基于栅格三元距离变换的GPS里程统计算法

为了提高GPS里程统计的精度,提出了一种基于栅格三元距离变换的GPS里程统计算法.首先,将离散的GPS轨迹数据映射成为连续的栅格序列,进而通过三元栅格子序列的空间排列定义距离变换算子,并基于统计分析建立距离变换算子的动态调整模型,进行误差补偿,最终实现高精度的GPS里程统计.为验证算法有效性,设置了连续线段法与栅格欧氏距离变换法两个传统里程统计算法作为对照组,进行里程统计对比实验.实验中,该算法里程统计误差均值约0.24％,标准差为0.55％.相较于对照组算法,该算法表现出了更好的误差特性,实现了更高的里程统计精度.     

CONTOUR: an efficient algorithm for discovering discriminating subsequences

In recent years we have witnessed several applications of frequent sequence mining, such as feature selection for protein sequence classification and mining block correlations in storage systems. In typical applications such as clustering, it is not the complete set but only a subset of discriminating frequent subsequences which is of interest. One approach to discovering the subset of useful frequent subsequences is to apply any existing frequent sequence mining algorithm to find the complete set of frequent subsequences. Then, a subset of interesting subsequences can be further identified. Unfortunately, it is very time consuming to mine the complete set of frequent subsequences for large sequence databases. In this paper, we propose a new algorithm, CONTOUR, which efficiently mines a subset of high-quality subsequences directly in order to cluster the input sequences. We mainly focus on how to design some effective search space pruning methods to accelerate the mining process and discuss how to construct an accurate clustering algorithm based on the result of CONTOUR. We conducted an extensive performance study to evaluate the efficiency and scalability of CONTOUR, and the accuracy of the frequent subsequence-based clustering algorithm.     

基于格代数的最长公共子序列近似求解

多条序列的最长公共子序列可以代表多条序列的公共信息,其在诸多领域里有着重要的应用,如信息检索、基因序列匹配等。求解多条序列的最长公共子序列是著名的NP难问题,本质为多解问题。一些近似算法虽然时间复杂度较低,但只能求出单解,对于有多解的序列集合,求得的结果信息量损失较大。因此提出一个新的近似算法来解决最长公共子序列问题。算法引入了代数结构“格”,通过动态规划求解出两条序列的公共格,并递归求解当前格与当前序列的公共格。公共格中的路径保存了多条公共子序列使得最终求解出的最长公共子序列为多个。对算法的相关定理给出了理论证明,并通过实验验证了算法的正确性。     

基于形状特征k-d树的多维时间序列相似搜索

多维时间序列是信息系统中一类重要的数据对象,相似搜索是其应用的一个核心.两个序列(子序列)相似度加以比较的常用方法是:将序列(子序列)转换成空间中的曲线,然后计算曲线间的欧几里德距离.这种方法的主要缺陷是它仅考虑了序列(子序列)间的整体距离关系,而不能体现它们自身的局部变化.针对此问题,提出了一种新的可应用于多维时间序列的快速相似搜索方法.该方法将序列(子序列)的局部变化特性与检索结构(k-d树)结合起来,使得在搜索k-d树的同时实现了序列(子序列)的局部变化匹配,从而极大地提高了查询效率和正确率.实验结果表明了算法的有效性.     

基于异时间窗划分的时间序列聚类

针对相同时间窗对时间序列进行子序列划分的缺点,提出一种异时间窗的子序列划分方法。为解决划分得到的子序列长度不同,而使用动态时间弯曲算法进行子序列相似性度量的计算速度慢的问题,给出一种不规则时间序列距离度量算法。对异时间窗的子序列划分方法和不规则时间序列距离度量算法进行了实验,结果证明了二者的优越性。     

HierarchyScan: A Hierarchical Algorithm for Similarity Search in Databases Consisting of Long Sequences

In this paper, a hierarchical algorithm, HierarchyScan, is proposed to efficiently locate one-dimensional subsequences within a collection of sequences with arbitrary length. The proposed algorithm performs correlation between the stored sequences and the template pattern in the transformed domain to identify subsequences in a scale- and phase-independent fashion. This is in contrast to those approaches based on the computation of Euclidean distance in the transformed domain. In the proposed hierarchical algorithm, the transformed domain representation of each original sequence is divided into multiple groups of coefficients. The matching is performed hierarchically from the group with the greatest filtering capability to the group with the lowest filtering capability. Only those subsequences whose maximum correlation value is higher than a predefined threshold will be selected for additional screening. This approach is compared to the sequential scanning and an order-of-magnitude speedup is observed.     

Training feedforward neural networks using multi-verse optimizer for binary classification problems

Discovering approximately recurrent motifs (ARMs) in timeseries is an active area of research in data mining. Exact motif discovery is defined as the problem of efficiently finding the most similar pairs of timeseries subsequences and can be used as a basis for discovering ARMs. The most efficient algorithm for solving this problem is the MK algorithm which was designed to find a single pair of timeseries subsequences with maximum similarity at a known length. This paper provides three extensions of the MK algorithm that allow it to find the top K similar subsequences at multiple lengths using both the Euclidean distance metric and scale invariant normalized version of it. The proposed algorithms are then applied to both synthetic data and real-world data with a focus on discovery of ARMs in human motion trajectories.     

Parameter-Free Search of Time-Series Discord

Time-series discord is widely used in data mining applications to characterize anomalous subsequences in time series. Compared to some other discord search algorithms, the direct search algorithm based on the recurrence plot shows the advantage of being fast and parameter free. The direct search algorithm, however, relies on quasi-periodicity in input time series, an assumption that limits the algorithm’s applicability. In this paper, we eliminate the periodicity assumption from the direct search algorithm by proposing a reference function for subsequences and a new sampling strategy based on the reference function. These measures result in a new algorithm with improved efficiency and robustness, as evidenced by our empirical evaluation.     

基于Segmental-DTW的无监督行为序列分割

行为序列分割是行为分析与识别中最初始、最基础的一个步骤.提出了一种无监督的行为序列分割算法,主要步骤包括:(1)采用等长有重叠的时间窗口对视频序列进行粗分割;(2)将粗分割的视频段两两作比较,通过Segmental-DTW算法分割出两个视频段中最相似的行为片断;(3)将行为片断的相似性转化为邻接图表示,通过图聚类方法对分割出的行为片断进行聚类.该算法采用了从粗到细的分割思想,能够准确地分割出视频序列中大量出现的行为的片断,并将相同行为的片断聚为一类.分割结果可以直接用于行为建模和识别.实验结果也表明了分割出的行为片断具有较好的代表性和有效性.     

Design and Performance Evaluation of Sequence Partition Algorithms

Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual solution optimality for realistic instances of an NP-hard problem is a factor in selecting algorithms in practice. We consider the problem of partitioning a sequence of n distinct numbers into minimum number of monotone （increasing or decreasing） subsequences. This problem is NP-hard and the number of monotone subsequences can reach [√2n＋1/1-1/2]in the worst case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no more than [√2n＋1/1-1/2]monotone subsequences in O（n^1.5） time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O（n^3）, a known greedy algorithm of time complexity O（n^1.5 log n）, and our new modified Yehuda-Fogel algorithm. Our results show that the solutions computed by the greedy algorithm and the modified Yehuda-Fogel algorithm are close to that computed by the approximation algorithm even though the theoretical worst-case error bounds of these two algorithms are not proved to be within a constant time of the optimal solution. Our study indicates that for practical use the greedy algorithm and the modified Yehuda-Fogel algorithm can be good choices if the running time is a major concern.     

A theoretical development for the total tardiness problem and its application in branch and bound algorithms

This paper deals with the single machine total tardiness problem, and proves that if the job sequences produced by two heuristics, named as Time Forward and Time Backward algorithms, have the same starting and ending job subsequences, then there exists an optimal job sequence with the starting and ending job subsequences. The computation experiments show that there is a significant improvement of the running time of a branch and bound algorithm with the incorporation of the new property.     

基于滑动窗口的多变量时间序列异常数据的挖掘

与其它多变量时间序列(MTS)子序列显著不同的子序列,称为异常子序列(含异常数据)。该文提出了一种基于滑动窗口的MTS异常子序列的挖掘算法,使用扩展的Frobenius 范数来计算两个MTS子序列之间相似性,使用两阶段顺序查询来进行K-近邻查找,将不可能成为候选异常子序列的MTS子序列剪去,对上海证券交易所股票交易情况MTS数据集进行了异常子序列(含异常数据)挖掘,结果表明了算法的有效性。     

时间序列中快速模式发现算法的研究

针对长时间序列,该文提出了一种新的能快速发现序列中时序模式的检索方法。首先将时间序列分成若干等长的子序列;接着从每个子序列中提取特征序列,该特征序列能够反映子序列中数据的变化趋势;然后根据每个特征序列将相应的子序列分配到一系列盒子中,使得不同盒子中的子序列因数据变化趋势不同而不相似,而在同一盒子中的序列由于数据变化趋势相同而有可能相似;最后通过计算每个盒子中任意两个子序列间的欧几里德距离来发现所有的模式。有关实验证明该算法是行之有效的。     

A fast projection algorithm for sequence data searching

In real life, data often appear in the form of sequences and this form of data is called sequence data. In this paper, a new definition on sequence similarity and a novel algorithm, Projection Algorithm, for sequence data searching are proposed. This algorithm is not required to access every datum in a sequence database. However, it guarantees that no qualified subsequence is falsely rejected. Moreover, the projection algorithm can be extended to match subsequences with different scales. With careful selection of parameters, most of the similar subsequences with different scales can be retrieved. We also show by experiments that the proposed algorithm can outperform the traditional sequential searching algorithm up to 96 times in terms of speed up.     

m子序列的密码学性质研究*

文中所提m子序列是根据m序列的状态转换特征,通过交叉改变状态转换次序而形成新的序列。通过随机性测试软件（NIST）验证m子序列具有和m序列相似的随机性,使用BM算法可以得出这种伪随机序列具有非常高的线性复杂度,同时验证了其补序列也具有非常高的线性复杂度,并说明m子序列具有良好的线性复杂度谱,抗线性攻击能力强。m子序列的数量庞大,一个周期为 的m序列,改变反馈函数就可以至少产生 个m子序列。产生m子序列的反馈函数经证明具有良好的代数免疫度,抗代数攻击能力较强。m子序列具有良好的密码学性质,应用前景良好。     

Partitioning a sequence into few monotone subsequences

In this paper we consider the problem of finding sets of long disjoint monotone subsequences of a sequence of numbers. We give an algorithm that, after preprocessing time, finds and deletes an increasing subsequence of size (if it exists) in time . Using this algorithm, it is possible to partition a sequence of numbers into monotone subsequences in time . Our algorithm yields improvements for two applications: The first is constructing good splitters for a set of lines in the plane. Good splitters are useful for two dimensional simplex range searching. The second application is in VLSI, where we seek a partitioning of a given graph into subsets, commonly refered to as the pages of a book, where all the vertices can be placed on the spine of the book, and each subgraph is planar. Received: 23 July 1990 / 19 June 1997     

Another look at the “longest ascending subsequence” problem

Summary Dijkstra has given a derivation of an efficient algorithm for a problem concerning monotonic subsequences, and extracted a proof of a related theorem from the algorithm. Here it is shown that a careful separation of concerns can lead to a beautiful conventional proof, a very different derivation of Dijkstra's algorithm, a more elegant proof from the algorithm, and the discovery of a duality property.     

基于小波滤波的时间序列子序列聚类

针对时间序列子序列聚类存在的平凡相似和水平伸缩等问题,提出了一种新的子序列聚类算法。它采用多孔平滑滤波器组对时间序列进行低通平滑处理,在所得到的多个尺度序列上生成平凡簇,然后将各个平凡簇的代表子序列作为数据样本进行聚类。新方法利用平凡簇克服了子序列聚类中的平凡相似问题,并且可以在时间序列上发现不等长的相似子序列,较好地解决了水平轴伸缩问题。实验结果证明新算法对于子序列聚类具有比较好的效果。     

基于散列和归并技术的有效并行排序方法

本文提出一个在共享存储多处理机系统上实现的快速、有效的并行排序算法：将长度为ｎ的待排序数据划分成ｐ个长度为ｎ／ｐ的子序列，引入散列技术并行地对这ｐ个子序列的数据进行二次散列排序，这一阶段所需的平均时间为Ｏ（ｎ／ｐ）；最后并行地将ｐ个有序子序列归并成一个长度为ｎ的有序序列，归并阶段所需的时间为Ｏ（ｎ－ｎ／
／ｐ）。整个排序算法的并行执行代价为Ｏ（ｎｐ）。本排序方法可以拓以网络并行机群环境。