要缺陷是存在奇異點(diǎn)和高時(shí)間復(fù)雜度的問(wèn)題。本文首先針對(duì)DTW的奇異點(diǎn)問(wèn)題提出一種改進(jìn)方法:通過(guò)同時(shí)考慮時(shí)間序列的數(shù)值信息和梯度信息來(lái)構(gòu)造新的特征,在不引入額外參數(shù)的條件下解決奇異點(diǎn)問(wèn)題(稱為SDTW)。然后,將特征提取和降維算法PLA與SDTW相結(jié)合來(lái)解決DTW的高時(shí)間復(fù)雜度問(wèn)題(稱為PLA-SDTW)。仿真對(duì)比實(shí)驗(yàn)驗(yàn)證了 SDTW在有效解決DTW奇異點(diǎn)問(wèn)題的同時(shí),能夠提高度量的準(zhǔn)確性。進(jìn)一步地,在保證與SDTW近乎相同度量效果的同時(shí),PLA-SDTW的時(shí)間消耗遠(yuǎn)遠(yuǎn)小于其他方法。(2)為了度量多維時(shí)間序列的相似性,需要將DTW從單維擴(kuò)展到多維,并需要同時(shí)解決多個(gè)變量之間的相關(guān)性度量。度量學(xué)習(xí)方法(如常用的LMNN)能夠從訓(xùn)練集學(xué)習(xí)得到特征空間中更好的距離度量準(zhǔn)則。本文將DTW與LMNN相結(jié)合得到LMNN-DTW模型,用來(lái)度量多維時(shí)間序列的相似度。首先,使用基于馬氏距離的DTW來(lái)度量多維時(shí)間序列的相似性,通過(guò)馬氏矩陣來(lái)表示多個(gè)變量之間的相關(guān)性度量。然后,使用LMNN算法,通過(guò)最小化特定的損失函數(shù),來(lái)優(yōu)化得到馬氏矩陣。仿真對(duì)比實(shí)驗(yàn)驗(yàn)證了 LMNN-DTW的效果與當(dāng)前最好的LDML-DTW方法相近,且明顯好于其他方法,從而證明了該模型的有效性和優(yōu)越性。(3)考慮到前文提出的SDTW能夠有效地解決DTW奇異點(diǎn)問(wèn)題,且具有更好的度量準(zhǔn)確性,因此用SDTW替換DTW,與LMNN結(jié)合得到LMNN-SDTW模型。仿真實(shí)驗(yàn)驗(yàn)證了 LMNN-SDTW的效果與當(dāng)前最好的LDML-DTW方法相近,且優(yōu)于LMNN-DTW,同時(shí)明顯好于其他方法,從而證明了 LMNN-SDTW模型對(duì)多維時(shí)間序列相似性度量的優(yōu)越性。
[Abstract]:Multi-dimensional time series is a widely existing data type in reality, so it is of great significance to the analysis and data mining of multidimensional time series. Similarity measurement is one of the key problems in multidimensional time series analysis. In this paper, a method to calculate the similarity of multidimensional time series is proposed. The DTW which measures the similarity of one-dimensional time series is extended to multi-dimensional time series, and the measurement learning algorithm LMNNs is combined to obtain a better similarity measurement effect for multi-dimensional time series. The main research work of this paper is as follows: 1 / 1 DTW is a common method to calculate the similarity of single dimensional time series. Its main defect is the existence of singularity and high time complexity. In this paper, an improved method is proposed to solve the singular point problem of DTW by taking into account the numerical and gradient information of time series at the same time to construct new features, and to solve the singular point problem without introducing additional parameters. Then, the feature extraction and dimension reduction algorithm PLA and SDTW are combined to solve the high time complexity problem of DTW (PLA-SDT WN). The simulation results show that SDTW can effectively solve the singular point problem of DTW and improve the accuracy of measurement. Furthermore, the time consumption of PLA-SDTW is much smaller than that of other methods while ensuring the same measurement effect as SDTW.) in order to measure the similarity of multidimensional time series, it is necessary to extend DTW from one-dimensional to multi-dimensional. We also need to solve the correlation measure of multiple variables at the same time. Metric learning methods, such as LMNNs, can obtain better distance metrics in feature spaces from training sets. In this paper, we combine DTW and LMNN to obtain the LMNN-DTW model, which is used to measure the similarity of multidimensional time series. Firstly, the DTW based on Markov distance is used to measure the similarity of multi-dimensional time series, and the correlation measure between multiple variables is represented by Markov matrix. Then, LMNN algorithm is used to optimize the Markov matrix by minimizing the specific loss function. The simulation results show that the effect of LMNN-DTW is close to that of the best LDML-DTW method, and it is obviously better than other methods, which proves the validity and superiority of the model. (3) taking into account the above mentioned SDTW, the singularity point problem of DTW can be solved effectively. And it has better measurement accuracy, so the LMNN-SDTW model is obtained by replacing DTW with SDTW and combining with LMNN. The simulation results show that the effectiveness of LMNN-SDTW is similar to that of the best LDML-DTW method, and is better than that of LMNN-DTW, and it is also better than other methods, which proves the superiority of LMNN-SDTW model in measuring the similarity of multidimensional time series.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211.61

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