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50
On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration
 SIGKDD'02
, 2002
"... ... mining time series data. Literally hundreds of papers have introduced new algorithms to index, classify, cluster and segment time series. In this work we make the following claim. Much of this work has very little utility because the contribution made (speed in the case of indexing, accuracy in ..."
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Cited by 220 (50 self)
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... mining time series data. Literally hundreds of papers have introduced new algorithms to index, classify, cluster and segment time series. In this work we make the following claim. Much of this work has very little utility because the contribution made (speed in the case of indexing, accuracy in the case of classification and clustering, model accuracy in the case of segmentation) offer an amount of "improvement" that would have been completely dwarfed by the variance that would have been observed by testing on many real world datasets, or the variance that would have been observed by changing minor (unstated) implementation details. To illustrate our point
Probabilistic discovery of time series motifs
, 2003
"... Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of thi ..."
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Cited by 119 (21 self)
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Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of this work were the poor scalability of the motif discovery algorithm, and the inability to discover motifs in the presence of noise. Here we address these limitations by introducing a novel algorithm inspired by recent advances in the problem of pattern discovery in biosequences. Our algorithm is probabilistic in nature, but as we show empirically and theoretically, it can find time series motifs with very high probability even in the presence of noise or “don’t care ” symbols. Not only is the algorithm fast, but it is an anytime algorithm, producing likely candidate motifs almost immediately, and gradually improving the quality of results over time.
MultiDimensional Regression Analysis of TimeSeries Data Streams
 PROC. VLDB 02
, 2002
"... Realtime production systems and other dynamic environments often generate tremendous (potentially infinite) amount of stream data; the volume of data is too huge to be stored on disks or scanned multiple times. Can we perform online, multidimensional analysis and data mining of such data to alert ..."
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Cited by 104 (23 self)
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Realtime production systems and other dynamic environments often generate tremendous (potentially infinite) amount of stream data; the volume of data is too huge to be stored on disks or scanned multiple times. Can we perform online, multidimensional analysis and data mining of such data to alert people about dramatic changes of situations and to initiate timely, highquality responses? This is a challenging task. In this paper,
Finding Motifs in Time Series
, 2002
"... The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously ..."
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Cited by 72 (15 self)
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The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs," because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition, it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification. In this work we carefully motivate, then introduce, a nontrivial definition of time series motifs. We propose an efficient algorithm to discover them, and we demonstrate the utility and efficiency of our approach on several real world datasets.
Comparing data streams using hamming norms (how to zero in)
, 2003
"... Massive data streams are now fundamental to many data processing applications. For example, Internet routers produce large scale diagnostic data streams. Such streams are rarely stored in traditional databases and instead must be processed “on the fly” as they are produced. Similarly, sensor networ ..."
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Cited by 71 (7 self)
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Massive data streams are now fundamental to many data processing applications. For example, Internet routers produce large scale diagnostic data streams. Such streams are rarely stored in traditional databases and instead must be processed “on the fly” as they are produced. Similarly, sensor networks produce multiple data streams of observations from their sensors. There is growing focus on manipulating data streams and, hence, there is a need to identify basic operations of interest in managing data streams, and to support them efficiently. We propose computation of the Hamming norm as a basic operation of interest. The Hamming norm formalizes ideas that are used throughout data processing. When applied to a single stream, the Hamming norm gives the number of distinct items that are present in that data stream, which is a statistic of great interest in databases. When applied to a pair of streams, the Hamming norm gives an important measure of (dis)similarity: the number of unequal item counts in the two streams. Hamming norms have many uses in comparing data streams. We present a novel approximation technique for estimating the Hamming norm for massive data streams; this relies on what we call the “l0 sketch ” and we prove its accuracy. We test our approximation method on a large quantity of synthetic and real stream data, and show that the estimation is accurate to within a few percentage points.
Beyond streams and graphs: Dynamic tensor analysis
 In KDD
, 2006
"... How do we find patterns in authorkeyword associations, evolving over time? Or in DataCubes, with productbranchcustomer sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable tools for mining, dimensionality reduction, feature selection, rule ..."
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Cited by 70 (11 self)
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How do we find patterns in authorkeyword associations, evolving over time? Or in DataCubes, with productbranchcustomer sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable tools for mining, dimensionality reduction, feature selection, rule identification in numerous settings like streaming data, text, graphs, social networks and many more. However, they have only two orders, like author and keyword, in the above example. We propose to envision such higher order data as tensors, and tap the vast literature on the topic. However, these methods do not necessarily scale up, let alone operate on semiinfinite streams. Thus, we introduce the dynamic tensor analysis (DTA) method, and its variants. DTA provides a compact summary for highorder and highdimensional data, and it also reveals the hidden correlations. Algorithmically, we designed DTA very carefully so that it is (a) scalable, (b) space efficient (it does not need to store the past) and (c) fully automatic with no need for user defined parameters. Moreover, we propose STA, a streaming tensor analysis method, which provides a fast, streaming approximation to DTA. We implemented all our methods, and applied them in two real settings, namely, anomaly detection and multiway latent semantic indexing. We used two real, large datasets, one on network flow data (100GB over 1 month) and one from DBLP (200MB over 25 years). Our experiments show that our methods are fast, accurate and that they find interesting patterns and outliers on the real datasets. 1.
A regressionbased temporal pattern mining scheme for data streams
 In VLDB
, 2003
"... We devise in this paper a regressionbased algorithm, called algorithm FTPDS (Frequent Temporal Patterns of Data Streams), to mine frequent temporal patterns for data streams. While providing a general framework of pattern frequency counting, algorithm FTPDS has two major features, namely one data ..."
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Cited by 42 (6 self)
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We devise in this paper a regressionbased algorithm, called algorithm FTPDS (Frequent Temporal Patterns of Data Streams), to mine frequent temporal patterns for data streams. While providing a general framework of pattern frequency counting, algorithm FTPDS has two major features, namely one data scan for online statistics collection and regressionbased compact pattern representation. To attain the feature of one data scan, the data segmentation and the pattern growth scenarios are explored for the frequency counting purpose. Algorithm FTPDS scans online transaction flows and generates candidate frequent patterns in real time. The second important feature of algorithm FTPDS is on the regressionbased compact pattern representation. Specifically, to meet the space constraint, we devise for pattern representation a compact ATF (standing for Accumulated Time and Frequency) form to aggregately comprise all the information required for regression analysis. In addition, we develop the techniques of the segmentation tuning and segment relaxation to enhance the functions of FTPDS. With these features, algorithm FTPDS is able to not only conduct mining with variable time intervals but also perform trend detection effectively. Synthetic data and a real dataset which contains net
Adaptive, handsoff stream mining
 In VLDB
, 2003
"... Sensor devices and embedded processors are becoming ubiquitous, especially in measurement and monitoring applications. Automatic discovery of patterns and trends in the large volumes of such data is of paramount importance. The combination of relatively limited resources (CPU, memory and/or communic ..."
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Cited by 32 (3 self)
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Sensor devices and embedded processors are becoming ubiquitous, especially in measurement and monitoring applications. Automatic discovery of patterns and trends in the large volumes of such data is of paramount importance. The combination of relatively limited resources (CPU, memory and/or communication bandwidth and power) poses some interesting challenges. We need both powerful and concise “languages ” to represent the important features of the data, which can (a) adapt and handle arbitrary periodic components, including bursts, and (b) require little memory and a single pass over the data. This allows sensors to automatically (a) discover interesting patterns and trends in the data, and (b) perform outlier detection to alert users. We need a way so that a sensor can discover something like “the hourly phone call volume so far follows a daily and a weekly periodicity, with bursts roughly every year, ” which a human might recognize as, e.g., the Mother’s day surge. When possible and if desired, the user can then issue explicit queries to further investigate the reported patterns. In this work we propose AWSOM (Arbitrary Window Stream mOdeling Method), which allows sensors operating in remote or hostile environments to discover patterns efficiently and
Mining Motifs in Massive Time Series Databases
 In Proceedings of IEEE International Conference on Data Mining (ICDM’02
, 2002
"... The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously ..."
Abstract

Cited by 30 (0 self)
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The problem of efficiently locating previously known patterns in a time series database (i.e., query by content) has received much attention and may now largely be regarded as a solved problem. However, from a knowledge discovery viewpoint, a more interesting problem is the enumeration of previously unknown, frequently occurring patterns. We call such patterns "motifs", because of their close analogy to their discrete counterparts in computation biology. An efficient motif discovery algorithm for time series would be useful as a tool for summarizing and visualizing massive time series databases. In addition it could be used as a subroutine in various other data mining tasks, including the discovery of association rules, clustering and classification.
Derandomized Dimensionality Reduction with Applications
 In Proc. 13th ACMSIAM Sympos. Discrete Algorithms
, 2002
"... The JohnsonLindenstrauss lemma provides a way to map a number of points in highdimensional space into a lowdimensional space, with only a small distortion of the distances between the points. The proofs of the lemma are nonconstructive: they show that a random mapping induces small distortions w ..."
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Cited by 28 (2 self)
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The JohnsonLindenstrauss lemma provides a way to map a number of points in highdimensional space into a lowdimensional space, with only a small distortion of the distances between the points. The proofs of the lemma are nonconstructive: they show that a random mapping induces small distortions with high probability, but they do not construct the actual mapping. In this paper, we provide a procedure that constructs such a mapping deterministically in time almost linear in the number of distances to preserve times the dimension of the original space. We then use that result (together with Nisan's pseudorandom generator) to obtain an efficient derandomization of several approximation algorithms based on semidefinite programming.