时间序列与聚类挖掘相关技术研究
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摘要
数据挖掘及其应用已经渗透到多个学科，并在人工智能与机器学习、数据库、模式识别、生物信息学、神经计算等领域取得了丰硕的成果。同时，数据挖掘也不仅是科学家的兴趣所在，更多地得到了政府、工业界的密切关注。通过引入数据挖掘，可以大大提高生产力，取得社会的更大进步。世界上许多国家和地区的政府及工业界都希望掌握数据挖掘技术，提升国家和企业的科技含量，并最终取得领先的地位。
数据挖掘涉及的研究范围较为广泛，本文主要讨论了序列数据与聚类挖掘相关技术，主要的主要的研究成果如下：
(1)给出小波变换在时间序列相似性查找中对距离上下界的一个严格估计，同时说明传统的算法只是本文下界的一部分。根据本文给出的小波变换的下界，相对于传统的算法，可以排除更多的不相似序列。根据给出的上界，可以直接判断出两条序列是否相似，进一步减少需要验证的原始序列的个数。
(2)在使用小波变换缩减维度解决高维时间序列查询时，传统的算法均使用变换后小波序列的前k个系数作为原始时间序列的一个近似估计。但是由于选择前k个系数不一定能很好地近似原始序列集合，可能对于中间某些系数的选取，可以更好的给出原始序列集合的一个表示。因此给出相关定理，说明选择小波系数集合的列平方和最大的k列，可以更好近似原始序列集合。
(3)对允许时间偏移的序列间相似性搜索，由于可以处理异常数据以及允许不同长度的时间序列间进行匹配，因此应用日益广泛。但是大部分研究都是基于两条时间序列间的全相似性匹配。给出了基于动态规划的子序列相似性搜索算法，对于给定的查询序列，可以搜索到长序列中和给定的查询序列最为相似的一段子序列。并进一步给出了两种优化算法，以减少子序列相似性搜索中距离矩阵需要计算的项的个数。
(4)时间序列的相似性搜索可以看成度量空间搜索的一种特例。提出一种新的度量空间索引数据结构，简称为bu-tree，它是基于自底向上的分层聚类来构造索引结构，而传统的度量空间数据结构大部分是基于自顶向下构造的方法。相对于传统的构造方法，bu-tree可以在更小的索引半径内包含更多的对象，这样有利于查询的筛选。给出了bu-tree的构造算法以及相应的范围查询算法。
(5)数据概要被用来压缩大规模的数据库，以便进行后续的分层聚类分析。bu-tree中每个节点也可以看成是一种数据概要。讨论了另一种常用的数据概要：数据泡。详细研究了递增数据泡的质量度量标准(数据概要指标)。当更新数据库时，我们指出哪些因素会影响数据概要指标的期望与均方差。基于这些因素，给
出一个对数据泡进行递增维护的一个动态算法。
(6)讨论了系统级故障诊断中对测试序列的聚类分析算法。在基于聚类的集团理论的基础上，利用贪婪算法中不同贪婪准则提出了四个针对系统及故障的概率诊断算法。每种算法在较少的测试数情况下，均表现出较高的诊断正确率，且时间复杂度不高。
Recently, data mining and its applications have already come into many disciplines and achieved plentiful fruits in diversified fields, including artificial intelligence and machine learning, database, pattern recognition, bioinformatics, neural computing, and so on. It not only appeals scientists but also catches the attention from governments and industries. The governments, industrial communities, and academic fields are so keen on mastering data mining techniques that they have invested a large deal of money and energy on the corresponding research. Therefore, the progress of data mining will promote the development of science and society.
Data mining have many research fields. In this dissertation, we focus on time series and cluster technology. The main works and contributions of the dissertation are summarized as follows:
(1) Wavelet transforms are used as a dimensionality reduction technique to permit efficient similarity search over high-dimensional time series data. This dissertation proposes the tight upper and lower bounds on the estimation distance using wavelet transform, and we show that the traditional distance estimation is only part of our lower bound. According to the lower bound, we can exclude more dissimilar time series than traditional method. And according to the upper bound, we can directly judge whether two time series are similar, and further reduce the number of time series to process in original time domain. The experiments have shown that using the upper and lower tight bounds can significantly improve filter efficiency and reduce running time than traditional method.
(2) For wavelet transform used in dimensional reduction, the traditional algorithms use the first k wavelet coefficients as an approximation of the original time series data set. But it is possible that choosing first k coefficients is not optimal, and perhaps choosing other k coefficients is better than the first k. A new method is proposed to better approximating the original time series data set. The main idea of the method is to choose the same k columns of the wavelet time series data set which have the maximum square sum. The experiments have shown that our method can reduce the relative error compared to traditional algorithms.
(3) Similarity search for time series under dynamic time shifting is prevailing. But most recent research focused on the full length similarity match of two time series.
A new basic subsequence similarity search algorithm based on dynamic programming is proposed. For a given query time series, the algorithm can find out the most similar subsequence in a long time series. Furthermore two improved algorithms are also given. They can reduce the computation amount of the distance matrix for subsequence similarity search. Experiments on real and synthetic data sets show that the improved algorithms can significantly reduce the computation amount and running time compared to the basic algorithm.
(4) Similarity search in many new database applications can generally be referred as similarity search in metric space. Time series can be seen as one application in metric space. A new index construction algorithm is proposed for similarity search in metric space. The new data structure, called bu-tree (bottom-up tree), is based on constructing the index tree from bottom-up, rather than the traditional top-down approaches. The construction algorithm of bu-tree and the range search algorithm based on it are given. And the update to bu-tree is also discussed. The experiments show that bu-tree is better than sa-tree in search efficiency, especially when the objects are not uniform distributed or the query has low selectivity.
(5) In many real world applications, with the databases frequent insertions and deletions, the ability of a data mining technique to detect and react quickly to dynamic changes in the data distribution and clustering over time is highly desired. Data summarizations (e.g., data bubbles) have been proposed to compress large databases into representative points suitable for subsequent hierarchical cluster analysis. We thoroughly investigate the quality measure (data summarization index) of incremental data bubbles. When updating databases, we show which factors could affect the mean and standard deviation of data summarization index or not. Based on these statements, a fully dynamic scheme to maintain data bubbles incrementally is proposed. An extensive experimental evaluation confirms our statements and shows that the fully dynamic incremental data bubbles are effective in preserving the quality of the data summarization for hierarchical clustering.
(6) Probabilistic diagnosis algorithm is very important in the system level fault diagnosis research. Based on cluster theory, we propose four probabilistic algorithms using greedy algorithm for system-level fault diagnosis. By computer simulation, it is shown that these diagnosis algorithms can achieve a high probability of correct under low time complexity. The greedy algorithm one has the best performance in the four
probabilistic algorithms. The results also indicate that our algorithms have better performance than the Compete algorithm and Majority algorithm, which are classic probabilistic algorithms in system level fault diagnosis.
数据挖掘涉及的研究范围较为广泛，本文主要讨论了序列数据与聚类挖掘相关技术，主要的主要的研究成果如下：
(1)给出小波变换在时间序列相似性查找中对距离上下界的一个严格估计，同时说明传统的算法只是本文下界的一部分。根据本文给出的小波变换的下界，相对于传统的算法，可以排除更多的不相似序列。根据给出的上界，可以直接判断出两条序列是否相似，进一步减少需要验证的原始序列的个数。
(2)在使用小波变换缩减维度解决高维时间序列查询时，传统的算法均使用变换后小波序列的前k个系数作为原始时间序列的一个近似估计。但是由于选择前k个系数不一定能很好地近似原始序列集合，可能对于中间某些系数的选取，可以更好的给出原始序列集合的一个表示。因此给出相关定理，说明选择小波系数集合的列平方和最大的k列，可以更好近似原始序列集合。
(3)对允许时间偏移的序列间相似性搜索，由于可以处理异常数据以及允许不同长度的时间序列间进行匹配，因此应用日益广泛。但是大部分研究都是基于两条时间序列间的全相似性匹配。给出了基于动态规划的子序列相似性搜索算法，对于给定的查询序列，可以搜索到长序列中和给定的查询序列最为相似的一段子序列。并进一步给出了两种优化算法，以减少子序列相似性搜索中距离矩阵需要计算的项的个数。
(4)时间序列的相似性搜索可以看成度量空间搜索的一种特例。提出一种新的度量空间索引数据结构，简称为bu-tree，它是基于自底向上的分层聚类来构造索引结构，而传统的度量空间数据结构大部分是基于自顶向下构造的方法。相对于传统的构造方法，bu-tree可以在更小的索引半径内包含更多的对象，这样有利于查询的筛选。给出了bu-tree的构造算法以及相应的范围查询算法。
(5)数据概要被用来压缩大规模的数据库，以便进行后续的分层聚类分析。bu-tree中每个节点也可以看成是一种数据概要。讨论了另一种常用的数据概要：数据泡。详细研究了递增数据泡的质量度量标准(数据概要指标)。当更新数据库时，我们指出哪些因素会影响数据概要指标的期望与均方差。基于这些因素，给
出一个对数据泡进行递增维护的一个动态算法。
(6)讨论了系统级故障诊断中对测试序列的聚类分析算法。在基于聚类的集团理论的基础上，利用贪婪算法中不同贪婪准则提出了四个针对系统及故障的概率诊断算法。每种算法在较少的测试数情况下，均表现出较高的诊断正确率，且时间复杂度不高。
Recently, data mining and its applications have already come into many disciplines and achieved plentiful fruits in diversified fields, including artificial intelligence and machine learning, database, pattern recognition, bioinformatics, neural computing, and so on. It not only appeals scientists but also catches the attention from governments and industries. The governments, industrial communities, and academic fields are so keen on mastering data mining techniques that they have invested a large deal of money and energy on the corresponding research. Therefore, the progress of data mining will promote the development of science and society.
Data mining have many research fields. In this dissertation, we focus on time series and cluster technology. The main works and contributions of the dissertation are summarized as follows:
(1) Wavelet transforms are used as a dimensionality reduction technique to permit efficient similarity search over high-dimensional time series data. This dissertation proposes the tight upper and lower bounds on the estimation distance using wavelet transform, and we show that the traditional distance estimation is only part of our lower bound. According to the lower bound, we can exclude more dissimilar time series than traditional method. And according to the upper bound, we can directly judge whether two time series are similar, and further reduce the number of time series to process in original time domain. The experiments have shown that using the upper and lower tight bounds can significantly improve filter efficiency and reduce running time than traditional method.
(2) For wavelet transform used in dimensional reduction, the traditional algorithms use the first k wavelet coefficients as an approximation of the original time series data set. But it is possible that choosing first k coefficients is not optimal, and perhaps choosing other k coefficients is better than the first k. A new method is proposed to better approximating the original time series data set. The main idea of the method is to choose the same k columns of the wavelet time series data set which have the maximum square sum. The experiments have shown that our method can reduce the relative error compared to traditional algorithms.
(3) Similarity search for time series under dynamic time shifting is prevailing. But most recent research focused on the full length similarity match of two time series.
A new basic subsequence similarity search algorithm based on dynamic programming is proposed. For a given query time series, the algorithm can find out the most similar subsequence in a long time series. Furthermore two improved algorithms are also given. They can reduce the computation amount of the distance matrix for subsequence similarity search. Experiments on real and synthetic data sets show that the improved algorithms can significantly reduce the computation amount and running time compared to the basic algorithm.
(4) Similarity search in many new database applications can generally be referred as similarity search in metric space. Time series can be seen as one application in metric space. A new index construction algorithm is proposed for similarity search in metric space. The new data structure, called bu-tree (bottom-up tree), is based on constructing the index tree from bottom-up, rather than the traditional top-down approaches. The construction algorithm of bu-tree and the range search algorithm based on it are given. And the update to bu-tree is also discussed. The experiments show that bu-tree is better than sa-tree in search efficiency, especially when the objects are not uniform distributed or the query has low selectivity.
(5) In many real world applications, with the databases frequent insertions and deletions, the ability of a data mining technique to detect and react quickly to dynamic changes in the data distribution and clustering over time is highly desired. Data summarizations (e.g., data bubbles) have been proposed to compress large databases into representative points suitable for subsequent hierarchical cluster analysis. We thoroughly investigate the quality measure (data summarization index) of incremental data bubbles. When updating databases, we show which factors could affect the mean and standard deviation of data summarization index or not. Based on these statements, a fully dynamic scheme to maintain data bubbles incrementally is proposed. An extensive experimental evaluation confirms our statements and shows that the fully dynamic incremental data bubbles are effective in preserving the quality of the data summarization for hierarchical clustering.
(6) Probabilistic diagnosis algorithm is very important in the system level fault diagnosis research. Based on cluster theory, we propose four probabilistic algorithms using greedy algorithm for system-level fault diagnosis. By computer simulation, it is shown that these diagnosis algorithms can achieve a high probability of correct under low time complexity. The greedy algorithm one has the best performance in the four
probabilistic algorithms. The results also indicate that our algorithms have better performance than the Compete algorithm and Majority algorithm, which are classic probabilistic algorithms in system level fault diagnosis.
引文
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