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55
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 185 (26 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.
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 111 (20 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.
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 ..."
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Cited by 49 (3 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.
SpecifictoGeneral Learning for Temporal Events with Application to Learning . . .
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2002
"... We develop, analyze, and evaluate a novel, supervised, specifictogeneral learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, eventdescription language called AMA that ..."
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Cited by 36 (4 self)
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We develop, analyze, and evaluate a novel, supervised, specifictogeneral learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, eventdescription language called AMA that is sufficiently expressive to represent many events yet sufficiently restrictive to support learning. We then give algorithms, along with lower and upper complexity bounds, for the subsumption and generalization problems for AMA formulas. We present a positiveexamples  only specifictogeneral learning method based on these algorithms. We also present a polynomialtime  computable "syntactic" subsumption test that implies semantic subsumption without being equivalent to it. A generalization algorithm based on syntactic subsumption can be used in place of semantic generalization to improve the asymptotic complexity of the resulting learning algorithm. Finally
Finding Informative Rules in Interval Sequences
 Intelligent Data Analysis
, 2001
"... Observing a binary feature over a period of time yields a sequence of observation intervals. To ease the access to continuous features (like time series), they are often broken down into attributed intervals, such that the attribute describes the series' behaviour within the segment (e.g. incre ..."
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Cited by 23 (2 self)
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Observing a binary feature over a period of time yields a sequence of observation intervals. To ease the access to continuous features (like time series), they are often broken down into attributed intervals, such that the attribute describes the series' behaviour within the segment (e.g. increasing, highvalue, highly convex, etc.). In both cases, we obtain a sequence of interval data, in which temporal patterns and rules can be identified. A temporal pattern is defined as a set of labeled intervals together with their interval relationships described in terms of Allen's interval logic. In this paper, we consider the evaluation of such rules in order to find the most informative rules. We discuss rule semantics and outline de ciencies of the previously used rule evaluation. We apply the Jmeasure to rules with a modified semantics in order to better cope with different lengths of the temporal patterns. We also consider the problem of specializing temporal rules by additional attributes of the state intervals.
Knowledge Discovery from Sequential Data
, 2003
"... A new framework for analyzing sequential or temporal data such as time series is proposed. It differs from other approaches by the special emphasis on the interpretability of the results, since interpretability is of vital importance for knowledge discovery, that is, the development of new knowl ..."
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Cited by 22 (0 self)
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A new framework for analyzing sequential or temporal data such as time series is proposed. It differs from other approaches by the special emphasis on the interpretability of the results, since interpretability is of vital importance for knowledge discovery, that is, the development of new knowledge (in the head of a human) from a list of discovered patterns. While traditional approaches try to model and predict all time series observations, the focus in this work is on modelling local dependencies in multivariate time series. This
Efficient mining of temporally annotated sequences
 In Proc. SDM’06
, 2006
"... Sequential patterns mining received much attention in recent years, thanks to its various potential application domains. A large part of them represent data as collections of timestamped itemsets, e.g., customers ’ purchases, logged web accesses, etc. Most approaches to sequence mining focus on seq ..."
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Cited by 20 (4 self)
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Sequential patterns mining received much attention in recent years, thanks to its various potential application domains. A large part of them represent data as collections of timestamped itemsets, e.g., customers ’ purchases, logged web accesses, etc. Most approaches to sequence mining focus on sequentiality of data, using timestamps only to order items and, in some cases, to constrain the temporal gap between items. In this paper, we propose an efficient algorithm for computing (temporally)annotated sequential patterns, i.e., sequential patterns where each transition is annotated with a typical transition time derived from the source data. The algorithm adopts a prefixprojection approach to mine candidate sequences, and it is tightly integrated with an annotation mining process that associates sequences with temporal annotations. The pruning capabilities of the two steps sum together, yielding significant improvements in performances, as demonstrated by a set of experiments performed on synthetic datasets. 1
Time series knowledge mining
, 2006
"... An important goal of knowledge discovery is the search for patterns in data that can help explain the underlying process that generated the data. The patterns are required to be new, useful, and understandable to humans. In this work we present a new method for the understandable description of loca ..."
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Cited by 20 (2 self)
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An important goal of knowledge discovery is the search for patterns in data that can help explain the underlying process that generated the data. The patterns are required to be new, useful, and understandable to humans. In this work we present a new method for the understandable description of local temporal relationships in multivariate data, called Time Series Knowledge Mining (TSKM). We define the Time Series Knowledge Representation (TSKR) as a new language for expressing temporal knowledge. The patterns have a hierarchical structure, each level corresponds to a single temporal concept. On the lowest level, intervals are used to represent duration. Overlapping parts of intervals represent coincidence on the next level. Several such blocks of intervals are connected with a partial order relation on the highest level. Each pattern element consists of a semiotic triple to connect syntactic and semantic information with pragmatics. The patterns are very compact, but offer details for each element on demand. In comparison with related approaches, the TSKR is shown to have advantages in robustness, expressivity, and comprehensibility. Efficient algorithms for the discovery of the patterns are proposed. The search for coincidence as well as partial order can be formulated as variants of the well known frequent itemset problem. One of the best known algorithms for this problem is therefore adapted for our purposes. Human interaction is used during the mining to analyze and validate partial results as early as possible and guide further processing steps. The efficacy of the methods is demonstrated using several data sets. In an application to sports medicine the results were recognized as valid and useful by an expert of the field.
C.: A multiresolution symbolic representation of time series
 In: Proc. IEEE Int. Conf. on Data Engineering (ICDE05
, 2005
"... Efficiently and accurately searching for similarities among time series and discovering interesting patterns is an important and nontrivial problem. In this paper, we introduce a new representation of time series, the Multiresolution Vector Quantized (MVQ) approximation, along with a new distance f ..."
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Cited by 18 (4 self)
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Efficiently and accurately searching for similarities among time series and discovering interesting patterns is an important and nontrivial problem. In this paper, we introduce a new representation of time series, the Multiresolution Vector Quantized (MVQ) approximation, along with a new distance function. The novelty of MVQ is that it keeps both local and global information about the original time series in a hierarchical mechanism, processing the original time series at multiple resolutions. Moreover, the proposed representation is symbolic employing key subsequences and potentially allows the application of textbased retrieval techniques into the similarity analysis of time series. The proposed method is fast and scales linearly with the size of
Learning Effects of Robot Actions using Temporal Associations
"... Agents need to know the effects of their actions. Strong associations between actions and effects can be found by counting how often they cooccur. We present an algorithm that learns temporal patterns expressed as fluents, propositions with temporal extent. The fluentlearning algorithm is hierarch ..."
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Cited by 16 (5 self)
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Agents need to know the effects of their actions. Strong associations between actions and effects can be found by counting how often they cooccur. We present an algorithm that learns temporal patterns expressed as fluents, propositions with temporal extent. The fluentlearning algorithm is hierarchical and unsupervised. It works by maintaining cooccurrence statistics on pairs of fluents. In experiments on a mobile robot, the fluentlearning algorithm found temporal associations that correspond to effects of the robot's actions.