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.

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 non-trivial 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.

We develop, analyze, and evaluate a novel, supervised, specific-to-general 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, event-description 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 positive-examples -- only specific-to-general learning method based on these algorithms. We also present a polynomial-time -- 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

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.

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, high-value, 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 J-measure 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.

Efficiently and accurately searching for similarities among time series and discovering interesting patterns is an important and non-trivial 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 text-based retrieval techniques into the similarity analysis of time series. The proposed method is fast and scales linearly with the size of

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

The detection of recurrent episodes in long strings of tokens has attracted some interest and a variety of useful methods have been developed. The temporal relationship between discovered episodes may also provide useful knowledge of the phenomenon but as yet has received little investigation. This paper discusses an approach for finding such relationships through the proposal of a robust and efficient search strategy and effective user interface both of which are validated through experiment. Keywords: Temporal Sequence Mining. 1 Introduction and Related Work While the mining of frequent episodes is an important capability, the manner in which such episodes interact can provide further useful knowledge in the search for a description of the behaviour of a phenomenon.

The understanding of complex muscle coordination is an important goal in human movement science. There are numerous applications in medicine, sports, and robotics. The coordination process can be studied by observing complex, often cyclic movements, which are dynamically re-peated in an almost identical manner. The muscle activation is measured using kinesiological EMG. Mining the EMG data to identify patterns, which explain the interplay and coordination of muscles is a very difficult Knowledge Discovery task. We present the Time Series Knowledge Min-ing framework to discover knowledge in multivariate time series and show how it can be used to extract such temporal patterns.

Agents need to know the effects of their actions. Strong associations between actions and effects can be found by counting how often they co-occur. We present an algorithm that learns temporal patterns expressed as fluents, propositions with temporal extent. The fluent-learning algorithm is hierarchical and unsupervised. It works by maintaining co-occurrence statistics on pairs of fluents. In experiments on a mobile robot, the fluent-learning algorithm found temporal associations that correspond to effects of the robot's actions.