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| 面向数据流的多粒度时变分形维数计算 |
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倪志伟1,2, 王超1,2,3, 胡汤磊1,2, 倪丽萍1,2
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1.合肥工业大学 管理学院, 安徽 合肥 230009;2.教育部过程优化与智能决策重点实验室合肥工业大学, 安徽 合肥 230009;3.安徽农业大学 信息与计算机学院, 安徽 合肥 230036
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| 摘要: |
| 在大数据时代,数据流是一种常见的数据模型,具有有序、海量、时变等特点.分形是许多复杂系统的重要特征,分形维数是度量系统分形特征的重要指标量.数据流作为动态的复杂系统,其上的分形维数应具有动态、时变、多粒度等特性.提出了多粒度时变分形维数的概念,并设计了基于小波变换技术的数据流多粒度时变分形维数算法.该算法通过对数据流进行离散小波变换,并利用多粒度小波变换树结构在内存中保存数据流的概要信息,可以同时在不同的时间粒度上实时地计算数据流时变分形维数.该方法具有较低的计算复杂度,实验结果表明:该方法可以有效地监控数据流分形维数在不同粒度上的时变特征,深刻地揭示数据流的演化规律. |
| 关键词: 数据流 分形维数 小波变换 多粒度 时变性 |
| DOI：10.13328/j.cnki.jos.004806 |
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| 基金项目:国家自然科学基金(71271071,71301041);国家高技术研究发展计划(863)(2011AA040501) |
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| Multi-Granularity and Time-Varying Fractal Dimension on Data Stream |
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NI Zhi-Wei1,2, WANG Chao1,2,3, HU Tang-Lei1,2, NI Li-Ping1,2
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1.School of Management, Hefei University of Technology, Hefei 230009, China;2.Key Laboratory of Process Optimization and Intelligent Decision-Making of the Ministry of Education Hefei University of Technology, Hefei 230009, China;3.School of Information and Computer, Anhui Agricultural University, Hefei 230036, China
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| Abstract: |
| In the era of big data, data stream is a common data model with characteristics such as orderly, massive and time-varying. Fractal is an important feature of many complex systems, and is mainly represented by fractal dimension. Data stream can be viewed as a dynamic and complex system, and its fractal dimension should also have characteristics of dynamic, time-varying and multi-granularity. This paper presents a method of measuring multi-granularity and time-varying fractal dimension on a data stream based on discrete wavelet transform. The method can simultaneously measure the time-varying fractal dimension on a data stream by using the summary information from wavelet transforming of the data stream saved in a multi-granularity wavelet transforming tree in memory. This method has low computational complexity, and effectively reveals the evolution of a data stream. Experimental results show that it can effectively monitor the time-varying characteristic of fractal dimension on a data stream at different granularity. |
| Key words: data stream fractal dimension wavelet transform multi-granularity time-varying |
