Sketching asynchronous data streams over sliding windows

We study the problem of maintaining a sketch of recent elements of a data stream. Motivated by applications involving network data, we consider streams that are asynchronous, in which the observed order of data is not the same as the time order in which the data was generated. The notion of recent elements of a stream is modeled by the sliding timestamp window, which is the set of elements with timestamps that are close to the current time. We design algorithms for maintaining sketches of all elements within the sliding timestamp window that can give provably accurate estimates of two basic aggregates, the sum and the median, of a stream of numbers. The space taken by the sketches, the time needed for querying the sketch, and the time for inserting new elements into the sketch are all polylogarithmic with respect to the maximum window size. Our sketches can be easily combined in a lossless and compact way, making them useful for distributed computations over data streams. Previous works on sketching recent elements of a data stream have all considered the more restrictive scenario of synchronous streams, where the observed order of data is the same as the time order in which the data was generated. Our notion of recency of elements is more general than that studied in previous work, and thus our sketches are more robust to network delays and asynchrony. The work of the authors was supported in part through NSF grants CNS 0520102 and CNS 0520009. A preliminary version of this paper appeared in Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC) 2006, pages 82–91. Work done while the third author was at Rensselaer Polytechnic Institute. Authors are listed in reverse alphabetical order.     

动态滑动窗口的数据流聚类方法

数据流聚类是聚类分析中的重要问题。针对数据流的流速是变化的问题,在两阶段聚类框架基础上提出基于动态滑动窗口的数据流聚类算法。在线阶段,引入微聚类特征来存储数据流的概要信息,利用存储的概要信息动态调整滑动窗口规模,并计算数据点与微聚类中心的距离,以维护微聚类特征;离线阶段,对在线聚类阶段的聚类结果采用K-means算法进行宏聚类,生成最终聚类。实验结果表明,该算法具有较高的聚类质量和较好的伸缩性。     

有效的基于滑动窗口数据流直方图方法

差分隐私作为现在的一种隐私保护机制得到了广泛的应用.目前虽然存在着很多种静态数据集上的直方图发布方法,但是对于数据流环境下的基于滑动窗口直方图发布方法较少,并且面临着直方图的发布误差较高的问题.对于此问题,提出了一种适用于滑动窗口模型的数据流差分隐私直方图发布算法(histogram pub-lishing algorithm for sliding window model,HPA-SW).该算法首先基于数据分块的思想来把一个滑动窗口划分为k个子块,并通过该参数来控制和调节数据直方图的统计误差;随后,该算法通过比较相邻两个直方图数据分布的差异来优化当前窗口的隐私预算分配,从而快速计算出局部最优直方图.为了验证算法的有效性,首先通过严格的理论推导证实了所设计的算法符合差分隐私要求,并且其近似误差不超过W/2k.其次,通过在真实数据集合上的实验对比,显示了该算法的发布误差较低,比SSHP算法降低了50％.     

Clustering distributed data streams in peer-to-peer environments

This paper describes a technique for clustering homogeneously distributed data in a peer-to-peer environment like sensor networks. The proposed technique is based on the principles of the K-Means algorithm. It works in a localized asynchronous manner by communicating with the neighboring nodes. The paper offers extensive theoretical analysis of the algorithm that bounds the error in the distributed clustering process compared to the centralized approach that requires downloading all the observed data to a single site. Experimental results show that, in contrast to the case when all the data is transmitted to a central location for application of the conventional clustering algorithm, the communication cost (an important consideration in sensor networks which are typically equipped with limited battery power) of the proposed approach is significantly smaller. At the same time, the accuracy of the obtained centroids is high and the number of samples which are incorrectly labeled is also small.     

Warping the time on data streams

Continuously monitoring through time the correlation/distance of multiple data streams is of interest in a variety of applications, including financial analysis, video surveillance, and mining of biological data. However, distance measures commonly adopted for comparing time series, such as Euclidean and Dynamic Time Warping (DTW), either are known to be inaccurate or are too time-consuming to be applied in a streaming environment. In this paper we propose a novel DTW-like distance measure, called Stream-DTW (SDTW), which unlike DTW can be efficiently updated at each time step. We formally and experimentally demonstrate that SDTW speeds up the monitoring process by a factor that grows linearly with the size of the window sliding over the streams. For instance, with a sliding window of 512 samples, SDTW is about 600 times faster than DTW. We also show that SDTW is a tight approximation of DTW, errors never exceeding 10%, and that it consistently outperforms approximations developed for the case of static time series.     

Mining evolving data streams for frequent patterns

A data stream is a potentially uninterrupted flow of data. Mining this flow makes it necessary to cope with uncertainty, as only a part of the stream can be stored. In this paper, we evaluate a statistical technique which biases the estimation of the support of patterns, so as to maximize either the precision or the recall, as chosen by the user, and limit the degradation of the other criterion. Theoretical results show that the technique is not far from the optimum, from the statistical standpoint. Experiments performed tend to demonstrate its potential, as it remains robust even under significant distribution drifts.     

演化数据流上的连续异常检测

基于滑动窗口的异常检测是数据流挖掘研究的一个重要课题,在许多应用中数据流通常在一个分布网络上传输,解决这类问题时常采用分布计算技术,以便获得实时高质量的计算结果。对分布演化数据流上连续异常检测问题,进行形式化地阐述,提出了两个基于核密度估计的异常检测定义和算法,并通过大量真实数据集的实验,表明该算法具有良好的高效性和可扩展性,完全适应数据流应用的需求。     

Tracking set-expression cardinalities over continuous update streams

There is growing interest in algorithms for processing and querying continuous data streams (i.e., data seen only once in a fixed order) with limited memory resources. In its most general form, a data stream is actually an update stream, i.e., comprising data-item deletions as well as insertions. Such massive update streams arise naturally in several application domains (e.g., monitoring of large IP network installations or processing of retail-chain transactions). Estimating the cardinality of set expressions defined over several (possibly distributed) update streams is perhaps one of the most fundamental query classes of interest; as an example, such a query may ask what is the number of distinct IP source addresses seen in passing packets from both router R ₁ and R ₂ but not router R ₃?. Earlier work only addressed very restricted forms of this problem, focusing solely on the special case of insert-only streams and specific operators (e.g., union). In this paper, we propose the first space-efficient algorithmic solution for estimating the cardinality of full-fledged set expressions over general update streams. Our estimation algorithms are probabilistic in nature and rely on a novel, hash-based synopsis data structure, termed 2-level hash sketch. We demonstrate how our 2-level hash sketch synopses can be used to provide low-error, high-confidence estimates for the cardinality of set expressions (including operators such as set union, intersection, and difference) over continuous update streams, using only space that is significantly sublinear in the sizes of the streaming input (multi-)sets. Furthermore, our estimators never require rescanning or resampling of past stream items, regardless of the number of deletions in the stream. We also present lower bounds for the problem, demonstrating that the space usage of our estimation algorithms is within small factors of the optimal. Finally, we propose an optimized, time-efficient stream synopsis (based on 2-level hash sketches) that provides similar, strong accuracy-space guarantees while requiring only guaranteed logarithmic maintenance time per update, thus making our methods applicable for truly rapid-rate data streams. Our results from an empirical study of our synopsis and estimation techniques verify the effectiveness of our approach.Received: 20 October 2003, Accepted: 16 April 2004, Published online: 14 September 2004Edited by: J. Gehrke and J. Hellerstein.Sumit Ganguly: sganguly@cse.iitk.ac.in Current affiliation: Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India     

Catch the moment: maintaining closed frequent itemsets over a data stream sliding window

This paper considers the problem of mining closed frequent itemsets over a data stream sliding window using limited memory space. We design a synopsis data structure to monitor transactions in the sliding window so that we can output the current closed frequent itemsets at any time. Due to time and memory constraints, the synopsis data structure cannot monitor all possible itemsets. However, monitoring only frequent itemsets will make it impossible to detect new itemsets when they become frequent. In this paper, we introduce a compact data structure, the closed enumeration tree (CET), to maintain a dynamically selected set of itemsets over a sliding window. The selected itemsets contain a boundary between closed frequent itemsets and the rest of the itemsets. Concept drifts in a data stream are reflected by boundary movements in the CET. In other words, a status change of any itemset (e.g., from non-frequent to frequent) must occur through the boundary. Because the boundary is relatively stable, the cost of mining closed frequent itemsets over a sliding window is dramatically reduced to that of mining transactions that can possibly cause boundary movements in the CET. Our experiments show that our algorithm performs much better than representative algorithms for the sate-of-the-art approaches. Yun Chi is currently a Ph.D. student at the Department of Computer Science, UCLA. His main areas of research include database systems, data mining, and bioinformatics. For data mining, he is interested in mining labeled trees and graphs, mining data streams, and mining data with uncertainty. Haixun Wang is currently a research staff member at IBM T. J. Watson Research Center. He received the B.S. and the M.S. degree, both in computer science, from Shanghai Jiao Tong University in 1994 and 1996. He received the Ph.D. degree in computer science from the University of California, Los Angeles in 2000. He has published more than 60 research papers in referred international journals and conference proceedings. He is a member of the ACM, the ACM SIGMOD, the ACM SIGKDD, and the IEEE Computer Society. He has served in program committees of international conferences and workshops, and has been a reviewer for some leading academic journals in the database field. Philip S. Yureceived the B.S. Degree in electrical engineering from National Taiwan University, the M.S. and Ph.D. degrees in electrical engineering from Stanford University, and the M.B.A. degree from New York University. He is with the IBM Thomas J. Watson Research Center and currently manager of the Software Tools and Techniques group. His research interests include data mining, Internet applications and technologies, database systems, multimedia systems, parallel and distributed processing, and performance modeling. Dr. Yu has published more than 430 papers in refereed journals and conferences. He holds or has applied for more than 250 US patents.Dr. Yu is a Fellow of the ACM and a Fellow of the IEEE. He is associate editors of ACM Transactions on the Internet Technology and ACM Transactions on Knowledge Discovery in Data. He is a member of the IEEE Data Engineering steering committee and is also on the steering committee of IEEE Conference on Data Mining. He was the Editor-in-Chief of IEEE Transactions on Knowledge and Data Engineering (2001–2004), an editor, advisory board member and also a guest co-editor of the special issue on mining of databases. He had also served as an associate editor of Knowledge and Information Systems. In addition to serving as program committee member on various conferences, he will be serving as the general chairman of 2006 ACM Conference on Information and Knowledge Management and the program chairman of the 2006 joint conferences of the 8th IEEE Conference on E-Commerce Technology (CEC' 06) and the 3rd IEEE Conference on Enterprise Computing, E-Commerce and E-Services (EEE' 06). He was the program chairman or co-chairs of the 11th IEEE International Conference on Data Engineering, the 6th Pacific Area Conference on Knowledge Discovery and Data Mining, the 9th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, the 2nd IEEE International Workshop on Research Issues on Data Engineering:Transaction and Query Processing, the PAKDD Workshop on Knowledge Discovery from Advanced Databases, and the 2nd IEEE International Workshop on Advanced Issues of E-Commerce and Web-based Information Systems. He served as the general chairman of the 14th IEEE International Conference on Data Engineering and the general co-chairman of the 2nd IEEE International Conference on Data Mining. He has received several IBM honors including 2 IBM Outstanding Innovation Awards, an Outstanding Technical Achievement Award, 2 Research Division Awards and the 84th plateau of Invention Achievement Awards. He received an Outstanding Contributions Award from IEEE International Conference on Data Mining in 2003 and also an IEEE Region 1 Award for “promoting and perpetuating numerous new electrical engineering concepts" in 1999. Dr. Yu is an IBM Master Inventor. Richard R. Muntz is a Professor and past chairman of the Computer Science Department, School of Engineering and Applied Science, UCLA. His current research interests are sensor rich environments, multimedia storage servers and database systems, distributed and parallel database systems, spatial and scientific database systems, data mining, and computer performance evaluation. He is the author of over one hundred and fifty research papers.Dr. Muntz received the BEE from Pratt Institute in 1963, the MEE from New York University in 1966, and the Ph.D. in Electrical Engineering from Princeton University in 1969. He is a member of the Board of Directors for SIGMETRICS and past chairman of IFIP WG7.3 on performance evaluation. He was a member of the Corporate Technology Advisory Board at NCR/Teradata, a member of the Science Advisory Board of NASA's Center of Excellence in Space Data Information Systems, and a member of the Goddard Space Flight Center Visiting Committee on Information Technology. He recently chaired a National Research Council study on “The Intersection of Geospatial Information and IT” which was published in 2003. He was an associate editor for the Journal of the ACM from 1975 to 1980 and the Editor-in-Chief of ACM Computing Surveys from 1992 to 1995. He is a Fellow of the ACM and a Fellow of the IEEE.     

Sliding window-based frequent pattern mining over data streams

Finding frequent patterns in a continuous stream of transactions is critical for many applications such as retail market data analysis, network monitoring, web usage mining, and stock market prediction. Even though numerous frequent pattern mining algorithms have been developed over the past decade, new solutions for handling stream data are still required due to the continuous, unbounded, and ordered sequence of data elements generated at a rapid rate in a data stream. Therefore, extracting frequent patterns from more recent data can enhance the analysis of stream data. In this paper, we propose an efficient technique to discover the complete set of recent frequent patterns from a high-speed data stream over a sliding window. We develop a Compact Pattern Stream tree (CPS-tree) to capture the recent stream data content and efficiently remove the obsolete, old stream data content. We also introduce the concept of dynamic tree restructuring in our CPS-tree to produce a highly compact frequency-descending tree structure at runtime. The complete set of recent frequent patterns is obtained from the CPS-tree of the current window using an FP-growth mining technique. Extensive experimental analyses show that our CPS-tree is highly efficient in terms of memory and time complexity when finding recent frequent patterns from a high-speed data stream.     

基于数据流的滑动窗口机制的研究

传统的关系数据库是在持久稳定的数据集合上进行数据查询,而数据流的长度是无界的,不可能将所有的数据存储下来,因此对数据流的查询处理大多采用了持续查询。对数据流进行持续查询时,往往感兴趣的不是所有的数据而是最近到达的部分数据,这样就引入滑动窗口模型。定义滑动窗口语义是数据流管理系统中一个非常基础性的工作,直接关系到数据流的存储和查询的执行效率。针对滑动窗口的模型和语义进行了研究。     

Sliding window based weighted maximal frequent pattern mining over data streams

As data have been accumulated more quickly in recent years, corresponding databases have also become huger, and thus, general frequent pattern mining methods have been faced with limitations that do not appropriately respond to the massive data. To overcome this problem, data mining researchers have studied methods which can conduct more efficient and immediate mining tasks by scanning databases only once. Thereafter, the sliding window model, which can perform mining operations focusing on recently accumulated parts over data streams, was proposed, and a variety of mining approaches related to this have been suggested. However, it is hard to mine all of the frequent patterns in the data stream environment since generated patterns are remarkably increased as data streams are continuously extended. Thus, methods for efficiently compressing generated patterns are needed in order to solve that problem. In addition, since not only support conditions but also weight constraints expressing items’ importance are one of the important factors in the pattern mining, we need to consider them in mining process. Motivated by these issues, we propose a novel algorithm, weighted maximal frequent pattern mining over data streams based on sliding window model (WMFP-SW) to obtain weighted maximal frequent patterns reflecting recent information over data streams. Performance experiments report that MWFP-SW outperforms previous algorithms in terms of runtime, memory usage, and scalability.     

分布式数据流上的Skyline计算

为了降低分布式数据流上的连续Skyline计算过程中的通信开销,提出了基于远程过滤的思想并对相关理论基础进行了证明,描述了系统的体系结构并提出了两个过滤模型v_Max和Distance。理论分析和实验结果证明了所提方法在某些数据分布情况下降低通信开销的有效性。     

一种分布式数据流相关性分析的有效方法

在分布式数据流中,数据流之间相关性分析可以揭示被监测对象之间存在的内在联系。提出了一个基于基窗口的相关系数的计算方法,该方法先将计算相关系数的公式变形为由适合基窗口聚集的因子组成,然后用基于基窗口的方法聚集每个因子。基于基窗口的聚集方法是将窗口中的数据项划分成一系列基窗口并分别对基窗口进行计算。当窗口随机滑动后,新窗口中数据项的聚集可以部分地利用上一次窗口聚集的结果。模拟实验表明,与每次对窗口中所有数据进行聚集相比,基于基窗口的方法可以有效地降低数据流相关系数的计算时间。     

Finding recently frequent itemsets adaptively over online transactional data streams

A data stream is a massive unbounded sequence of data elements continuously generated at a rapid rate. Consequently, the knowledge embedded in a data stream is more likely to be changed as time goes by. Identifying the recent change of a data stream, especially for an online data stream, can provide valuable information for the analysis of the data stream. However, most of mining algorithms or frequency approximation algorithms over a data stream do not differentiate the information of recently generated data elements from the obsolete information of old data elements which may be no longer useful or possibly invalid at present. Therefore, they are not able to extract the recent change of information in a data stream adaptively. This paper proposes a data mining method for finding recently frequent itemsets adaptively over an online transactional data stream. The effect of old transactions on the current mining result of a data steam is diminished by decaying the old occurrences of each itemset as time goes by. Furthermore, several optimization techniques are devised to minimize processing time as well as memory usage. Finally, the performance of the proposed method is analyzed by a series of experiments to identify its various characteristics.     

滑动窗口模型下的概率数据流聚类

提出一种基于滑动窗口的概率数据流聚类方法PWStream。PWStream采用聚类特征指数直方图保存最近数据元组的信息摘要,在允许的误差范围内删除过期的数据元组;并针对数据流上概率元组提出强簇、过渡簇和弱簇的概念,设计了一种基于距离和存在概率的簇选择策略,从而可以发现更多的强簇。理论分析和实验结果表明,该方法具有良好的聚类质量和较快的数据处理能力。     

A survey of outlier detection in high dimensional data streams

The rapid evolution of technology has led to the generation of high dimensional data streams in a wide range of fields, such as genomics, signal processing, and finance. The combination of the streaming scenario and high dimensionality is particularly challenging especially for the outlier detection task. This is due to the special characteristics of the data stream such as the concept drift, the limited time and space requirements, in addition to the impact of the well-known curse of dimensionality in high dimensional space. To the best of our knowledge, few studies have addressed these challenges simultaneously, and therefore detecting anomalies in this context requires a great deal of attention. The main objective of this work is to study the main approaches existing in the literature, to identify a set of comparison criteria, such as the computational cost and the interpretation of outliers, which will help us to reveal the different challenges and additional research directions associated with this problem. At the end of this study, we will draw up a summary report which summarizes the main limits identified and we will detail the different directions of research related to this issue in order to promote research for this community.     

滑动窗口模型下的优化数据流聚类算法

为提高对进化数据流的聚类质量及效率,采用聚类特征指数直方图支持数据处理,减少直方图结构的维护数,改进滑动窗口下的流数据聚类算法。实验表明,与传统基于界标模型的聚类算法相比,优化算法可获得较好的工作效率、较小的内存开销和快速的数据处理能力,拓展了流数据挖掘技术的应用领域。     

RLC: ranking lag correlations with flexible sliding windows in data streams

Lag correlation between two time series is the correlation shifted in time relative to one another. Existing work focuses on two computation models, landmark (where the lag correlation is computed over the entire stream) and sliding window (where the lag correlation is computed over the current window). However, these models may suffer from problems like result freshness (e.g., perished items in the landmark model) and parametric tuning (e.g., setting a proper length in the sliding window model). In this work, we attempt to analyze the lag correlation which is computed based on flexible sliding windows. In view of that, a new query called RLC (ranking lag correlations with flexible sliding windows in data streams) is proposed. The key challenge in answering the RLC query is that the number of windows to be analyzed will grow quadratically with the length of the stream, resulting a quadratic computation cost. To boost the computation, we employ the running sum and the geometric probing techniques to facilitate the query processing. We also present an approximate solution that further reduces the computation cost with an acceptable error rate in practice. The extensive experiments verify the efficiency of our proposed methods. We also demonstrate some lag correlations discovered from real datasets to show the practicality of this work.     

数据流上最近频繁项集挖掘算法

数据流频繁项集挖掘是指在数据流中找出出现频数大于给定的最小支持度的项集过程。随着一些新兴应用如传感器网络、网络监控等的出现,数据流中频繁项集挖掘引起了很大的重视。提出了一种新颖的数据流频繁项集挖掘算法RFIF。不同于现有算法,RFIF算法针对现实中的一些实际应用,更多的考虑最近时间发生的事件,但也不完全抛弃历史数据,通过引入GIMT函数,逐渐加大项集支持度的阈值,减少对历史数据中频繁项集的维护。实验验证了算法的有效性。